input
stringlengths 29
13k
| output
stringlengths 9
73.4k
|
|---|---|
Write a program which reads a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and swap specified elements by a list of the following operation:
* swapRange($b, e, t$): For each integer $k$ ($0 \leq k < (e - b)$, swap element $(b + k)$ and element $(t + k)$.
Constraints
* $1 \leq n \leq 1,000$
* $-1,000,000,000 \leq a_i \leq 1,000,000,000$
* $1 \leq q \leq 1,000$
* $0 \leq b_i < e_i \leq n$
* $0 \leq t_i < t_i + (e_i - b_i) \leq n$
* Given swap ranges do not overlap each other
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ...,\; a_{n-1}$
$q$
$b_1 \; e_1 \; t_1$
$b_2 \; e_2 \; t_2$
:
$b_{q} \; e_{q} \; t_{q}$
In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \; e_i \; t_i$ in the following $q$ lines.
Output
Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element.
Example
Input
11
1 2 3 4 5 6 7 8 9 10 11
1
1 4 7
Output
1 8 9 10 5 6 7 2 3 4 11 | #include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <map>
#include <numeric>
#include <string>
#include <cmath>
#include <iomanip>
#include <queue>
#include <list>
#include <stack>
#include <cctype>
#include <cmath>
using namespace std;
/* typedef */
typedef long long ll;
/* constant */
const int INF = 1 << 30;
const int MAX = 10000;
const int mod = 1000000007;
const double pi = 3.141592653589;
/* global variables */
/* function */
void printVec(vector<int> &vec);
/* main */
int main(){
int n; cin >> n;
vector<int> v(n);
for (int i = 0; i < n; i++) cin >> v[i];
int q; cin >> q;
int l, r, t;
for (int i = 0; i < q; i++) {
cin >> l >> r >> t;
// swap_ranges(begin, end, swap_begin);
// begin ~ end <-> swap_begin ~ swap_begin + (end - begin)
swap_ranges(v.begin() + l, v.begin() + r, v.begin() + t);
}
printVec(v);
return 0;
}
void printVec(vector<int> &vec) {
for (int i = 0; i < vec.size(); i++) {
if (i) cout << ' ' ;
cout << vec[i];
} cout << '\n';
}
|
Recently Johnny have learned bogosort sorting algorithm. He thought that it is too ineffective. So he decided to improve it. As you may know this algorithm shuffles the sequence randomly until it is sorted. Johnny decided that we don't need to shuffle the whole sequence every time. If after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if they are in the right places. For example, if the initial sequence is (3, 5, 1, 6, 4, 2) and after one shuffle Johnny gets (1, 2, 5, 4, 3, 6) he will fix 1, 2 and 6 and proceed with sorting (5, 4, 3) using the same algorithm. Johnny hopes that this optimization will significantly improve the algorithm. Help him calculate the expected amount of shuffles for the improved algorithm to sort the sequence of the first n natural numbers given that no elements are in the right places initially.
Input
The first line of input file is number t - the number of test cases. Each of the following t lines hold single number n - the number of elements in the sequence.
Constraints
1 <= t <= 150
2 <= n <= 150
Output
For each test case output the expected amount of shuffles needed for the improved algorithm to sort the sequence of first n natural numbers in the form of irreducible fractions.
Example
Input:
3
2
6
10
Output:
2
1826/189
877318/35343 | def gcd(a,b):
if b==0:
return a
return gcd(b,a%b)
def simplify(a,b):
g=gcd(a,b)
return (a/g,b/g)
E = {0:(0,1), 1:(1,1), 2:(2,1)}
for i in xrange(3,151):
a,b=E[i-1]
c,d=E[i-2]
E[i]=simplify(b*d*(i*i-3*i+3)+2*a*d*(i-1)-b*c,b*d*(2*i-3))
t=input()
while t:
t-=1
n=input()
a,b=E[n]
if b>1:
print "%d/%d" % (a,b)
else:
print a |
Chef had a hard time arguing with his friend, and after getting a great old kick Chef saw a colored array with N cells, numbered from 1 to N.
The kick was so strong that Chef suddenly understood the rules of the game.
Each cell is painted with a color. Here the colors are numbered from 1 to M.
For any cell i, Chef can repaint it with any color q, and the cost of such operation is Ci,q points.
However Chef can do at most K repaintings (0 repaintings is possible).
After performing all repaintings, each cell will have some color. For each cell i, if cell i has color q then Chef will receive Bi,q points.
Now Chef is wondering how many points can he receive in total when he repaints optimally.
Input
The first line of the input contains an integer T, denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains three space-separated integers N, M and K, denoting the number of cells and the number of colors, the maximal possible number of repaintings respectively. The next line contains N space-separated integers A1, A2, ..., AN, denoting the initial colors of the cells. Then N lines follow. The i^th line of them contains M integers Bi1, Bi2, ..., BiM, where Bij denotes how many points Chef will receive if the cell i will be painted with j-th color after all operations. Then N lines follow. The i^th line of them contains M integers Ci1, Ci2, ..., CiM, where Cij denotes how many points Chef will lose if he repaints the cell i with color j.
Note: Be careful that the size of input files can be large.
Output
For each test case, output a single line containing the maximal possible points.
Constraints
1 ≤ T ≤ 5
0 ≤ K ≤ 1000
1 ≤ N, M ≤ 1000
1 ≤ Ai ≤ M
0 ≤ Bi,j ≤ 1000
0 ≤ Ci,j ≤ 1000
If j = Ai, then Ci,j = 0
Example
Input:
1
4 2 1
1 1 2 2
1 1
1 1
1 1
3 1
0 1
0 1
1 0
1 0
Output:
5
Explanation:
For this sample, we can repaint only once, since K = 1. We should repaint 4^th cell with color 1. We will pay 1 for this, and receive:
1 (1^st cell - 1^st color) +
1 (2^nd cell -1^st color) +
1 (3^rd cell - 2^nd color) +
3 (4^th cell - 1^st color) = 6.
Hence we get 6 − 1 = 5 points in total, and it is the optimal answer. | t = int(raw_input())
for _ in range(t):
n, m, k = map(int, raw_input().split())
a = map(int, raw_input().split())
b = [] # gain
for _ in range(n):
b.append(map(int, raw_input().split()))
c = [] # loss
for _ in range(n):
c.append(map(int, raw_input().split()))
init_cost = [0]*n
for i in range(n):
init_cost[i] = b[i][a[i] -1]
max_gain = [0]*n
for i in range(n):
mp = 0 # max profit
for j in range(m):
np = b[i][j] - c[i][j]
mp = max(mp, np)
# calc gain with respect to init cost
max_gain[i] = mp - init_cost[i]
max_gain.sort()
max_gain.reverse()
print sum(init_cost) + sum(max_gain[:k]) |
Two players are playing a game. The game is played on a sequence of positive integer pairs. The players make their moves alternatively. During his move the player chooses a pair and decreases the larger integer in the pair by a positive multiple of the smaller integer in the pair in such a way that both integers in the pair remain positive. If two numbers in some pair become equal then the pair is removed from the sequence. The player who can not make any move loses (or in another words the player who encounters an empty sequence loses). Given the sequence of positive integer pairs determine whether the first player can win or not (assuming that both players are playing optimally).
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each test starts with an integer N denoting the number of pairs. Each of the next N lines contains a pair of positive integers.
Output
For each test case, output a single line containing "YES" if the first player can win and "NO" otherwise.
Constraints
1 ≤ T ≤ 100
1 ≤ N ≤ 100
All other integers are between 1 to 10^8
The integers in each pair will be different
Example
Input:
3
1
2 3
2
4 5
5 6
2
2 3
3 5
Output:
NO
NO
YES
Explanation
Example case 1. The first player don't have any choice other subtracting 2 from 3. So during the turn of the second player integer pair will be (2,1). The second player will win by subtracting 1 from 2.
Example case 2. If the first player choose to move (4,5) to (4,1) the second player will make it to (1,1). If the first player choose to move (5,6) to (5,1) the second player will make it to (1,1). So regardless of the move of the first player, the second will always win.
Example case 3. The first player will select pair (3,5) and make it to (3,2). Now both pairs are equal. So whatever the move of second player he will just mirror that move in another pair. This will ensure his win. | #!/usr/bin/env python
#-*- coding:utf-8 -*-
def convert_pair(a, b):
res = []
if a < b:
a, b = b, a
while b:
res.append(a / b)
a, b = b, a % b
res[-1] -= 1
while res[-1] == 0:
del res[-1]
return tuple(res)
def grundy(col):
res = 0
for N in reversed(col):
if res >= N:
res = N - 1
else:
res = N
return res
t = int(raw_input())
for _ in range(t):
n = int(raw_input())
cols = []
for _ in range(n):
a, b = map(int, raw_input().strip().split())
cols.append(convert_pair(a, b))
nimsum = reduce(lambda a, b: a ^ b, [grundy(col) for col in cols])
print "NO" if nimsum == 0 else "YES" |
Chef loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Chef has a positive integer N. He can apply any of the following operations as many times as he want in any order:
Add 1 to the number N.
Take some digit of N and replace it by any non-zero digit.
Add any non-zero leading digit to N.
Find the minimum number of operations that is needed for changing N to the lucky number.
Input
The first line contains a single positive integer T, the number of test cases. T test cases follow. The only line of each test case contains a positive integer N without leading zeros.
Output
For each T test cases print one integer, the minimum number of operations that is needed for changing N to the lucky number.
Constraints
1 ≤ T ≤ 10
1 ≤ N < 10^100000
Example
Input:
3
25
46
99
Output:
2
1
2 | t=input()
while t:
t-=1
n=raw_input().strip()
print len(n)-n.count('4')-n.count('7') |
In PrimeLand, there existed a very handsome young prince named Prima. He greatly desired the Princess of Mathematics – Facie. However, before accepting his hand in marriage, Facie asked Prima to solve the following problem:
The figure below shows a simple multiplication problem. However, not all the decimal digits are available. Prima has to find an assignment of digits to the marked places so that the multiplication is valid.
* * *
x * *
-------
* * * <-- partial product 1
* * * <-- partial product 2
-------
* * * *
Digits can appear only in places marked by `*'. Of course, leading zeroes are not allowed.
Write a program to help Prima that will find all solutions to this problem for any subset of digits from the set {1,2,3,4,5,6,7,8,9}.
Input
The first line contains N, the number of digits that will be used
The second line contains N space separated digits
Output
A single line with the total number of unique solutions. Here is the single solution for the sample input:
2 2 2
x 2 2
------
4 4 4
4 4 4
---------
4 8 8 4
Example
Input:
5
2 3 4 6 8
Output:
1 | def isvalid(s, c):
if c.difference(s):
return False
return True
def main():
n = input()
l = raw_input().split()
s = set(l)
answer = 0
for _ in xrange(111, 1000):
a = [i for i in str(_)]
if isvalid(s, set(a)):
for __ in xrange(11, 100):
b = [i for i in str(__)]
if isvalid(s, set(b)):
a1 = _ * int(b[0])
a2 = _ * int(b[1])
final = (a1*10)+a2
a1_set = set([i for i in str(a1)])
a2_set = set([i for i in str(a2)])
final_set = set([i for i in str(final)])
if a1<1000 and a2 < 1000 and final < 10000 and isvalid(s, a1_set) and isvalid(s, a2_set) and isvalid(s, final_set):
answer += 1
print answer
main() |
You are given a square with 'n' points on each side of the square. None of these points co-incide with the corners of this square. You have to compute the total number of triangles that can be formed using these '4n' points (n points on each side of the square) as vertices of the triangle.
Input
First line contains the integer 'T', the number of test cases. This is followed by 'T' lines with a single integer 'n' on each line n ≤ 100.
Output
The total number of triangles that can be formed.
Example
Input:
1
1
Output:
4 | t = int(input())
for i in range(t):
n = int(input())
print(int(10 * n * n * n - 6 * n * n)) |
Innopolis University scientists continue to investigate the periodic table. There are n·m known elements and they form a periodic table: a rectangle with n rows and m columns. Each element can be described by its coordinates (r, c) (1 ≤ r ≤ n, 1 ≤ c ≤ m) in the table.
Recently scientists discovered that for every four different elements in this table that form a rectangle with sides parallel to the sides of the table, if they have samples of three of the four elements, they can produce a sample of the fourth element using nuclear fusion. So if we have elements in positions (r1, c1), (r1, c2), (r2, c1), where r1 ≠ r2 and c1 ≠ c2, then we can produce element (r2, c2).
<image>
Samples used in fusion are not wasted and can be used again in future fusions. Newly crafted elements also can be used in future fusions.
Innopolis University scientists already have samples of q elements. They want to obtain samples of all n·m elements. To achieve that, they will purchase some samples from other laboratories and then produce all remaining elements using an arbitrary number of nuclear fusions in some order. Help them to find the minimal number of elements they need to purchase.
Input
The first line contains three integers n, m, q (1 ≤ n, m ≤ 200 000; 0 ≤ q ≤ min(n·m, 200 000)), the chemical table dimensions and the number of elements scientists already have.
The following q lines contain two integers ri, ci (1 ≤ ri ≤ n, 1 ≤ ci ≤ m), each describes an element that scientists already have. All elements in the input are different.
Output
Print the minimal number of elements to be purchased.
Examples
Input
2 2 3
1 2
2 2
2 1
Output
0
Input
1 5 3
1 3
1 1
1 5
Output
2
Input
4 3 6
1 2
1 3
2 2
2 3
3 1
3 3
Output
1
Note
For each example you have a picture which illustrates it.
The first picture for each example describes the initial set of element samples available. Black crosses represent elements available in the lab initially.
The second picture describes how remaining samples can be obtained. Red dashed circles denote elements that should be purchased from other labs (the optimal solution should minimize the number of red circles). Blue dashed circles are elements that can be produced with nuclear fusion. They are numbered in order in which they can be produced.
Test 1
We can use nuclear fusion and get the element from three other samples, so we don't need to purchase anything.
<image>
Test 2
We cannot use any nuclear fusion at all as there is only one row, so we have to purchase all missing elements.
<image>
Test 3
There are several possible solutions. One of them is illustrated below.
Note that after purchasing one element marked as red it's still not possible to immidiately produce the middle element in the bottom row (marked as 4). So we produce the element in the left-top corner first (marked as 1), and then use it in future fusions.
<image> | #include <bits/stdc++.h>
using namespace std;
const int N = 4e5 + 10;
int fa[N];
int n, m, q;
int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); }
void solve() {
scanf("%d%d%d", &n, &m, &q);
for (int i = 1; i <= n + m; i++) {
fa[i] = i;
}
int res = n + m - 1;
for (int i = 1; i <= q; i++) {
int x, y;
scanf("%d%d", &x, &y);
int fx = find(x), fy = find(y + n);
if (fx != fy) {
fa[fx] = fy;
res--;
}
}
printf("%d\n", res);
}
int main() {
solve();
return 0;
}
|
You are given an array a of n integers and an integer s. It is guaranteed that n is odd.
In one operation you can either increase or decrease any single element by one. Calculate the minimum number of operations required to make the median of the array being equal to s.
The median of the array with odd length is the value of the element which is located on the middle position after the array is sorted. For example, the median of the array 6, 5, 8 is equal to 6, since if we sort this array we will get 5, 6, 8, and 6 is located on the middle position.
Input
The first line contains two integers n and s (1≤ n≤ 2⋅ 10^5-1, 1≤ s≤ 10^9) — the length of the array and the required value of median.
The second line contains n integers a_1, a_2, …, a_n (1≤ a_i ≤ 10^9) — the elements of the array a.
It is guaranteed that n is odd.
Output
In a single line output the minimum number of operations to make the median being equal to s.
Examples
Input
3 8
6 5 8
Output
2
Input
7 20
21 15 12 11 20 19 12
Output
6
Note
In the first sample, 6 can be increased twice. The array will transform to 8, 5, 8, which becomes 5, 8, 8 after sorting, hence the median is equal to 8.
In the second sample, 19 can be increased once and 15 can be increased five times. The array will become equal to 21, 20, 12, 11, 20, 20, 12. If we sort this array we get 11, 12, 12, 20, 20, 20, 21, this way the median is 20. |
# -*- coding: utf-8 -*-
# @Date : 2018-09-03 08:46:01
# @Author : raj lath ([email protected])
# @Link : http://codeforces.com/contest/1037/problem/B
# @Version : 1.0.0
import os
from sys import stdin
max_val=int(10e12)
min_val=int(-10e12)
def read_int() : return int(stdin.readline())
def read_ints() : return [int(x) for x in stdin.readline().split()]
def read_str() : return input()
def read_strs() : return [x for x in stdin.readline().split()]
def read_str_list(): return [x for x in stdin.readline().split().split()]
nb_elemets, value_needed = read_ints()
elements = sorted(read_ints())
mid = nb_elemets//2
ans = abs(elements[mid] - value_needed)
ans += sum( max(0, (a - value_needed)) for a in elements[:mid] )
ans += sum( max(0, (value_needed - a)) for a in elements[mid+1:] )
print(ans)
|
Each item in the game has a level. The higher the level is, the higher basic parameters the item has. We shall consider only the following basic parameters: attack (atk), defense (def) and resistance to different types of impact (res).
Each item belongs to one class. In this problem we will only consider three of such classes: weapon, armor, orb.
Besides, there's a whole new world hidden inside each item. We can increase an item's level travelling to its world. We can also capture the so-called residents in the Item World
Residents are the creatures that live inside items. Each resident gives some bonus to the item in which it is currently located. We will only consider residents of types: gladiator (who improves the item's atk), sentry (who improves def) and physician (who improves res).
Each item has the size parameter. The parameter limits the maximum number of residents that can live inside an item. We can move residents between items. Within one moment of time we can take some resident from an item and move it to some other item if it has a free place for a new resident. We cannot remove a resident from the items and leave outside — any of them should be inside of some item at any moment of time.
Laharl has a certain number of items. He wants to move the residents between items so as to equip himself with weapon, armor and a defensive orb. The weapon's atk should be largest possible in the end. Among all equipping patterns containing weapon's maximum atk parameter we should choose the ones where the armor’s def parameter is the largest possible. Among all such equipment patterns we should choose the one where the defensive orb would have the largest possible res parameter. Values of the parameters def and res of weapon, atk and res of armor and atk and def of orb are indifferent for Laharl.
Find the optimal equipment pattern Laharl can get.
Input
The first line contains number n (3 ≤ n ≤ 100) — representing how many items Laharl has.
Then follow n lines. Each line contains description of an item. The description has the following form: "name class atk def res size" — the item's name, class, basic attack, defense and resistance parameters and its size correspondingly.
* name and class are strings and atk, def, res and size are integers.
* name consists of lowercase Latin letters and its length can range from 1 to 10, inclusive.
* class can be "weapon", "armor" or "orb".
* 0 ≤ atk, def, res ≤ 1000.
* 1 ≤ size ≤ 10.
It is guaranteed that Laharl has at least one item of each class.
The next line contains an integer k (1 ≤ k ≤ 1000) — the number of residents.
Then k lines follow. Each of them describes a resident. A resident description looks like: "name type bonus home" — the resident's name, his type, the number of points the resident adds to the item's corresponding parameter and the name of the item which currently contains the resident.
* name, type and home are strings and bonus is an integer.
* name consists of lowercase Latin letters and its length can range from 1 to 10, inclusive.
* type may be "gladiator", "sentry" or "physician".
* 1 ≤ bonus ≤ 100.
It is guaranteed that the number of residents in each item does not exceed the item's size.
The names of all items and residents are pairwise different.
All words and numbers in the input are separated by single spaces.
Output
Print on the first line the name of the weapon in the optimal equipping pattern; then print the number of residents the weapon contains; then print the residents' names.
Print on the second and third lines in the same form the names of the armor and defensive orb as well as the residents they contain.
Use single spaces for separation.
If there are several possible solutions, print any of them.
Examples
Input
4
sword weapon 10 2 3 2
pagstarmor armor 0 15 3 1
iceorb orb 3 2 13 2
longbow weapon 9 1 2 1
5
mike gladiator 5 longbow
bobby sentry 6 pagstarmor
petr gladiator 7 iceorb
teddy physician 6 sword
blackjack sentry 8 sword
Output
sword 2 petr mike
pagstarmor 1 blackjack
iceorb 2 teddy bobby
Input
4
sword weapon 10 2 3 2
pagstarmor armor 0 15 3 1
iceorb orb 3 2 13 2
longbow weapon 9 1 2 1
6
mike gladiator 5 longbow
bobby sentry 6 pagstarmor
petr gladiator 7 iceorb
teddy physician 6 sword
blackjack sentry 8 sword
joe physician 6 iceorb
Output
longbow 1 mike
pagstarmor 1 bobby
iceorb 2 petr joe
Note
In the second sample we have no free space inside the items, therefore we cannot move the residents between them. | #include <bits/stdc++.h>
using namespace std;
int n, m;
struct lut {
string name;
int cl;
int val;
int size;
};
struct an {
string name;
string whr;
int cl;
int val;
int num;
};
vector<lut> l;
vector<an> anim;
vector<an> d[3];
vector<bool> used;
int all_size;
void Inputdata() {
cin >> n;
l.resize(n);
for (int i = 0; i < n; i++) {
string name;
string cls;
int a, b, c, s;
cin >> name >> cls >> a >> b >> c >> s;
l[i].name = name;
l[i].size = s;
all_size += s;
if (cls == "weapon") {
l[i].cl = 0;
l[i].val = a;
}
if (cls == "armor") {
l[i].cl = 1;
l[i].val = b;
}
if (cls == "orb") {
l[i].cl = 2;
l[i].val = c;
}
}
cin >> m;
anim.resize(m);
used.resize(m);
for (int i = 0; i < m; i++) {
string name, type, whr;
int val;
cin >> name >> type >> val >> whr;
anim[i].name = name;
anim[i].whr = whr;
anim[i].val = val;
anim[i].num = i;
if (type == "gladiator") anim[i].cl = 0;
if (type == "sentry") anim[i].cl = 1;
if (type == "physician") anim[i].cl = 2;
d[anim[i].cl].push_back(anim[i]);
}
}
bool Comp(const an &a, const an &b) { return a.val > b.val; }
void Solve() {
sort(d[0].begin(), d[0].end(), Comp);
sort(d[1].begin(), d[1].end(), Comp);
sort(d[2].begin(), d[2].end(), Comp);
int ans[3];
int max_val[3];
for (int i = 0; i < 3; i++) max_val[i] = -10;
if (all_size > m) {
for (int i = 0; i < n; i++) {
int type = l[i].cl;
int now_val = l[i].val;
for (int j = 0; j < min(l[i].size, int(d[type].size())); j++)
now_val += d[type][j].val;
if (max_val[type] < now_val) {
max_val[type] = now_val;
ans[type] = i;
}
}
vector<string> ans_out[3];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < min(l[ans[i]].size, int(d[i].size())); j++) {
ans_out[i].push_back(d[i][j].name);
used[d[i][j].num] = true;
}
}
for (int i = 0; i < 3; i++) {
int cnt = int(ans_out[i].size());
for (int j = 0; j < m; j++) {
if (cnt >= l[ans[i]].size) break;
if (!used[j]) {
ans_out[i].push_back(anim[j].name);
used[j] = true;
cnt++;
}
}
}
for (int i = 0; i < 3; i++) {
cout << l[ans[i]].name << ' ';
cout << ans_out[i].size() << ' ';
for (int j = 0; j < ans_out[i].size(); j++) cout << ans_out[i][j] << ' ';
cout << endl;
}
} else {
int max_val[3];
int ans[3];
for (int i = 0; i < n; i++) {
int type = l[i].cl;
int now_val = l[i].val;
for (int j = 0; j < m; j++)
if (anim[j].whr == l[i].name && l[i].cl == anim[j].cl)
now_val += anim[j].val;
if (max_val[type] < now_val) {
max_val[type] = now_val;
ans[type] = i;
}
}
vector<string> ans_out[3];
for (int i = 0; i < 3; i++) {
int type = l[ans[i]].cl;
for (int j = 0; j < m; j++)
if (anim[j].whr == l[ans[i]].name) ans_out[i].push_back(anim[j].name);
}
for (int i = 0; i < 3; i++) {
cout << l[ans[i]].name << ' ';
cout << ans_out[i].size() << ' ';
for (int j = 0; j < ans_out[i].size(); j++) cout << ans_out[i][j] << ' ';
cout << endl;
}
}
}
int main() {
Inputdata();
Solve();
return 0;
}
|
Chouti was tired of the tedious homework, so he opened up an old programming problem he created years ago.
You are given a connected undirected graph with n vertices and m weighted edges. There are k special vertices: x_1, x_2, …, x_k.
Let's define the cost of the path as the maximum weight of the edges in it. And the distance between two vertexes as the minimum cost of the paths connecting them.
For each special vertex, find another special vertex which is farthest from it (in terms of the previous paragraph, i.e. the corresponding distance is maximum possible) and output the distance between them.
The original constraints are really small so he thought the problem was boring. Now, he raises the constraints and hopes you can solve it for him.
Input
The first line contains three integers n, m and k (2 ≤ k ≤ n ≤ 10^5, n-1 ≤ m ≤ 10^5) — the number of vertices, the number of edges and the number of special vertices.
The second line contains k distinct integers x_1, x_2, …, x_k (1 ≤ x_i ≤ n).
Each of the following m lines contains three integers u, v and w (1 ≤ u,v ≤ n, 1 ≤ w ≤ 10^9), denoting there is an edge between u and v of weight w. The given graph is undirected, so an edge (u, v) can be used in the both directions.
The graph may have multiple edges and self-loops.
It is guaranteed, that the graph is connected.
Output
The first and only line should contain k integers. The i-th integer is the distance between x_i and the farthest special vertex from it.
Examples
Input
2 3 2
2 1
1 2 3
1 2 2
2 2 1
Output
2 2
Input
4 5 3
1 2 3
1 2 5
4 2 1
2 3 2
1 4 4
1 3 3
Output
3 3 3
Note
In the first example, the distance between vertex 1 and 2 equals to 2 because one can walk through the edge of weight 2 connecting them. So the distance to the farthest node for both 1 and 2 equals to 2.
In the second example, one can find that distance between 1 and 2, distance between 1 and 3 are both 3 and the distance between 2 and 3 is 2.
The graph may have multiple edges between and self-loops, as in the first example. | import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;
/**
* Built using CHelper plug-in
* Actual solution is at the top
*
* @author ijxjdjd
*/
public class Main {
public static void main(String[] args) {
InputStream inputStream = System.in;
OutputStream outputStream = System.out;
InputReader in = new InputReader(inputStream);
PrintWriter out = new PrintWriter(outputStream);
TaskD solver = new TaskD();
solver.solve(1, in, out);
out.close();
}
static class TaskD {
boolean[] special;
int res = 0;
public void solve(int testNumber, InputReader in, PrintWriter out) {
int N = in.nextInt();
int M = in.nextInt();
int K = in.nextInt();
special = new boolean[N];
for (int i = 0; i < K; i++) {
special[in.nextInt() - 1] = true;
}
ArrayList<Edge> arr = new ArrayList<>();
for (int i = 0; i < M; i++) {
int a = in.nextInt() - 1;
int b = in.nextInt() - 1;
int d = in.nextInt();
arr.add(new Edge(a, b, d));
}
Collections.sort(arr, new Comparator<Edge>() {
public int compare(Edge o1, Edge o2) {
return Integer.compare(o1.d, o2.d);
}
});
DSU dsu = new DSU(N);
for (Edge e : arr) {
dsu.merge(e.a, e.b, e.d);
}
for (int i = 0; i < K; i++) {
out.println(res);
}
}
class Edge {
int a;
int b;
int d;
Edge(int a, int b, int d) {
this.a = a;
this.b = b;
this.d = d;
}
}
class DSU {
int[] rank;
int[] cnt;
int[] par;
DSU(int N) {
rank = new int[N];
par = new int[N];
cnt = new int[N];
for (int i = 0; i < N; i++) {
rank[i] = 1;
par[i] = i;
if (special[i]) {
cnt[i] = 1;
}
}
}
int find(int x) {
if (par[x] == x) {
return x;
}
return par[x] = find(par[x]);
}
void merge(int x, int y, int d) {
int parX = find(x);
int parY = find(y);
if (parX != parY) {
if (cnt[parX] != 0 && cnt[parY] != 0) {
res = d;
}
if (rank[parX] > rank[parY]) {
rank[parX] += rank[parY];
par[parY] = parX;
cnt[parX] += cnt[parY];
} else {
rank[parY] += rank[parX];
par[parX] = parY;
cnt[parY] += cnt[parX];
}
}
}
}
}
static class InputReader {
public BufferedReader reader;
public StringTokenizer tokenizer;
public InputReader(InputStream stream) {
reader = new BufferedReader(new InputStreamReader(stream), 32768);
tokenizer = null;
}
public String next() {
while (tokenizer == null || !tokenizer.hasMoreTokens()) {
try {
tokenizer = new StringTokenizer(reader.readLine());
} catch (IOException e) {
throw new RuntimeException(e);
}
}
return tokenizer.nextToken();
}
public int nextInt() {
return Integer.parseInt(next());
}
}
}
|
This is an interactive task.
Dasha and NN like playing chess. While playing a match they decided that normal chess isn't interesting enough for them, so they invented a game described below.
There are 666 black rooks and 1 white king on the chess board of size 999 × 999. The white king wins if he gets checked by rook, or, in other words, if he moves onto the square which shares either a row or column with a black rook.
The sides take turns, starting with white. NN plays as a white king and on each of his turns he moves a king to one of the squares that are adjacent to his current position either by side or diagonally, or, formally, if the king was on the square (x, y), it can move to the square (nx, ny) if and only max (|nx - x|, |ny - y|) = 1 , 1 ≤ nx, ny ≤ 999. NN is also forbidden from moving onto the squares occupied with black rooks, however, he can move onto the same row or column as a black rook.
Dasha, however, neglects playing by the chess rules, and instead of moving rooks normally she moves one of her rooks on any space devoid of other chess pieces. It is also possible that the rook would move onto the same square it was before and the position wouldn't change. However, she can't move the rook on the same row or column with the king.
Each player makes 2000 turns, if the white king wasn't checked by a black rook during those turns, black wins.
NN doesn't like losing, but thinks the task is too difficult for him, so he asks you to write a program that will always win playing for the white king. Note that Dasha can see your king and play depending on its position.
Input
In the beginning your program will receive 667 lines from input. Each line contains two integers x and y (1 ≤ x, y ≤ 999) — the piece's coordinates. The first line contains the coordinates of the king and the next 666 contain the coordinates of the rooks. The first coordinate denotes the number of the row where the piece is located, the second denotes the column. It is guaranteed that initially the king isn't in check and that all pieces occupy different squares.
Output
After getting king checked, you program should terminate immediately without printing anything extra.
Interaction
To make a move with the king, output two integers x and y (1 ≤ x, y ≤ 999) — the square to which the king would be moved. The king cannot move onto the square already occupied by a rook. It is guaranteed that the king would always have a valid move.
After each of your turns read the rook's turn in the following format: a single line containing three integers k, x and y (1 ≤ k ≤ 666, 1 ≤ x_i, y_i ≤ 999) — the number of the rook that would move and the square it would move to. It is guaranteed that the rook wouldn't move to a square already occupied by another chess piece, but it can move onto the square where it was before the turn so that its position wouldn't change. It is guaranteed that the move does not put your king into a check. If your king got in check, all three integers would be equal to -1 and in that case your program should terminate immediately.
After printing your turn do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use:
* fflush(stdout) or cout.flush() in C++;
* System.out.flush() in Java;
* flush(output) in Pascal;
* stdout.flush() in Python;
* see documentation for other languages.
Answer "0 0 0" instead of a correct answer means that you made an invalid query. Exit immediately after receiving "0 0 0" and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.
Hacks are not allowed for this problem.
Example
Input
999 999
1 1
1 2
2 1
2 2
1 3
2 3
<...>
26 13
26 14
26 15
26 16
1 700 800
2 1 2
<...>
-1 -1 -1
Output
999 998
999 997
<...>
999 26
Note
The example is trimmed. The full initial positions of the rooks in the first test are available at <https://pastebin.com/qQCTXgKP>. It is not guaranteed that they will behave as in the example. | import java.util.*;
public class Main {
public static Scanner sc = new Scanner(System.in);
public static Pair king;
public static Pair []rook = new Pair[666];
public static boolean finished;
public static boolean checkWhereCorner = false;
public static long movX;
public static long movY;
public static boolean notBeenInTheMiddle = true;
public static void main(String[] args) {
king = new Pair(sc.nextInt(), sc.nextInt());
for (int i = 0;i <= 665;i++){
rook[i] = new Pair(sc.nextInt() , sc.nextInt());
}
finished = false;
while (!finished){
moverseAlMedio();
leerMovimientoMaquina();
}
}
public static void moverseAlMedio(){
boolean notInTheMiddle = true;
long preMovX = 0, preMovY = 0;
if(king.x == 500 && king.y == 500){
notInTheMiddle = false;
notBeenInTheMiddle = false;
}
if(notBeenInTheMiddle && notInTheMiddle){
if(king.x < 500){
preMovX = 1;
} else if(king.x > 500){
preMovX = -1;
}
if(king.y < 500){
preMovY = 1;
} else if(king.y > 500){
preMovY = -1;
}
}
if(!notBeenInTheMiddle){
if(!checkWhereCorner){
int contador1 = 0;
int contador2 = 0;
int contador3 = 0;
int contador4 = 0;
for(Pair p : rook){
if(p.x<500){
if(p.y<500){
contador1 += 1;
}else{
contador2 += 1;
}
}else{
if(p.y<500){
contador3 += 1;
}else{
contador4 += 1;
}
}
}
Vector<Pair> ari = new Vector<Pair>();
ari.add(new Pair(contador1,1));
ari.add(new Pair(contador2,2));
ari.add(new Pair(contador3,3));
ari.add(new Pair(contador4,4));
Collections.sort(ari);
if(ari.get(0).y == 1){
movX = 1;
movY = 1;
}else if(ari.get(0).y == 2){
movX = 1;
movY = -1;
}else if(ari.get(0).y == 3){
movX = -1;
movY = 1;
}else{
movX = -1;
movY = -1;
}
checkWhereCorner = true;
}
if(checkWhereCorner){
preMovX = movX;
preMovY = movY;
}
}
boolean exception = false;
for (Pair p: rook){
if (king.x + preMovX == p.x && king.y + preMovY == p.y){
exception = true;
}
}
if (exception){
preMovX = 0;
}
king.x += preMovX;
king.y += preMovY;
System.out.println(king.x + " " + king.y);
System.out.flush();
}
public static void leerMovimientoMaquina(){
Integer k, x , y;
k = sc.nextInt();
x = sc.nextInt();
y = sc.nextInt();
if (k == -1 && x == -1 && y == -1){
finished = true;
return;
}
rook[k-1].x = x;
rook[k-1].y = y;
}
}
class Pair implements Comparable<Pair>{
public long x;
public long y;
Pair(long x, long y) {
this.x = x;
this.y = y;
}
@Override
public int compareTo(Pair other) {
// As of Java 7, this can be replaced with
// return x != other.x ? Integer.compare(x, other.x)
// : Integer.compare(y, other.y);
if (x < other.x || (x == other.x && y < other.y)) {
return -1;
}
return x == other.x && y == other.y ? 0 : 1;
}
@Override
public boolean equals(Object o){
if (o instanceof Pair){
Pair ot = (Pair)o;
if (ot.x == this.x && ot.y == this.y){
return true;
}
return false;
}
return o == this;
}
@Override
public int hashCode() {
return (int)(this.x + this.y * 23233);
}
} |
Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visit after station i is station i+1 if 1 ≤ i < n or station 1 if i = n. It takes the train 1 second to travel to its next station as described.
Bob gave Alice a fun task before he left: to deliver m candies that are initially at some stations to their independent destinations using the train. The candies are enumerated from 1 through m. Candy i (1 ≤ i ≤ m), now at station a_i, should be delivered to station b_i (a_i ≠ b_i).
<image> The blue numbers on the candies correspond to b_i values. The image corresponds to the 1-st example.
The train has infinite capacity, and it is possible to load off any number of candies at a station. However, only at most one candy can be loaded from a station onto the train before it leaves the station. You can choose any candy at this station. The time it takes to move the candies is negligible.
Now, Alice wonders how much time is needed for the train to deliver all candies. Your task is to find, for each station, the minimum time the train would need to deliver all the candies were it to start from there.
Input
The first line contains two space-separated integers n and m (2 ≤ n ≤ 5 000; 1 ≤ m ≤ 20 000) — the number of stations and the number of candies, respectively.
The i-th of the following m lines contains two space-separated integers a_i and b_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i) — the station that initially contains candy i and the destination station of the candy, respectively.
Output
In the first and only line, print n space-separated integers, the i-th of which is the minimum time, in seconds, the train would need to deliver all the candies were it to start from station i.
Examples
Input
5 7
2 4
5 1
2 3
3 4
4 1
5 3
3 5
Output
10 9 10 10 9
Input
2 3
1 2
1 2
1 2
Output
5 6
Note
Consider the second sample.
If the train started at station 1, the optimal strategy is as follows.
1. Load the first candy onto the train.
2. Proceed to station 2. This step takes 1 second.
3. Deliver the first candy.
4. Proceed to station 1. This step takes 1 second.
5. Load the second candy onto the train.
6. Proceed to station 2. This step takes 1 second.
7. Deliver the second candy.
8. Proceed to station 1. This step takes 1 second.
9. Load the third candy onto the train.
10. Proceed to station 2. This step takes 1 second.
11. Deliver the third candy.
Hence, the train needs 5 seconds to complete the tasks.
If the train were to start at station 2, however, it would need to move to station 1 before it could load the first candy, which would take one additional second. Thus, the answer in this scenario is 5+1 = 6 seconds. | import java.util.*;
import java.io.*;
public class a
{
public static void main(String[] Args) throws Exception
{
FS sc = new FS(System.in);
PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
int n = sc.nextInt();
int m = sc.nextInt();
ArrayList<Integer>[] als = new ArrayList[n];
for (int i = 0; i < n; i++)
{
als[i] = new ArrayList<Integer>();
}
for (int i = 0; i < m; i++)
{
int a = sc.nextInt() - 1;
int b = sc.nextInt() - 1;
b += n - a;
while (b > n)
b -= n;
als[a].add(b);
}
for (int i = 0; i < n; i++)
{
Collections.sort(als[i]);
}
for (int i = 0; i < n; i++)
{
int ans = 0;
for (int j = 0; j < n; j++)
{
int jj = (j + i);
int tans = 0;
while (jj >= n)
jj-=n;
if (als[jj].size() > 0)
tans = j + (als[jj].size() - 1) * n + als[jj].get(0);
if (tans > ans)
ans = tans;
}
out.print(ans +" " );
}
out.close();
}
public static class FS
{
StringTokenizer st;
BufferedReader br;
FS(InputStream in) throws Exception
{
br = new BufferedReader(new InputStreamReader(in));
st = new StringTokenizer("");
}
String next() throws Exception
{
if (st.hasMoreTokens())
{
return st.nextToken();
}
st = new StringTokenizer(br.readLine());
return next();
}
int nextInt() throws Exception
{
return Integer.parseInt(next());
}
}
}
|
During the archaeological research in the Middle East you found the traces of three ancient religions: First religion, Second religion and Third religion. You compiled the information on the evolution of each of these beliefs, and you now wonder if the followers of each religion could coexist in peace.
The Word of Universe is a long word containing the lowercase English characters only. At each moment of time, each of the religion beliefs could be described by a word consisting of lowercase English characters.
The three religions can coexist in peace if their descriptions form disjoint subsequences of the Word of Universe. More formally, one can paint some of the characters of the Word of Universe in three colors: 1, 2, 3, so that each character is painted in at most one color, and the description of the i-th religion can be constructed from the Word of Universe by removing all characters that aren't painted in color i.
The religions however evolve. In the beginning, each religion description is empty. Every once in a while, either a character is appended to the end of the description of a single religion, or the last character is dropped from the description. After each change, determine if the religions could coexist in peace.
Input
The first line of the input contains two integers n, q (1 ≤ n ≤ 100 000, 1 ≤ q ≤ 1000) — the length of the Word of Universe and the number of religion evolutions, respectively. The following line contains the Word of Universe — a string of length n consisting of lowercase English characters.
Each of the following line describes a single evolution and is in one of the following formats:
* + i c (i ∈ \{1, 2, 3\}, c ∈ \{a, b, ..., z\}: append the character c to the end of i-th religion description.
* - i (i ∈ \{1, 2, 3\}) – remove the last character from the i-th religion description. You can assume that the pattern is non-empty.
You can assume that no religion will have description longer than 250 characters.
Output
Write q lines. The i-th of them should be YES if the religions could coexist in peace after the i-th evolution, or NO otherwise.
You can print each character in any case (either upper or lower).
Examples
Input
6 8
abdabc
+ 1 a
+ 1 d
+ 2 b
+ 2 c
+ 3 a
+ 3 b
+ 1 c
- 2
Output
YES
YES
YES
YES
YES
YES
NO
YES
Input
6 8
abbaab
+ 1 a
+ 2 a
+ 3 a
+ 1 b
+ 2 b
+ 3 b
- 1
+ 2 z
Output
YES
YES
YES
YES
YES
NO
YES
NO
Note
In the first example, after the 6th evolution the religion descriptions are: ad, bc, and ab. The following figure shows how these descriptions form three disjoint subsequences of the Word of Universe:
<image> | #include <bits/stdc++.h>
using namespace std;
void fast() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
}
vector<string> vec_splitter(string s) {
s += ',';
vector<string> res;
while (!s.empty()) {
res.push_back(s.substr(0, s.find(',')));
s = s.substr(s.find(',') + 1);
}
return res;
}
void debug_out(vector<string> __attribute__((unused)) args,
__attribute__((unused)) int idx,
__attribute__((unused)) int LINE_NUM) {
cerr << endl;
}
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {
if (idx > 0)
cerr << ", ";
else
cerr << "Line(" << LINE_NUM << ") ";
stringstream ss;
ss << H;
cerr << args[idx] << " = " << ss.str();
debug_out(args, idx + 1, LINE_NUM, T...);
}
double get_time() { return 1.0 * clock() / CLOCKS_PER_SEC; }
int main() {
fast();
int n, q;
cin >> n >> q;
string s;
cin >> s;
vector<vector<int>> nxt(26, vector<int>(n + 2, n + 1));
for (int i = n - 1; i >= 0; i--) {
nxt[s[i] - 'a'][i] = i;
}
for (int i = 0; i < 26; i++) {
for (int j = n - 1; j >= 0; j--) nxt[i][j] = min(nxt[i][j], nxt[i][j + 1]);
}
vector<vector<vector<int>>> dp(
256, vector<vector<int>>(256, vector<int>(256, n + 1)));
dp[0][0][0] = 0;
vector<int> l(3);
vector<string> t(3, "");
while (q--) {
char ch, c;
int idx;
cin >> ch >> idx;
idx--;
if (ch == '+') {
cin >> c;
l[idx]++;
t[idx] += c;
}
42;
int lim0 = (idx == 0 ? l[0] : 0);
int lim1 = (idx == 1 ? l[1] : 0);
int lim2 = (idx == 2 ? l[2] : 0);
for (int i = lim0; i <= l[0]; i++) {
for (int j = lim1; j <= l[1]; j++) {
for (int k = lim2; k <= l[2]; k++) {
dp[i][j][k] = n + 1;
if (ch == '+') {
if (i > 0)
dp[i][j][k] =
min(dp[i][j][k], nxt[t[0][i - 1] - 'a'][dp[i - 1][j][k]] + 1);
if (j > 0)
dp[i][j][k] =
min(dp[i][j][k], nxt[t[1][j - 1] - 'a'][dp[i][j - 1][k]] + 1);
if (k > 0)
dp[i][j][k] =
min(dp[i][j][k], nxt[t[2][k - 1] - 'a'][dp[i][j][k - 1]] + 1);
}
}
}
}
if (ch == '-') {
l[idx]--;
t[idx] = t[idx].substr(0, (int)t[idx].size() - 1);
}
if (dp[l[0]][l[1]][l[2]] < n + 1)
cout << "YES" << '\n';
else
cout << "NO" << '\n';
}
}
|
After playing Neo in the legendary "Matrix" trilogy, Keanu Reeves started doubting himself: maybe we really live in virtual reality? To find if this is true, he needs to solve the following problem.
Let's call a string consisting of only zeroes and ones good if it contains different numbers of zeroes and ones. For example, 1, 101, 0000 are good, while 01, 1001, and 111000 are not good.
We are given a string s of length n consisting of only zeroes and ones. We need to cut s into minimal possible number of substrings s_1, s_2, …, s_k such that all of them are good. More formally, we have to find minimal by number of strings sequence of good strings s_1, s_2, …, s_k such that their concatenation (joining) equals s, i.e. s_1 + s_2 + ... + s_k = s.
For example, cuttings 110010 into 110 and 010 or into 11 and 0010 are valid, as 110, 010, 11, 0010 are all good, and we can't cut 110010 to the smaller number of substrings as 110010 isn't good itself. At the same time, cutting of 110010 into 1100 and 10 isn't valid as both strings aren't good. Also, cutting of 110010 into 1, 1, 0010 isn't valid, as it isn't minimal, even though all 3 strings are good.
Can you help Keanu? We can show that the solution always exists. If there are multiple optimal answers, print any.
Input
The first line of the input contains a single integer n (1≤ n ≤ 100) — the length of the string s.
The second line contains the string s of length n consisting only from zeros and ones.
Output
In the first line, output a single integer k (1≤ k) — a minimal number of strings you have cut s into.
In the second line, output k strings s_1, s_2, …, s_k separated with spaces. The length of each string has to be positive. Their concatenation has to be equal to s and all of them have to be good.
If there are multiple answers, print any.
Examples
Input
1
1
Output
1
1
Input
2
10
Output
2
1 0
Input
6
100011
Output
2
100 011
Note
In the first example, the string 1 wasn't cut at all. As it is good, the condition is satisfied.
In the second example, 1 and 0 both are good. As 10 isn't good, the answer is indeed minimal.
In the third example, 100 and 011 both are good. As 100011 isn't good, the answer is indeed minimal. | #include <bits/stdc++.h>
using namespace std;
int main() {
string s;
int n;
cin >> n >> s;
int cnt0 = 0, cnt1 = 0;
for (int i = 0; i < n; i++) {
if (s[i] == '0') {
cnt0++;
} else
cnt1++;
}
if (cnt0 != cnt1) {
cout << "1" << endl;
cout << s << endl;
} else {
cout << "2" << endl;
cout << s[0] << " " << s.substr(1, n);
}
return 0;
}
|
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | import java.io.*;
import static java.lang.Integer.parseInt;
import java.util.*;
import javax.swing.*;
public class Start
{
public static void main(String arge[]) throws IOException
{
BufferedReader in =new BufferedReader(new InputStreamReader(System.in));
StringBuilder out =new StringBuilder();
StringTokenizer tk;
int tc=parseInt(in.readLine());
while(tc-- >0)
{
tk=new StringTokenizer(in.readLine());
int a=parseInt(tk.nextToken()),b=parseInt(tk.nextToken()),n=parseInt(tk.nextToken());
int ans=get(a,b,n%3);
out.append(ans).append("\n");
}
System.out.print(out);
}
public static int get(int a,int b,int n)
{
if (n==0)
return a;
if (n==1)
return b;
return a^b;
}
}
|
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments. | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t;
cin >> t;
while (t--) {
int n, i;
cin >> n;
int l[n], r[n];
for (i = 0; i < n; i++) {
cin >> l[i] >> r[i];
}
if (n == 1)
cout << 0 << endl;
else {
sort(l, l + n);
sort(r, r + n);
if (l[n - 1] > r[0]) {
int ans = abs(r[0] - l[n - 1]);
cout << ans << endl;
} else
cout << 0 << endl;
}
}
}
|
You are given an infinite checkered field. You should get from a square (x1; y1) to a square (x2; y2). Using the shortest path is not necessary. You can move on the field squares in four directions. That is, when you are positioned in any square, you can move to any other side-neighboring one.
A square (x; y) is considered bad, if at least one of the two conditions is fulfilled:
* |x + y| ≡ 0 (mod 2a),
* |x - y| ≡ 0 (mod 2b).
Your task is to find the minimum number of bad cells one will have to visit on the way from (x1; y1) to (x2; y2).
Input
The only line contains integers a, b, x1, y1, x2 and y2 — the parameters of the bad squares, the coordinates of the initial and the final squares correspondingly (2 ≤ a, b ≤ 109 and |x1|,|y1|,|x2|,|y2| ≤ 109). It is guaranteed that the initial and the final square aren't bad.
Output
Print a single number — the minimum number of bad cells that one will have to visit in order to travel from square (x1; y1) to square (x2; y2).
Examples
Input
2 2 1 0 0 1
Output
1
Input
2 2 10 11 0 1
Output
5
Input
2 4 3 -1 3 7
Output
2
Note
In the third sample one of the possible paths in (3;-1)->(3;0)->(3;1)->(3;2)->(4;2)->(4;3)->(4;4)->(4;5)->(4;6)->(4;7)->(3;7). Squares (3;1) and (4;4) are bad. | #include <bits/stdc++.h>
using namespace std;
int f(string s) {
int k = 0;
for (int i = 0; i < s.size(); i++) k = 10 * k + int(s[i]) - 48;
return k;
}
int main() {
int n, k, l, m, i, j;
int x3, y3, x4, y4, a, b, x1, x2, y1, y2;
cin >> a >> b >> x1 >> y1 >> x2 >> y2;
if (x1 + y1 >= 0)
x3 = (x1 + y1) / (2 * a);
else
x3 = (x1 + y1) / (2 * a) - 1;
if (x1 - y1 >= 0)
y3 = (x1 - y1) / (2 * b);
else
y3 = (x1 - y1) / (2 * b) - 1;
if (x2 + y2 >= 0)
x4 = (x2 + y2) / (2 * a);
else
x4 = (x2 + y2) / (2 * a) - 1;
if (x2 - y2 >= 0)
y4 = (x2 - y2) / (2 * b);
else
y4 = (x2 - y2) / (2 * b) - 1;
k = max(abs(x3 - x4), abs(y3 - y4));
cout << k;
return 0;
}
|
You are given a positive integer m and two integer sequence: a=[a_1, a_2, …, a_n] and b=[b_1, b_2, …, b_n]. Both of these sequence have a length n.
Permutation is a sequence of n different positive integers from 1 to n. For example, these sequences are permutations: [1], [1,2], [2,1], [6,7,3,4,1,2,5]. These are not: [0], [1,1], [2,3].
You need to find the non-negative integer x, and increase all elements of a_i by x, modulo m (i.e. you want to change a_i to (a_i + x) mod m), so it would be possible to rearrange elements of a to make it equal b, among them you need to find the smallest possible x.
In other words, you need to find the smallest non-negative integer x, for which it is possible to find some permutation p=[p_1, p_2, …, p_n], such that for all 1 ≤ i ≤ n, (a_i + x) mod m = b_{p_i}, where y mod m — remainder of division of y by m.
For example, if m=3, a = [0, 0, 2, 1], b = [2, 0, 1, 1], you can choose x=1, and a will be equal to [1, 1, 0, 2] and you can rearrange it to make it equal [2, 0, 1, 1], which is equal to b.
Input
The first line contains two integers n,m (1 ≤ n ≤ 2000, 1 ≤ m ≤ 10^9): number of elemens in arrays and m.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i < m).
The third line contains n integers b_1, b_2, …, b_n (0 ≤ b_i < m).
It is guaranteed that there exists some non-negative integer x, such that it would be possible to find some permutation p_1, p_2, …, p_n such that (a_i + x) mod m = b_{p_i}.
Output
Print one integer, the smallest non-negative integer x, such that it would be possible to find some permutation p_1, p_2, …, p_n such that (a_i + x) mod m = b_{p_i} for all 1 ≤ i ≤ n.
Examples
Input
4 3
0 0 2 1
2 0 1 1
Output
1
Input
3 2
0 0 0
1 1 1
Output
1
Input
5 10
0 0 0 1 2
2 1 0 0 0
Output
0 | import sys
input=sys.stdin.readline
from collections import deque
n,m=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
a.sort()
b.sort()
a=deque(a)
b=deque(b)
ans=0
for _ in range(n):
if a==b:
break
f=1
for j in range(n-1):
if b[j+1]-a[j+1]!=b[j]-a[j]:
f=0
break
if f:
if b[0]>a[0]:
print(ans+b[0]-a[0])
exit()
else:
print(ans+b[0]-a[0]+m)
exit()
p=m-a[-1]
ans+=p
ww=0
for j in range(n):
a[j]+=p
if a[j]==m:
ww=n-j
break
for j in range(ww):
a.pop()
a.appendleft(0)
print(ans) |
You're given an array a_1, …, a_n of n non-negative integers.
Let's call it sharpened if and only if there exists an integer 1 ≤ k ≤ n such that a_1 < a_2 < … < a_k and a_k > a_{k+1} > … > a_n. In particular, any strictly increasing or strictly decreasing array is sharpened. For example:
* The arrays [4], [0, 1], [12, 10, 8] and [3, 11, 15, 9, 7, 4] are sharpened;
* The arrays [2, 8, 2, 8, 6, 5], [0, 1, 1, 0] and [2, 5, 6, 9, 8, 8] are not sharpened.
You can do the following operation as many times as you want: choose any strictly positive element of the array, and decrease it by one. Formally, you can choose any i (1 ≤ i ≤ n) such that a_i>0 and assign a_i := a_i - 1.
Tell if it's possible to make the given array sharpened using some number (possibly zero) of these operations.
Input
The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 15\ 000) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer n (1 ≤ n ≤ 3 ⋅ 10^5).
The second line of each test case contains a sequence of n non-negative integers a_1, …, a_n (0 ≤ a_i ≤ 10^9).
It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.
Output
For each test case, output a single line containing "Yes" (without quotes) if it's possible to make the given array sharpened using the described operations, or "No" (without quotes) otherwise.
Example
Input
10
1
248618
3
12 10 8
6
100 11 15 9 7 8
4
0 1 1 0
2
0 0
2
0 1
2
1 0
2
1 1
3
0 1 0
3
1 0 1
Output
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
No
Note
In the first and the second test case of the first test, the given array is already sharpened.
In the third test case of the first test, we can transform the array into [3, 11, 15, 9, 7, 4] (decrease the first element 97 times and decrease the last element 4 times). It is sharpened because 3 < 11 < 15 and 15 > 9 > 7 > 4.
In the fourth test case of the first test, it's impossible to make the given array sharpened. | t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
rok = True
rrok = True
if n == 2 and a[0] == 0 and a[1] == 0:
print("No")
else:
if n%2 == 0:
ar = [0]*n
for i in range(n//2):
ar[i] = i
ar[n-i-1] = i
ar[n//2] = n//2
for i in range(1, n-1):
if a[i] < ar[i]:
rok = False
ar = ar[::-1]
for i in range(1, n-1):
if a[i] < ar[i]:
rrok = False
print("Yes" if (rok or rrok) else "No")
else:
for i in range(n):
if a[i] < min(i, n-i-1):
rok = False
break
print("Yes" if rok else "No") |
You want to perform the combo on your opponent in one popular fighting game. The combo is the string s consisting of n lowercase Latin letters. To perform the combo, you have to press all buttons in the order they appear in s. I.e. if s="abca" then you have to press 'a', then 'b', 'c' and 'a' again.
You know that you will spend m wrong tries to perform the combo and during the i-th try you will make a mistake right after p_i-th button (1 ≤ p_i < n) (i.e. you will press first p_i buttons right and start performing the combo from the beginning). It is guaranteed that during the m+1-th try you press all buttons right and finally perform the combo.
I.e. if s="abca", m=2 and p = [1, 3] then the sequence of pressed buttons will be 'a' (here you're making a mistake and start performing the combo from the beginning), 'a', 'b', 'c', (here you're making a mistake and start performing the combo from the beginning), 'a' (note that at this point you will not perform the combo because of the mistake), 'b', 'c', 'a'.
Your task is to calculate for each button (letter) the number of times you'll press it.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Then t test cases follow.
The first line of each test case contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 2 ⋅ 10^5) — the length of s and the number of tries correspondingly.
The second line of each test case contains the string s consisting of n lowercase Latin letters.
The third line of each test case contains m integers p_1, p_2, ..., p_m (1 ≤ p_i < n) — the number of characters pressed right during the i-th try.
It is guaranteed that the sum of n and the sum of m both does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ m ≤ 2 ⋅ 10^5).
It is guaranteed that the answer for each letter does not exceed 2 ⋅ 10^9.
Output
For each test case, print the answer — 26 integers: the number of times you press the button 'a', the number of times you press the button 'b', ..., the number of times you press the button 'z'.
Example
Input
3
4 2
abca
1 3
10 5
codeforces
2 8 3 2 9
26 10
qwertyuioplkjhgfdsazxcvbnm
20 10 1 2 3 5 10 5 9 4
Output
4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 9 4 5 3 0 0 0 0 0 0 0 0 9 0 0 3 1 0 0 0 0 0 0 0
2 1 1 2 9 2 2 2 5 2 2 2 1 1 5 4 11 8 2 7 5 1 10 1 5 2
Note
The first test case is described in the problem statement. Wrong tries are "a", "abc" and the final try is "abca". The number of times you press 'a' is 4, 'b' is 2 and 'c' is 2.
In the second test case, there are five wrong tries: "co", "codeforc", "cod", "co", "codeforce" and the final try is "codeforces". The number of times you press 'c' is 9, 'd' is 4, 'e' is 5, 'f' is 3, 'o' is 9, 'r' is 3 and 's' is 1. | from sys import stdin
from bisect import bisect_left
from collections import Counter
for k in range(int(stdin.readline())):
n,m=[int(x) for x in stdin.readline().split()]
s=input()
d=Counter(s)
l=list(map(int,stdin.readline().split()))
l.sort()
ans=[0 for j in range(0,26)]
for j in range(0,len(s)):
n=len(l)-bisect_left(l,j+1)
ans[ord(s[j])-97]+=(n)
e=list(d.keys())
try:
for i in range(0,len(e)):
ans[ord(e[i])-97]+=(d[e[i]])
except(Exception):
pass
print(*ans) |
Polycarp has recently created a new level in this cool new game Berlio Maker 85 and uploaded it online. Now players from all over the world can try his level.
All levels in this game have two stats to them: the number of plays and the number of clears. So when a player attempts the level, the number of plays increases by 1. If he manages to finish the level successfully then the number of clears increases by 1 as well. Note that both of the statistics update at the same time (so if the player finishes the level successfully then the number of plays will increase at the same time as the number of clears).
Polycarp is very excited about his level, so he keeps peeking at the stats to know how hard his level turns out to be.
So he peeked at the stats n times and wrote down n pairs of integers — (p_1, c_1), (p_2, c_2), ..., (p_n, c_n), where p_i is the number of plays at the i-th moment of time and c_i is the number of clears at the same moment of time. The stats are given in chronological order (i.e. the order of given pairs is exactly the same as Polycarp has written down).
Between two consecutive moments of time Polycarp peeked at the stats many players (but possibly zero) could attempt the level.
Finally, Polycarp wonders if he hasn't messed up any records and all the pairs are correct. If there could exist such a sequence of plays (and clears, respectively) that the stats were exactly as Polycarp has written down, then he considers his records correct.
Help him to check the correctness of his records.
For your convenience you have to answer multiple independent test cases.
Input
The first line contains a single integer T (1 ≤ T ≤ 500) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the number of moments of time Polycarp peeked at the stats.
Each of the next n lines contains two integers p_i and c_i (0 ≤ p_i, c_i ≤ 1000) — the number of plays and the number of clears of the level at the i-th moment of time.
Note that the stats are given in chronological order.
Output
For each test case print a single line.
If there could exist such a sequence of plays (and clears, respectively) that the stats were exactly as Polycarp has written down, then print "YES".
Otherwise, print "NO".
You can print each letter in any case (upper or lower).
Example
Input
6
3
0 0
1 1
1 2
2
1 0
1000 3
4
10 1
15 2
10 2
15 2
1
765 432
2
4 4
4 3
5
0 0
1 0
1 0
1 0
1 0
Output
NO
YES
NO
YES
NO
YES
Note
In the first test case at the third moment of time the number of clears increased but the number of plays did not, that couldn't have happened.
The second test case is a nice example of a Super Expert level.
In the third test case the number of plays decreased, which is impossible.
The fourth test case is probably an auto level with a single jump over the spike.
In the fifth test case the number of clears decreased, which is also impossible.
Nobody wanted to play the sixth test case; Polycarp's mom attempted it to make him feel better, however, she couldn't clear it. | T=int(input())
list=[]
c=-1
d=-1
for i in range(T):
n=int(input())
k="Yes"
for j in range(n):
a,b=map(int,input().split())
if a>=b and c<=a and d<=b and (b-d)<=(a-c):
g=0
else:
k="No"
c=a
d=b
c=-1
d=-1
list.append(k)
for i in range(len(list)):
print(list[i]) |
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | # Why do we fall ? So we can learn to pick ourselves up.
from math import pi,cos
t = int(input())
for _ in range(0,t):
n = int(input())
theta = pi/4
delta = pi/n
maxi,mini,x = 0,0,0
for i in range(0,2*n):
x += cos(theta)
theta -= delta
maxi = max(maxi,x)
mini = min(mini,x)
print(maxi-mini)
"""
3
3
5
199
""" |
You are given an integer n. In one move, you can either multiply n by two or divide n by 6 (if it is divisible by 6 without the remainder).
Your task is to find the minimum number of moves needed to obtain 1 from n or determine if it's impossible to do that.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print the answer — the minimum number of moves needed to obtain 1 from n if it's possible to do that or -1 if it's impossible to obtain 1 from n.
Example
Input
7
1
2
3
12
12345
15116544
387420489
Output
0
-1
2
-1
-1
12
36
Note
Consider the sixth test case of the example. The answer can be obtained by the following sequence of moves from the given integer 15116544:
1. Divide by 6 and get 2519424;
2. divide by 6 and get 419904;
3. divide by 6 and get 69984;
4. divide by 6 and get 11664;
5. multiply by 2 and get 23328;
6. divide by 6 and get 3888;
7. divide by 6 and get 648;
8. divide by 6 and get 108;
9. multiply by 2 and get 216;
10. divide by 6 and get 36;
11. divide by 6 and get 6;
12. divide by 6 and get 1. | t=int(input())
for i in range(t):
n=int(input())
if n==1:
print(0)
else:
if n%3!=0:
print(-1)
else:
threes=0
twos=0
while n%3==0:
threes+=1
n=n//3
while n%2==0:
twos+=1
n=n//2
if n!=1 or twos>threes:
print(-1)
else:
print(2*threes-twos)
|
You are given an array a of n integers.
You want to make all elements of a equal to zero by doing the following operation exactly three times:
* Select a segment, for each number in this segment we can add a multiple of len to it, where len is the length of this segment (added integers can be different).
It can be proven that it is always possible to make all elements of a equal to zero.
Input
The first line contains one integer n (1 ≤ n ≤ 100 000): the number of elements of the array.
The second line contains n elements of an array a separated by spaces: a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
Output
The output should contain six lines representing three operations.
For each operation, print two lines:
* The first line contains two integers l, r (1 ≤ l ≤ r ≤ n): the bounds of the selected segment.
* The second line contains r-l+1 integers b_l, b_{l+1}, ..., b_r (-10^{18} ≤ b_i ≤ 10^{18}): the numbers to add to a_l, a_{l+1}, …, a_r, respectively; b_i should be divisible by r - l + 1.
Example
Input
4
1 3 2 4
Output
1 1
-1
3 4
4 2
2 4
-3 -6 -6 | #include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
using namespace std;
const int BUBEN = 550;
const int MOD = 1e9 + 7;
const int BASE = 29;
const int MOD1 = 998244353;
const int BASE1 = 31;
char _getchar_nolock() { return getchar_unlocked(); }
char _putchar_nolock(char i) { return putchar_unlocked(i); }
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n;
cin >> n;
vector<long long> arr(n);
for (int i = 0; i < n; i++) {
cin >> arr[i];
}
if (n == 1) {
cout << "1 1\n" << -arr[0] << "\n1 1\n0\n1 1\n0";
} else {
cout << "1 " << n - 1 << '\n';
for (int i = 0; i + 1 < n; i++) {
cout << (n - 1) * (arr[i] % n) << ' ';
arr[i] += (n - 1) * (arr[i] % n);
}
cout << '\n' << n << ' ' << n << '\n';
cout << n - (arr[n - 1] % n) << '\n';
arr[n - 1] += n - (arr[n - 1] % n);
cout << 1 << ' ' << n << '\n';
for (int i = 0; i < n; i++) {
cout << -arr[i] << ' ';
}
}
}
|
Ori and Sein have overcome many difficult challenges. They finally lit the Shrouded Lantern and found Gumon Seal, the key to the Forlorn Ruins. When they tried to open the door to the ruins... nothing happened.
Ori was very surprised, but Sein gave the explanation quickly: clever Gumon decided to make an additional defence for the door.
There are n lamps with Spirit Tree's light. Sein knows the time of turning on and off for the i-th lamp — l_i and r_i respectively. To open the door you have to choose k lamps in such a way that there will be a moment of time when they all will be turned on.
While Sein decides which of the k lamps to pick, Ori is interested: how many ways there are to pick such k lamps that the door will open? It may happen that Sein may be wrong and there are no such k lamps. The answer might be large, so print it modulo 998 244 353.
Input
First line contains two integers n and k (1 ≤ n ≤ 3 ⋅ 10^5, 1 ≤ k ≤ n) — total number of lamps and the number of lamps that must be turned on simultaneously.
Next n lines contain two integers l_i ans r_i (1 ≤ l_i ≤ r_i ≤ 10^9) — period of time when i-th lamp is turned on.
Output
Print one integer — the answer to the task modulo 998 244 353.
Examples
Input
7 3
1 7
3 8
4 5
6 7
1 3
5 10
8 9
Output
9
Input
3 1
1 1
2 2
3 3
Output
3
Input
3 2
1 1
2 2
3 3
Output
0
Input
3 3
1 3
2 3
3 3
Output
1
Input
5 2
1 3
2 4
3 5
4 6
5 7
Output
7
Note
In first test case there are nine sets of k lamps: (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 3, 6), (1, 4, 6), (2, 3, 6), (2, 4, 6), (2, 6, 7).
In second test case k=1, so the answer is 3.
In third test case there are no such pairs of lamps.
In forth test case all lamps are turned on in a time 3, so the answer is 1.
In fifth test case there are seven sets of k lamps: (1, 2), (1, 3), (2, 3), (2, 4), (3, 4), (3, 5), (4, 5). | import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10**19
MOD = 998244353
EPS = 10**-10
def compress(S):
zipped, unzipped = {}, {}
for i, a in enumerate(sorted(S)):
zipped[a] = i
unzipped[i] = a
return zipped, unzipped
class ModTools:
def __init__(self, MAX, MOD):
MAX += 1
self.MAX = MAX
self.MOD = MOD
factorial = [1] * MAX
factorial[0] = factorial[1] = 1
for i in range(2, MAX):
factorial[i] = factorial[i-1] * i % MOD
inverse = [1] * MAX
inverse[MAX-1] = pow(factorial[MAX-1], MOD-2, MOD)
for i in range(MAX-2, -1, -1):
inverse[i] = inverse[i+1] * (i+1) % MOD
self.fact = factorial
self.inv = inverse
def nCr(self, n, r):
if n < r: return 0
r = min(r, n-r)
numerator = self.fact[n]
denominator = self.inv[r] * self.inv[n-r] % self.MOD
return numerator * denominator % self.MOD
N, K = MAP()
LR = []
S = set()
for i in range(N):
l, r = MAP()
r += 1
LR.append((l, r))
S.add(l)
S.add(r)
zipped, _ = compress(S)
M = len(zipped)
lcnt = [0] * M
rcnt = [0] * M
for i in range(N):
LR[i] = (zipped[LR[i][0]], zipped[LR[i][1]])
lcnt[LR[i][0]] += 1
rcnt[LR[i][1]] += 1
cur = 0
ans = 0
mt = ModTools(N, MOD)
for i in range(M):
cur -= rcnt[i]
while lcnt[i]:
if cur >= K-1:
ans += mt.nCr(cur, K-1)
ans %= MOD
cur += 1
lcnt[i] -= 1
print(ans)
|
You are given an array a_1, a_2, …, a_n of integers. This array is non-increasing.
Let's consider a line with n shops. The shops are numbered with integers from 1 to n from left to right. The cost of a meal in the i-th shop is equal to a_i.
You should process q queries of two types:
* 1 x y: for each shop 1 ≤ i ≤ x set a_{i} = max(a_{i}, y).
* 2 x y: let's consider a hungry man with y money. He visits the shops from x-th shop to n-th and if he can buy a meal in the current shop he buys one item of it. Find how many meals he will purchase. The man can buy a meal in the shop i if he has at least a_i money, and after it his money decreases by a_i.
Input
The first line contains two integers n, q (1 ≤ n, q ≤ 2 ⋅ 10^5).
The second line contains n integers a_{1},a_{2}, …, a_{n} (1 ≤ a_{i} ≤ 10^9) — the costs of the meals. It is guaranteed, that a_1 ≥ a_2 ≥ … ≥ a_n.
Each of the next q lines contains three integers t, x, y (1 ≤ t ≤ 2, 1≤ x ≤ n, 1 ≤ y ≤ 10^9), each describing the next query.
It is guaranteed that there exists at least one query of type 2.
Output
For each query of type 2 output the answer on the new line.
Example
Input
10 6
10 10 10 6 6 5 5 5 3 1
2 3 50
2 4 10
1 3 10
2 2 36
1 4 7
2 2 17
Output
8
3
6
2
Note
In the first query a hungry man will buy meals in all shops from 3 to 10.
In the second query a hungry man will buy meals in shops 4, 9, and 10.
After the third query the array a_1, a_2, …, a_n of costs won't change and will be \{10, 10, 10, 6, 6, 5, 5, 5, 3, 1\}.
In the fourth query a hungry man will buy meals in shops 2, 3, 4, 5, 9, and 10.
After the fifth query the array a of costs will be \{10, 10, 10, 7, 6, 5, 5, 5, 3, 1\}.
In the sixth query a hungry man will buy meals in shops 2 and 4. | #include <bits/stdc++.h>
using namespace std;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vc<vc<T>>;
template <class T>
void mkuni(vector<T> &v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
long long rand_int(long long l, long long r) {
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
return uniform_int_distribution<long long>(l, r)(gen);
}
template <class T>
void print(T x, int suc = 1) {
cout << x;
if (suc == 1)
cout << '\n';
else
cout << ' ';
}
template <class T>
void print(const vector<T> &v, int suc = 1) {
for (int i = 0; i < v.size(); i++)
print(v[i], i == (int)(v.size()) - 1 ? suc : 2);
}
const int N = 3e5 + 10;
struct Tree {
long long l, r, lazy, sum, mi, ma;
} tree[N << 2];
void push_up(int rt) {
tree[rt].sum = tree[rt << 1].sum + tree[rt << 1 | 1].sum;
tree[rt].ma = tree[rt << 1].ma;
tree[rt].mi = tree[rt << 1 | 1].mi;
}
void build(int l, int r, int rt, vector<int> &a) {
tree[rt].l = l, tree[rt].r = r, tree[rt].lazy = 0;
if (l == r) {
tree[rt].sum = tree[rt].mi = tree[rt].ma = a[l];
return;
}
int mid = l + r >> 1;
build(l, mid, rt << 1, a);
build(mid + 1, r, rt << 1 | 1, a);
push_up(rt);
}
void push_down(int rt) {
if (tree[rt].lazy) {
int x = tree[rt].lazy, l = tree[rt].l, r = tree[rt].r;
tree[rt].lazy = 0;
tree[rt << 1].sum = 1ll * (tree[rt << 1].r - tree[rt << 1].l + 1) * x;
tree[rt << 1].mi = tree[rt << 1].ma = x;
tree[rt << 1].lazy = x;
tree[rt << 1 | 1].sum =
1ll * (tree[rt << 1 | 1].r - tree[rt << 1 | 1].l + 1) * x;
tree[rt << 1 | 1].mi = tree[rt << 1 | 1].ma = x;
tree[rt << 1 | 1].lazy = x;
}
}
void update_range(int L, int R, long long Y, int rt) {
int l = tree[rt].l, r = tree[rt].r;
if (tree[rt].mi >= Y || l > R) return;
if (tree[rt].ma <= Y && r <= R) {
tree[rt].sum = 1ll * (r - l + 1) * Y;
tree[rt].mi = tree[rt].ma = Y;
tree[rt].lazy = Y;
return;
}
push_down(rt);
update_range(L, R, Y, rt << 1);
update_range(L, R, Y, rt << 1 | 1);
push_up(rt);
}
int query_range(int L, int R, int rt, long long &Y) {
int l = tree[rt].l, r = tree[rt].r;
if (tree[rt].mi > Y || r < L) return 0;
if (tree[rt].sum <= Y && l >= L) {
Y -= tree[rt].sum;
return r - l + 1;
}
push_down(rt);
long long res = 0;
res += query_range(L, R, rt << 1, Y);
res += query_range(L, R, rt << 1 | 1, Y);
return res;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, q;
cin >> n >> q;
vector<int> a(n + 1);
for (int i = 1; i <= n; ++i) cin >> a[i];
build(1, n, 1, a);
while (q--) {
long long x, y, op;
cin >> op >> x >> y;
if (op == 1) {
update_range(1, x, y, 1);
} else
cout << query_range(x, n, 1, y) << '\n';
}
}
|
After his wife's tragic death, Eurydice, Orpheus descended to the realm of death to see her. Reaching its gates was uneasy, but passing through them proved to be even more challenging. Mostly because of Cerberus, the three-headed hound of Hades.
Orpheus, a famous poet, and musician plans to calm Cerberus with his poetry and safely walk past him. He created a very peculiar poem for Cerberus. It consists only of lowercase English letters.
We call a poem's substring a palindrome if and only if it reads the same backwards and forwards. A string a is a substring of a string b if a can be obtained from b by deleting several (possibly zero or all) characters from the beginning and several (possibly zero or all) characters from the end.
Unfortunately, Cerberus dislikes palindromes of length greater than 1. For example in the poem abaa the hound of Hades wouldn't like substrings aba and aa.
Orpheus can only calm Cerberus if the hound likes his poetry. That's why he wants to change his poem so that it does not contain any palindrome substrings of length greater than 1.
Orpheus can modify the poem by replacing a letter at any position with any lowercase English letter. He can use this operation arbitrarily many times (possibly zero). Since there can be many palindromes in his poem, he may have to make some corrections. But how many, exactly? Given the poem, determine the minimal number of letters that have to be changed so that the poem does not contain any palindromes of length greater than 1.
Input
The first line of the input contains a single integer t (1 ≤ t ≤ 10^5) denoting the number of test cases, then t test cases follow.
The first and only line of each test case contains a non-empty string of lowercase English letters, Orpheus' poem.
The sum of the length of Orpheus' poems in all test cases will not exceed 10^5.
Output
You should output t lines, i-th line should contain a single integer, answer to the i-th test case.
Example
Input
7
babba
abaac
codeforces
zeroorez
abcdcba
bbbbbbb
a
Output
1
1
0
1
1
4
0
Note
In the first test case, we can replace the third character with c and obtain a palindrome-less poem bacba.
In the second test case, we can replace the third character with d and obtain a palindrome-less poem abdac.
In the third test case, the initial poem already doesn't contain any palindromes, so Orpheus doesn't need to change anything there. | #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define FOR(i, st, n) for (int i = st; i < n; i++)
const int INF = 1e9+100;
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin>>t;
while (t--){
string s;
cin>>s;
int n = s.size();
int ans = 0;
for (int i = 0; i < n-1; i++){
if (i < n-2 && s[i] == s[i+1] && s[i] == s[i+2]){
ans+=2;
i += 2;
}else if(s[i] == s[i+1]){
ans++;
i++;
}else if(i < n-2 && s[i] == s[i+2]){
ans++;
if (i < n-3 && s[i+1] == s[i+3]){
ans++;
i+=3;
}else{
i+=2;
}
}
}
cout<<ans<<'\n';
}
return 0;
}
|
A permutation — is a sequence of length n integers from 1 to n, in which all the numbers occur exactly once. For example, [1], [3, 5, 2, 1, 4], [1, 3, 2] — permutations, and [2, 3, 2], [4, 3, 1], [0] — no.
Polycarp was recently gifted a permutation a[1 ... n] of length n. Polycarp likes trees more than permutations, so he wants to transform permutation a into a rooted binary tree. He transforms an array of different integers into a tree as follows:
* the maximum element of the array becomes the root of the tree;
* all elements to the left of the maximum — form a left subtree (which is built according to the same rules but applied to the left part of the array), but if there are no elements to the left of the maximum, then the root has no left child;
* all elements to the right of the maximum — form a right subtree (which is built according to the same rules but applied to the right side of the array), but if there are no elements to the right of the maximum, then the root has no right child.
For example, if he builds a tree by permutation a=[3, 5, 2, 1, 4], then the root will be the element a_2=5, and the left subtree will be the tree that will be built for the subarray a[1 ... 1] = [3], and the right one — for the subarray a[3 ... 5] = [2, 1, 4]. As a result, the following tree will be built:
<image> The tree corresponding to the permutation a=[3, 5, 2, 1, 4].
Another example: let the permutation be a=[1, 3, 2, 7, 5, 6, 4]. In this case, the tree looks like this:
<image> The tree corresponding to the permutation a=[1, 3, 2, 7, 5, 6, 4].
Let us denote by d_v the depth of the vertex a_v, that is, the number of edges on the path from the root to the vertex numbered a_v. Note that the root depth is zero. Given the permutation a, for each vertex, find the value of d_v.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
The first line of each test case contains an integer n (1 ≤ n ≤ 100) — the length of the permutation.
This is followed by n numbers a_1, a_2, …, a_n — permutation a.
Output
For each test case, output n values — d_1, d_2, …, d_n.
Example
Input
3
5
3 5 2 1 4
1
1
4
4 3 1 2
Output
1 0 2 3 1
0
0 1 3 2 | //firstly save by ctrl+s before running the code
//press f5 to debug and input in terminal
//typcast by e.g (long long)variable and for constant e.g 5ll
//-----------------------------------------------------------------------------------------------------------------------------
//count set bits using __builtin_popcount(n);
// cout << fixed << setprecision(10) << pi <<" "<<npi<<endl;-->synax to set precision for float/double datatype pi , npi
//ceil or floor used for double and return double
//log also return double
//use floor(n)==n to see if a double n is integer
//for int x,y to get ceil in x/y do as (x+(y-1))/y and x/y itself equals floor only (but returns int)
//log2(n)==floor(log2(n))-->to check if power of 2
//------------------------------------------FUN BEIGINS!-----------------------------------------------------------------------
#include<bits/stdc++.h>
#include<fstream>
#define N 1000000007
#define M 998244353
using namespace std;
#define ll long long
#define pll pair<ll,ll>
#define vll vector<ll>
#define vpll vector<pll>
#define vvll vector<vll>
#define endl "\n" //"\n" not flushes output but endl do
#define umap unordered_map<ll,ll>
//------------------------------------------------------------------------------------------------------------------------------
vector<vector<long long>>adj;
map<long,bool>vis,viss;
vector<long long>rnk,parent,sz;
#define sieve_max 1000000
ll spf[sieve_max+1];
umap mp;
void yg(vll v, ll l, ll r,ll prev){
if(r<l)return;
if(r==l){mp[r]=prev; return;}
ll mx=LLONG_MIN;
ll ct=0;
for(ll i=l;i<=r;i++){if(v[i]>mx){
mx=v[i]; ct=i;
}}
mp[ct]=prev;
yg(v,l,ct-1,prev+1); yg(v,ct+1,r,prev+1);
return;
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(NULL);
ll t,temp;
cin>>t;
while(t--){
mp.clear();
ll n;
cin>>n; vll v;
for(ll i=0;i<n;i++){
cin>>temp; v.push_back(temp);
}
yg(v,0,n-1,0);
for(ll i=0;i<n;i++)cout<<mp[i]<<" ";
cout<<endl;
}
return 0;
} |
Let us denote by d(n) the sum of all divisors of the number n, i.e. d(n) = ∑_{k | n} k.
For example, d(1) = 1, d(4) = 1+2+4=7, d(6) = 1+2+3+6=12.
For a given number c, find the minimum n such that d(n) = c.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by one integer c (1 ≤ c ≤ 10^7).
Output
For each test case, output:
* "-1" if there is no such n that d(n) = c;
* n, otherwise.
Example
Input
12
1
2
3
4
5
6
7
8
9
10
39
691
Output
1
-1
2
3
-1
5
4
7
-1
-1
18
-1 | //#pragma GCC optimize ("O3", "unroll-loops")
//#pragma GCC target ("avx2")
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define LL long long
#define PII pair<int, int>
#define PLL pair<LL, LL>
#define all_of(v) (v).begin(), (v).end()
#define sort_unique(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define fi first
#define se second
const int MAXN = (int)1e7 + 9487;
//const LL INF = (LL) 1e9 + 8763;
//const LL MOD = (LL) 998244353;
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define div dddivvvvvvvvvv
int mpf[MAXN], pw[MAXN], ans[MAXN];
LL div[MAXN];
vector<int> P;
void solve() {
int c;
cin >> c;
cout << ans[c] << '\n';
}
void prep() {
for (int i = 1; i < MAXN; i++) {
ans[i] = -1;
mpf[i] = i;
}
div[1] = 1, pw[1] = 1;
for (int i = 2; i < MAXN; i++) {
ans[i] = -1;
if (mpf[i] == i) {
P.push_back(i);
pw[i] = i;
div[i] = (i + 1);
}
// assert(i % pw[i] == 0 && i / pw[i] % mpf[i] != 0);
// if (i <= 10000000) {
// LL sum = 0;
// for (LL x = 1; x * x <= i; x++) {
// if (i % x == 0) {
// sum += x;
// if (x != i / x) {
// sum += i / x;
// }
// }
// }
//
// if (sum != div[i]) {
// cout << "WTF " << i << " -> " << sum << ' ' << div[i] << endl;
// }
//// cout << "CHK " << i << endl;
// }
for (int p : P) {
if ((LL)i * p >= MAXN) {
break;
}
mpf[i * p] = p;
if (i % p == 0) {
pw[i * p] = pw[i] * p;
div[i * p] = div[i / pw[i]] * (((LL)pw[i * p] * p - 1) / (p - 1));
break;
}
else {
pw[i * p] = p;
div[i * p] = div[i] * (1 + p);
}
}
}
for (int i = MAXN - 1; i >= 1; i--) {
if (div[i] < MAXN) {
ans[div[i]] = i;
}
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
prep();
int tc = 1;
cin >> tc;
for (int i = 1; i <= tc; i++) {
solve();
}
return 0;
} |
In some country live wizards. They love playing with numbers.
The blackboard has two numbers written on it — a and b. The order of the numbers is not important. Let's consider a ≤ b for the sake of definiteness. The players can cast one of the two spells in turns:
* Replace b with b - ak. Number k can be chosen by the player, considering the limitations that k > 0 and b - ak ≥ 0. Number k is chosen independently each time an active player casts a spell.
* Replace b with b mod a.
If a > b, similar moves are possible.
If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses.
To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second.
Input
The first line contains a single integer t — the number of input data sets (1 ≤ t ≤ 104). Each of the next t lines contains two integers a, b (0 ≤ a, b ≤ 1018). The numbers are separated by a space.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.
Output
For any of the t input sets print "First" (without the quotes) if the player who moves first wins. Print "Second" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input.
Examples
Input
4
10 21
31 10
0 1
10 30
Output
First
Second
Second
First
Note
In the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win.
In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win.
In the third sample, the first player has no moves.
In the fourth sample, the first player wins in one move, taking 30 modulo 10. | #include <bits/stdc++.h>
using namespace std;
bool check(long long a, long long b) {
if (!a || !b) return false;
if (a > b) swap(a, b);
if (!check(a, b % a)) return true;
return !(((b / a) % (a + 1)) & 1);
}
int main() {
int T;
cin >> T;
for (; T; --T) {
long long a, b;
cin >> a >> b;
printf("%s\n", (check(a, b)) ? "First" : "Second");
}
}
|
Flatland is inhabited by pixels of three colors: red, green and blue. We know that if two pixels of different colors meet in a violent fight, only one of them survives the fight (that is, the total number of pixels decreases by one). Besides, if pixels of colors x and y (x ≠ y) meet in a violent fight, then the pixel that survives the fight immediately changes its color to z (z ≠ x; z ≠ y). Pixels of the same color are friends, so they don't fight.
The King of Flatland knows that his land will be peaceful and prosperous when the pixels are of the same color. For each of the three colors you know the number of pixels of this color that inhabit Flatland. Help the king and determine whether fights can bring peace and prosperity to the country and if it is possible, find the minimum number of fights needed to make the land peaceful and prosperous.
Input
The first line contains three space-separated integers a, b and c (0 ≤ a, b, c ≤ 231; a + b + c > 0) — the number of red, green and blue pixels, correspondingly.
Output
Print a single number — the minimum number of pixel fights before the country becomes peaceful and prosperous. If making the country peaceful and prosperous is impossible, print -1.
Examples
Input
1 1 1
Output
1
Input
3 1 0
Output
3
Note
In the first test sample the country needs only one fight to achieve peace and prosperity. Besides, it can be any fight whatsoever. For example, let's assume that the green and the blue pixels fight, then the surviving pixel will be red. As a result, after the fight there are two red pixels. There won't be other pixels.
In the second sample the following sequence of fights is possible: red and blue, green and red, red and blue. As a result, after all fights there is one green pixel left. | #include <bits/stdc++.h>
using namespace std;
template <class T>
inline void read(T& num) {
num = 0;
bool f = 1;
char ch = getchar();
while (ch < '0' || ch > '9') {
if (ch == '-') f = 0;
ch = getchar();
}
while (ch >= '0' && ch <= '9') {
num = num * 10 + ch - '0';
ch = getchar();
}
num = f ? num : -num;
}
template <class T>
inline void write(T x, char ch) {
int s[100];
if (x == 0) {
putchar('0');
putchar(ch);
return;
}
if (x < 0) {
putchar('-');
x = -x;
}
int num = 0;
while (x) {
s[num++] = (x % 10);
x = x / 10;
}
for (int i = (num - 1); i >= (0); i--) putchar(s[i] + '0');
putchar(ch);
}
const double pi = acos(-1);
const double eps = 1e-8;
int main() {
long long ans = 100000000000000;
long long A[4], ord[4];
for (int i = (1); i <= (3); i++) {
read(A[i]);
ord[i] = i;
}
do {
long long a = A[ord[1]], b = A[ord[2]], c = A[ord[3]];
if (b < c) swap(b, c);
long long res = c;
a += c, b -= c;
res += (b / 2) * 2;
if (b & 1) res += a;
ans = min(ans, res);
} while (next_permutation(ord + 1, ord + 4));
write(ans, '\n');
}
|
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get. | import java.util.*;
public class CodeForces236C{
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
long n = input.nextLong();
if(n == 1){
System.out.println(1);
}
else if(n == 2){
System.out.println(2);
}
else if(n == 3){
System.out.println(6);
}
else{
if(n%2 == 1){
System.out.println(n*(n-1)*(n-2));
}
else{
if(n%3 == 0){
System.out.println((n-1)*(n-2)*(n-3));
}
else{
System.out.println(n*(n-1)*(n-3));
}
}
}
}
} |
Berland Government decided to improve relations with neighboring countries. First of all, it was decided to build new roads so that from each city of Berland and neighboring countries it became possible to reach all the others. There are n cities in Berland and neighboring countries in total and exactly n - 1 two-way roads. Because of the recent financial crisis, the Berland Government is strongly pressed for money, so to build a new road it has to close some of the existing ones. Every day it is possible to close one existing road and immediately build a new one. Your task is to determine how many days would be needed to rebuild roads so that from each city it became possible to reach all the others, and to draw a plan of closure of old roads and building of new ones.
Input
The first line contains integer n (2 ≤ n ≤ 1000) — amount of cities in Berland and neighboring countries. Next n - 1 lines contain the description of roads. Each road is described by two space-separated integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — pair of cities, which the road connects. It can't be more than one road between a pair of cities. No road connects the city with itself.
Output
Output the answer, number t — what is the least amount of days needed to rebuild roads so that from each city it became possible to reach all the others. Then output t lines — the plan of closure of old roads and building of new ones. Each line should describe one day in the format i j u v — it means that road between cities i and j became closed and a new road between cities u and v is built. Cities are numbered from 1. If the answer is not unique, output any.
Examples
Input
2
1 2
Output
0
Input
7
1 2
2 3
3 1
4 5
5 6
6 7
Output
1
3 1 3 7 | inp=input()
#1:37 start code
adj={}
rem=[]
remv=set()
vis=set()
part=[]
for i in xrange(inp-1):
u,v=map(int,raw_input().split())
if u not in adj:adj[u]=[]
if v not in adj:adj[v]=[]
adj[u].append(v)
adj[v].append(u)
def dfs(node,before):
vis.add(node)
if node not in adj:return
for i in adj[node]:
if i==before:
continue
elif i in vis:
if (i,node) in remv or (node,i) in remv:
continue
rem.append((i,node))
remv.add((node,i))
else:
dfs(i,node)
for i in xrange(1,inp+1):
if i not in vis:
part.append(i)
dfs(i,i)
print len(part)-1
for i in range(len(part)-1):
print rem[i][0],rem[i][1],part[i],part[i+1]
#01:43 finish code
#01:53 finish debug |
Bessie and the cows have recently been playing with "cool" sequences and are trying to construct some. Unfortunately they are bad at arithmetic, so they need your help!
A pair (x, y) of positive integers is "cool" if x can be expressed as the sum of y consecutive integers (not necessarily positive). A sequence (a1, a2, ..., an) is "cool" if the pairs (a1, a2), (a2, a3), ..., (an - 1, an) are all cool.
The cows have a sequence of n positive integers, a1, a2, ..., an. In one move, they may replace some ai with any other positive integer (there are no other limits on the new value of ai). Determine the smallest number of moves needed to make the resulting sequence cool.
Input
The first line contains a single integer, n (2 ≤ n ≤ 5000). The next line contains n space-separated integers, a1, a2, ..., an (1 ≤ ai ≤ 1015).
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
A single integer, the minimum number of ai that must be changed to make the sequence cool.
Examples
Input
3
6 4 1
Output
0
Input
4
20 6 3 4
Output
2
Note
In the first sample, the sequence is already cool, so we don't need to change any elements. In the second sample, we can change a2 to 5 and a3 to 10 to make (20, 5, 10, 4) which is cool. This changes 2 elements. | #include <bits/stdc++.h>
using namespace std;
const int N = 5005;
const int INF = 0x3f3f3f3f;
int n;
long long a[N], g[2][N];
int dp[2][N];
inline long long read() {
long long f = 1, x = 0;
char ch = getchar();
while (ch > '9' || ch < '0') {
if (ch == '-') f = -1;
ch = getchar();
}
while (ch >= '0' && ch <= '9') {
x = x * 10 + ch - '0';
ch = getchar();
}
return f * x;
}
inline void upd(int& x, int y) { x = min(x, y); }
inline long long f(long long x) {
if (x % 2 == 0) return x / 2;
return x;
}
int main() {
n = read(), a[0] = 1;
for (int i = (n), iend = (1); i >= iend; i--) a[i] = read();
dp[0][0] = 0, g[0][0] = 1;
for (int i = (1), iend = (n); i <= iend; i++) {
for (int j = (0), jend = (i); j <= jend; j++) dp[i & 1][j] = INF;
for (int j = (0), jend = (i - 1); j <= jend; j++) {
int t = i & 1;
if ((2 * a[i]) % g[t ^ 1][j] == 0 &&
(2 * a[i] / g[t ^ 1][j]) % 2 != g[t ^ 1][j] % 2)
upd(dp[t][i], dp[t ^ 1][j]), g[t][i] = a[i];
upd(dp[t][j], dp[t ^ 1][j] + 1), g[t][j] = f(g[t ^ 1][j]);
}
}
int ans = INF;
for (int i = (0), iend = (n); i <= iend; i++) upd(ans, dp[n & 1][i]);
printf("%d", ans);
return 0;
}
|
Polycarpus is sure that his life fits the description: "first there is a white stripe, then a black one, then a white one again". So, Polycarpus is sure that this rule is going to fulfill during the next n days. Polycarpus knows that he is in for w good events and b not-so-good events. At least one event is going to take place during each day. As each day is unequivocally characterizes as a part of a white or a black stripe, then each day is going to have events of the same type only (ether good or not-so-good).
What is the number of distinct ways this scenario can develop over the next n days if Polycarpus is in for a white stripe (a stripe that has good events only, the stripe's length is at least 1 day), the a black stripe (a stripe that has not-so-good events only, the stripe's length is at least 1 day) and a white stripe again (a stripe that has good events only, the stripe's length is at least 1 day). Each of n days will belong to one of the three stripes only.
Note that even the events of the same type are distinct from each other. Even if some events occur on the same day, they go in some order (there are no simultaneous events).
Write a code that prints the number of possible configurations to sort the events into days. See the samples for clarifications on which scenarios should be considered distinct. Print the answer modulo 1000000009 (109 + 9).
Input
The single line of the input contains integers n, w and b (3 ≤ n ≤ 4000, 2 ≤ w ≤ 4000, 1 ≤ b ≤ 4000) — the number of days, the number of good events and the number of not-so-good events. It is guaranteed that w + b ≥ n.
Output
Print the required number of ways modulo 1000000009 (109 + 9).
Examples
Input
3 2 1
Output
2
Input
4 2 2
Output
4
Input
3 2 2
Output
4
Note
We'll represent the good events by numbers starting from 1 and the not-so-good events — by letters starting from 'a'. Vertical lines separate days.
In the first sample the possible ways are: "1|a|2" and "2|a|1". In the second sample the possible ways are: "1|a|b|2", "2|a|b|1", "1|b|a|2" and "2|b|a|1". In the third sample the possible ways are: "1|ab|2", "2|ab|1", "1|ba|2" and "2|ba|1". | #include <bits/stdc++.h>
long long ans;
long long jc[4010];
long long c[4010][4010];
int w, n, b;
int main() {
int i, j;
for (i = 0; i <= 4000; ++i) {
c[i][0] = 1;
for (j = 1; j <= i; ++j) {
c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
if (c[i][j] >= 1000000009) c[i][j] -= 1000000009;
}
}
jc[0] = 1;
for (i = 1; i <= 4000; ++i) jc[i] = jc[i - 1] * i % 1000000009;
scanf("%d%d%d", &n, &w, &b);
for (i = 2; n - i; ++i)
ans = (ans + c[w - 1][i - 1] * c[b - 1][n - i - 1] % 1000000009 * (i - 1)) %
1000000009;
ans = ans * jc[w] % 1000000009 * jc[b] % 1000000009;
printf("%d\n", (int)ans);
return 0;
}
|
Don't put up with what you're sick of! The Smart Beaver decided to escape from the campus of Beaver Science Academy (BSA). BSA is a b × b square on a plane. Each point x, y (0 ≤ x, y ≤ b) belongs to BSA. To make the path quick and funny, the Beaver constructed a Beaveractor, an effective and comfortable types of transport.
The campus obeys traffic rules: there are n arrows, parallel to the coordinate axes. The arrows do not intersect and do not touch each other. When the Beaveractor reaches some arrow, it turns in the arrow's direction and moves on until it either reaches the next arrow or gets outside the campus. The Beaveractor covers exactly one unit of space per one unit of time. You can assume that there are no obstacles to the Beaveractor.
The BSA scientists want to transport the brand new Beaveractor to the "Academic Tractor" research institute and send the Smart Beaver to do his postgraduate studies and sharpen pencils. They have q plans, representing the Beaveractor's initial position (xi, yi), the initial motion vector wi and the time ti that have passed after the escape started.
Your task is for each of the q plans to determine the Smart Beaver's position after the given time.
Input
The first line contains two integers: the number of traffic rules n and the size of the campus b, 0 ≤ n, 1 ≤ b. Next n lines contain the rules. Each line of the rules contains four space-separated integers x0, y0, x1, y1 — the beginning and the end of the arrow. It is guaranteed that all arrows are parallel to the coordinate axes and have no common points. All arrows are located inside the campus, that is, 0 ≤ x0, y0, x1, y1 ≤ b holds.
Next line contains integer q — the number of plans the scientists have, 1 ≤ q ≤ 105. The i-th plan is represented by two integers, xi, yi are the Beaveractor's coordinates at the initial time, 0 ≤ xi, yi ≤ b, character wi, that takes value U, D, L, R and sets the initial direction up, down, to the left or to the right correspondingly (the Y axis is directed upwards), and ti — the time passed after the escape started, 0 ≤ ti ≤ 1015.
* to get 30 points you need to solve the problem with constraints n, b ≤ 30 (subproblem D1);
* to get 60 points you need to solve the problem with constraints n, b ≤ 1000 (subproblems D1+D2);
* to get 100 points you need to solve the problem with constraints n, b ≤ 105 (subproblems D1+D2+D3).
Output
Print q lines. Each line should contain two integers — the Beaveractor's coordinates at the final moment of time for each plan. If the Smart Beaver manages to leave the campus in time ti, print the coordinates of the last point in the campus he visited.
Examples
Input
3 3
0 0 0 1
0 2 2 2
3 3 2 3
12
0 0 L 0
0 0 L 1
0 0 L 2
0 0 L 3
0 0 L 4
0 0 L 5
0 0 L 6
2 0 U 2
2 0 U 3
3 0 U 5
1 3 D 2
1 3 R 2
Output
0 0
0 1
0 2
1 2
2 2
3 2
3 2
2 2
3 2
1 3
2 2
1 3 | #include <bits/stdc++.h>
using namespace std;
const int inf = 1e9;
const double eps = 1e-9;
const double INF = inf;
const double EPS = eps;
int dx[4] = {1, -1, 0, 0};
int dy[4] = {0, 0, 1, -1};
int N[2][1100 * 1100 * 4];
long long T[110000];
int V[110000];
int main() {
int x, y, n, q, a, b, c, d, bb, it;
int i, j, k, nx, ny;
char ch;
scanf("%d%d", &n, &b);
for (i = 0; i <= b; i++)
for (j = 0; j <= b; j++)
for (k = 0; k < 4; k++) {
nx = i + dx[k], ny = j + dy[k];
nx = max(nx, 0), nx = min(nx, b);
ny = max(ny, 0), ny = min(ny, b);
N[0][(i * (b + 1) + j) * 4 + k] = (nx * (b + 1) + ny) * 4 + k;
}
for (i = 0; i < n; i++) {
scanf("%d%d%d%d", &a, &bb, &c, &d);
assert(a != c || bb != d);
int len = abs(a - c) + abs(bb - d);
for (it = 0; it < 4; it++)
if (c == a + len * dx[it] && d == bb + len * dy[it]) {
for (j = 0; j <= len; j++) {
x = a + j * dx[it], y = bb + j * dy[it];
int id = (x * (b + 1) + y) * 4;
for (k = 0; k < 4; k++) {
N[0][id + k] = N[0][id + it];
}
}
break;
}
}
scanf("%d", &q);
for (i = 0; i < q; i++) {
scanf("%d%d %c %I64d", &x, &y, &ch, &T[i]);
V[i] = (x * (b + 1) + y) * 4;
if (ch == 'L') V[i]++;
if (ch == 'U') V[i] += 2;
if (ch == 'D') V[i] += 3;
}
for (it = 0; it < 55; it++) {
for (i = 0; i < q; i++)
if (T[i] & (1ll << it)) V[i] = N[0][V[i]];
for (j = 0; j < (b + 1) * (b + 1) * 4; j++) N[1][j] = N[0][N[0][j]];
memcpy(N[0], N[1], sizeof(N[0]));
}
for (i = 0; i < q; i++)
printf("%d %d\n", V[i] / (4 * (b + 1)), (V[i] / 4) % (b + 1));
;
return 0;
}
|
Given an n × n table T consisting of lowercase English letters. We'll consider some string s good if the table contains a correct path corresponding to the given string. In other words, good strings are all strings we can obtain by moving from the left upper cell of the table only to the right and down. Here's the formal definition of correct paths:
Consider rows of the table are numbered from 1 to n from top to bottom, and columns of the table are numbered from 1 to n from left to the right. Cell (r, c) is a cell of table T on the r-th row and in the c-th column. This cell corresponds to letter Tr, c.
A path of length k is a sequence of table cells [(r1, c1), (r2, c2), ..., (rk, ck)]. The following paths are correct:
1. There is only one correct path of length 1, that is, consisting of a single cell: [(1, 1)];
2. Let's assume that [(r1, c1), ..., (rm, cm)] is a correct path of length m, then paths [(r1, c1), ..., (rm, cm), (rm + 1, cm)] and [(r1, c1), ..., (rm, cm), (rm, cm + 1)] are correct paths of length m + 1.
We should assume that a path [(r1, c1), (r2, c2), ..., (rk, ck)] corresponds to a string of length k: Tr1, c1 + Tr2, c2 + ... + Trk, ck.
Two players play the following game: initially they have an empty string. Then the players take turns to add a letter to the end of the string. After each move (adding a new letter) the resulting string must be good. The game ends after 2n - 1 turns. A player wins by the following scenario:
1. If the resulting string has strictly more letters "a" than letters "b", then the first player wins;
2. If the resulting string has strictly more letters "b" than letters "a", then the second player wins;
3. If the resulting string has the same number of letters "a" and "b", then the players end the game with a draw.
Your task is to determine the result of the game provided that both players played optimally well.
Input
The first line contains a single number n (1 ≤ n ≤ 20).
Next n lines contain n lowercase English letters each — table T.
Output
In a single line print string "FIRST", if the first player wins, "SECOND", if the second player wins and "DRAW", if the game ends with a draw.
Examples
Input
2
ab
cd
Output
DRAW
Input
2
xa
ay
Output
FIRST
Input
3
aab
bcb
bac
Output
DRAW
Note
Consider the first sample:
Good strings are strings: a, ab, ac, abd, acd.
The first player moves first and adds letter a to the string, as there is only one good string of length 1. Then the second player can add b or c and the game will end with strings abd or acd, correspondingly. In the first case it will be a draw (the string has one a and one b), in the second case the first player wins. Naturally, in this case the second player prefers to choose letter b and end the game with a draw.
Consider the second sample:
Good strings are: x, xa, xay.
We can see that the game will end with string xay and the first player wins. | #include <bits/stdc++.h>
using namespace std;
inline int read() {
int x = 0, f = 1;
char ch = getchar();
while (ch < '0' || ch > '9') {
if (ch == '-') f = -1;
ch = getchar();
}
while (ch >= '0' && ch <= '9') {
x = x * 10 + ch - '0';
ch = getchar();
}
return x * f;
}
const int N = 1e5 + 10;
const int inf = 110101010;
char a[25][25];
int dp[40][1 << 20], n;
bool vis[40][1 << 20];
int dfs(int x, int st) {
if (vis[x][st]) return dp[x][st];
int &res = dp[x][st];
vis[x][st] = 1;
if (x == n * 2 - 2)
res = 0;
else {
if (x & 1)
res = -inf;
else
res = inf;
int mask[30];
memset(mask, 0, sizeof(mask));
int cnt = 0;
for (int j = 0; j <= x + 1; j++) {
int first = x + 1 - j;
int second = j;
if (first >= n || second >= n) continue;
mask[a[first][second] - 'a'] |= (1 << cnt);
cnt++;
}
for (int i = 0; i <= 25; i++)
if (mask[i]) {
int xt;
if (x + 1 < n)
xt = (st | (st << 1)) & mask[i];
else
xt = (st | (st >> 1)) & mask[i];
if (!xt) continue;
int tmp = 0;
if (!i)
tmp = 1;
else if (i == 1)
tmp = -1;
if (x & 1)
res = max(res, tmp + dfs(x + 1, xt));
else
res = min(res, tmp + dfs(x + 1, xt));
}
}
if (!x) {
if (a[0][0] == 'a')
res++;
else if (a[0][0] == 'b')
res--;
}
return res;
}
int main() {
n = read();
for (int i = 0; i <= n - 1; i++) scanf("%s", a[i]);
int res = dfs(0, 1);
if (!res)
printf("DRAW\n");
else if (res > 0)
printf("FIRST\n");
else
printf("SECOND\n");
return 0;
}
|
Pavel loves grid mazes. A grid maze is an n × m rectangle maze where each cell is either empty, or is a wall. You can go from one cell to another only if both cells are empty and have a common side.
Pavel drew a grid maze with all empty cells forming a connected area. That is, you can go from any empty cell to any other one. Pavel doesn't like it when his maze has too little walls. He wants to turn exactly k empty cells into walls so that all the remaining cells still formed a connected area. Help him.
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 500, 0 ≤ k < s), where n and m are the maze's height and width, correspondingly, k is the number of walls Pavel wants to add and letter s represents the number of empty cells in the original maze.
Each of the next n lines contains m characters. They describe the original maze. If a character on a line equals ".", then the corresponding cell is empty and if the character equals "#", then the cell is a wall.
Output
Print n lines containing m characters each: the new maze that fits Pavel's requirements. Mark the empty cells that you transformed into walls as "X", the other cells must be left without changes (that is, "." and "#").
It is guaranteed that a solution exists. If there are multiple solutions you can output any of them.
Examples
Input
3 4 2
#..#
..#.
#...
Output
#.X#
X.#.
#...
Input
5 4 5
#...
#.#.
.#..
...#
.#.#
Output
#XXX
#X#.
X#..
...#
.#.# | #include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
const int INF = 0x3f3f3f3f;
template <class K, class V>
ostream& operator<<(ostream& out, const pair<K, V>& v) {
out << '(' << v.first << ',' << v.second << ')';
return out;
}
template <class C, class = typename C::iterator>
struct _cprint {
using type = void;
};
template <>
struct _cprint<string> {};
template <class C, class = typename _cprint<C>::type>
ostream& operator<<(ostream& out, const C& v) {
for (auto x : v) out << x << ' ';
return out;
}
template <class C>
inline void chmax(C& x, const C& a) {
if (x < a) x = a;
}
template <class C>
inline void chmin(C& x, const C& a) {
if (x > a) x = a;
}
template <class C>
inline C mod(C a, C b) {
return (a % b + b) % b;
}
int n, m, k;
vector<string> grid;
int di[] = {-1, 1, 0, 0};
int dj[] = {0, 0, -1, 1};
void dfs(int i, int j) {
if (k == 0) return;
if (i < 0 || i >= n || j < 0 || j >= m) return;
if (grid[i][j] != '.') return;
grid[i][j] = 'T';
for (int k = 0; k < 4; k++) dfs(i + di[k], j + dj[k]);
if (k) grid[i][j] = 'X', k--;
}
int main() {
cin >> n >> m >> k;
grid.resize(n);
for (int i = 0; i < n; i++) cin >> grid[i];
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (grid[i][j] == '.') {
dfs(i, j);
goto stop;
}
stop:
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (grid[i][j] == 'T') grid[i][j] = '.';
for (int i = 0; i < n; i++) cout << grid[i] << endl;
}
|
You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items.
Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty.
Who loses if both players play optimally and Stas's turn is first?
Input
The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n.
Output
Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing".
Examples
Input
2 2 10
Output
Masha
Input
5 5 16808
Output
Masha
Input
3 1 4
Output
Stas
Input
1 4 10
Output
Missing
Note
In the second example the initial number of ways is equal to 3125.
* If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat.
* But if Stas increases the number of items, then any Masha's move will be losing. | #include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
map<pair<int, int>, int> Set;
int a, b, n, ret;
void init() { scanf("%d%d%d", &a, &b, &n); }
int solve(int a, int b) {
pair<int, int> cur = make_pair(a, b);
if (Set.find(cur) != Set.end()) return Set[cur];
bool A = false, B = false;
if (log(n) / log(a + 1) - eps > b) A = true;
if (pow((double)a, b + 1) < n - eps) B = true;
int ret = 0;
if (!A && !B) {
ret = -1;
} else if (a == 1 && !A) {
ret = 0;
} else if (b == 1 && !B) {
ret = ((n - a) & 1) ? -1 : 1;
} else {
ret = 1;
if (B) {
int tmp = solve(a, b + 1);
if (tmp < ret) ret = tmp;
}
if (A) {
int tmp = solve(a + 1, b);
if (tmp < ret) ret = tmp;
}
if (ret != 0) ret = -ret;
}
Set[cur] = ret;
return ret;
}
void work() { ret = solve(a, b); }
void print() {
if (ret == 1)
printf("Masha\n");
else if (ret == -1)
printf("Stas\n");
else
printf("Missing\n");
}
int main() {
init();
work();
print();
return 0;
}
|
As usual, Sereja has array a, its elements are integers: a[1], a[2], ..., a[n]. Let's introduce notation:
<image>
A swap operation is the following sequence of actions:
* choose two indexes i, j (i ≠ j);
* perform assignments tmp = a[i], a[i] = a[j], a[j] = tmp.
What maximum value of function m(a) can Sereja get if he is allowed to perform at most k swap operations?
Input
The first line contains two integers n and k (1 ≤ n ≤ 200; 1 ≤ k ≤ 10). The next line contains n integers a[1], a[2], ..., a[n] ( - 1000 ≤ a[i] ≤ 1000).
Output
In a single line print the maximum value of m(a) that Sereja can get if he is allowed to perform at most k swap operations.
Examples
Input
10 2
10 -1 2 2 2 2 2 2 -1 10
Output
32
Input
5 10
-1 -1 -1 -1 -1
Output
-1 | //package codeforces;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.ListIterator;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;
public class A implements Closeable {
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
A() throws IOException {
// reader = new BufferedReader(new FileReader("input.txt"));
// writer = new PrintWriter(new FileWriter("output.txt"));
}
StringTokenizer stringTokenizer;
String next() throws IOException {
while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
stringTokenizer = new StringTokenizer(reader.readLine());
}
return stringTokenizer.nextToken();
}
int nextInt() throws IOException {
return Integer.parseInt(next());
}
long nextLong() throws IOException {
return Long.parseLong(next());
}
private final int MOD = 1000 * 1000 * 1000 + 7;
int sum(int a, int b) {
a += b;
return a >= MOD ? a - MOD : a;
}
int product(int a, int b) {
return (int) (1l * a * b % MOD);
}
int pow(int x, int k) {
int result = 1;
while (k > 0) {
if (k % 2 == 1) {
result = product(result, x);
}
x = product(x, x);
k /= 2;
}
return result;
}
int inv(int x) {
return pow(x, MOD - 2);
}
void solve() throws IOException {
int n = nextInt(), k = nextInt();
int[] a = new int[n];
for(int i = 0; i < n; i++) {
a[i] = nextInt();
}
Queue<Integer> minQ = new PriorityQueue<>(), maxQ = new PriorityQueue<>(n, Collections.reverseOrder());
int answer = Integer.MIN_VALUE;
for(int i = 0; i < n; i++) {
for(int j = i + 1; j <= n; j++) {
minQ.clear();
maxQ.clear();
for(int l = 0; l < i; l++) {
maxQ.add(a[l]);
}
int s = 0;
for(int l = i; l < j; l++) {
minQ.add(a[l]);
s += a[l];
}
for(int l = j; l < n; l++) {
maxQ.add(a[l]);
}
for(int l = 0; !maxQ.isEmpty() && !minQ.isEmpty() && l < k; l++) {
if(maxQ.peek() > minQ.peek()) {
s += maxQ.poll() - minQ.poll();
}
}
answer = Math.max(answer, s);
}
}
writer.println(answer);
}
public static void main(String[] args) throws IOException {
try (A a = new A()) {
a.solve();
}
}
@Override
public void close() throws IOException {
reader.close();
writer.close();
}
}
|
Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k.
Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers.
Input
The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).
Examples
Input
3
2 3 3
Output
0
Input
4
0 1 2 3
Output
10
Input
6
5 2 0 5 2 1
Output
53 | #include <bits/stdc++.h>
long long memo[(1 << 21)];
long long modexp(long long a, long long n) {
long long res = 1;
while (n) {
if (n & 1) res = ((res % 1000000007) * (a % 1000000007)) % 1000000007;
a = ((a % 1000000007) * (a % 1000000007)) % 1000000007;
n >>= 1;
}
return res;
}
int main(void) {
std::ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
std::cout.tie(NULL);
int n;
std::cin >> n;
for (int i = 0; i < n; i++) {
int t;
std::cin >> t;
memo[t]++;
}
for (int p = 0; p < 21; p++) {
for (int mask = ((1 << 21) - 1); mask >= 0; mask--) {
if (!(mask & (1 << p))) memo[mask] += memo[mask ^ (1 << p)];
}
}
long long ans = 0;
for (int mask = 0; mask < (1 << 21); mask++) {
int z = __builtin_popcount(mask);
if (z & 1)
ans = ((ans % 1000000007) - (modexp(2, memo[mask]) % 1000000007) +
1000000007) %
1000000007;
else
ans = ((ans % 1000000007) + (modexp(2, memo[mask]) % 1000000007)) %
1000000007;
}
std::cout << ans << "\n";
return 0;
}
|
Malek has recently found a treasure map. While he was looking for a treasure he found a locked door. There was a string s written on the door consisting of characters '(', ')' and '#'. Below there was a manual on how to open the door. After spending a long time Malek managed to decode the manual and found out that the goal is to replace each '#' with one or more ')' characters so that the final string becomes beautiful.
Below there was also written that a string is called beautiful if for each i (1 ≤ i ≤ |s|) there are no more ')' characters than '(' characters among the first i characters of s and also the total number of '(' characters is equal to the total number of ')' characters.
Help Malek open the door by telling him for each '#' character how many ')' characters he must replace it with.
Input
The first line of the input contains a string s (1 ≤ |s| ≤ 105). Each character of this string is one of the characters '(', ')' or '#'. It is guaranteed that s contains at least one '#' character.
Output
If there is no way of replacing '#' characters which leads to a beautiful string print - 1. Otherwise for each character '#' print a separate line containing a positive integer, the number of ')' characters this character must be replaced with.
If there are several possible answers, you may output any of them.
Examples
Input
(((#)((#)
Output
1
2
Input
()((#((#(#()
Output
2
2
1
Input
#
Output
-1
Input
(#)
Output
-1
Note
|s| denotes the length of the string s. | #include <bits/stdc++.h>
using namespace std;
int main() {
int t = 0, sl = 0;
char s[100010];
cin >> s;
for (int i = 0; i < strlen(s); i++)
if (s[i] == '#') {
t++;
} else if (s[i] == '(')
sl++;
else
sl--;
if (sl <= 0)
cout << "-1";
else {
int t1 = 0, t2 = 0;
for (int i = 0; i < strlen(s); i++) {
if (s[i] == '#') {
t1++;
if (t1 != t) {
t2--;
} else
t2 = t2 - sl + t - 1;
} else if (s[i] == '(')
t2++;
else
t2--;
if (t2 < 0) {
cout << "-1";
return 0;
}
}
for (int i = 1; i < t; i++) cout << '1' << endl;
cout << sl - t + 1;
}
}
|
After bracket sequences Arthur took up number theory. He has got a new favorite sequence of length n (a1, a2, ..., an), consisting of integers and integer k, not exceeding n.
This sequence had the following property: if you write out the sums of all its segments consisting of k consecutive elements (a1 + a2 ... + ak, a2 + a3 + ... + ak + 1, ..., an - k + 1 + an - k + 2 + ... + an), then those numbers will form strictly increasing sequence.
For example, for the following sample: n = 5, k = 3, a = (1, 2, 4, 5, 6) the sequence of numbers will look as follows: (1 + 2 + 4, 2 + 4 + 5, 4 + 5 + 6) = (7, 11, 15), that means that sequence a meets the described property.
Obviously the sequence of sums will have n - k + 1 elements.
Somebody (we won't say who) replaced some numbers in Arthur's sequence by question marks (if this number is replaced, it is replaced by exactly one question mark). We need to restore the sequence so that it meets the required property and also minimize the sum |ai|, where |ai| is the absolute value of ai.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 105), showing how many numbers are in Arthur's sequence and the lengths of segments respectively.
The next line contains n space-separated elements ai (1 ≤ i ≤ n).
If ai = ?, then the i-th element of Arthur's sequence was replaced by a question mark.
Otherwise, ai ( - 109 ≤ ai ≤ 109) is the i-th element of Arthur's sequence.
Output
If Arthur is wrong at some point and there is no sequence that could fit the given information, print a single string "Incorrect sequence" (without the quotes).
Otherwise, print n integers — Arthur's favorite sequence. If there are multiple such sequences, print the sequence with the minimum sum |ai|, where |ai| is the absolute value of ai. If there are still several such sequences, you are allowed to print any of them. Print the elements of the sequence without leading zeroes.
Examples
Input
3 2
? 1 2
Output
0 1 2
Input
5 1
-10 -9 ? -7 -6
Output
-10 -9 -8 -7 -6
Input
5 3
4 6 7 2 9
Output
Incorrect sequence | #include <bits/stdc++.h>
using namespace std;
int a[220020], l, r, n, k, t, st, p;
bool f[220020];
char s[100];
int main() {
scanf("%d%d", &n, &k);
for (int i = 1; i <= n; i++) {
scanf("%s", s);
if (s[0] == '?')
f[i] = 0;
else {
f[i] = 1;
sscanf(s, "%d", &a[i]);
}
}
for (int i = 1; i <= k; i++) {
a[i + n] = 1020000000;
f[i + n] = 1;
}
for (int i = 1; i <= k; i++) {
l = -1020000000;
t = 0;
for (int j = i; j <= n + k; j += k)
if (!f[j])
t++;
else {
if (t >= a[j] - l) {
printf("Incorrect sequence\n");
return 0;
}
r = a[j];
if (min(-l, r) * 2 > t)
st = -(t / 2);
else if ((-l) < r)
st = l + 1;
else
st = r - t;
for (int p = t; p > 0; p--) a[j - p * k] = st++;
t = 0;
l = r;
}
}
for (int i = 1; i < n; i++) printf("%d ", a[i]);
printf("%d\n", a[n]);
return 0;
}
|
You have multiset of n strings of the same length, consisting of lowercase English letters. We will say that those strings are easy to remember if for each string there is some position i and some letter c of the English alphabet, such that this string is the only string in the multiset that has letter c in position i.
For example, a multiset of strings {"abc", "aba", "adc", "ada"} are not easy to remember. And multiset {"abc", "ada", "ssa"} is easy to remember because:
* the first string is the only string that has character c in position 3;
* the second string is the only string that has character d in position 2;
* the third string is the only string that has character s in position 2.
You want to change your multiset a little so that it is easy to remember. For aij coins, you can change character in the j-th position of the i-th string into any other lowercase letter of the English alphabet. Find what is the minimum sum you should pay in order to make the multiset of strings easy to remember.
Input
The first line contains two integers n, m (1 ≤ n, m ≤ 20) — the number of strings in the multiset and the length of the strings respectively. Next n lines contain the strings of the multiset, consisting only of lowercase English letters, each string's length is m.
Next n lines contain m integers each, the i-th of them contains integers ai1, ai2, ..., aim (0 ≤ aij ≤ 106).
Output
Print a single number — the answer to the problem.
Examples
Input
4 5
abcde
abcde
abcde
abcde
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
Output
3
Input
4 3
abc
aba
adc
ada
10 10 10
10 1 10
10 10 10
10 1 10
Output
2
Input
3 3
abc
ada
ssa
1 1 1
1 1 1
1 1 1
Output
0 | #include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 21;
const int maxs = 1 << 21;
int n, m;
int a[maxn][maxn];
char str[maxn][maxn];
int dp[maxs];
int lowzero(int s) {
for (int i = 0; i < maxn; ++i) {
if (!(s & (1 << i))) return i;
}
return maxn - 1;
}
int main() {
while (~scanf("%d%d", &n, &m)) {
for (int i = 0; i < n; ++i) {
scanf("%s", str[i]);
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
scanf("%d", &a[i][j]);
}
}
memset(dp, 0xff, sizeof(dp));
dp[0] = 0;
int M = 1 << n;
for (int s = 0; s < M; ++s) {
if (dp[s] == -1) continue;
int bit = lowzero(s);
for (int j = 0; j < m; ++j) {
if (dp[s | (1 << bit)] == -1 ||
dp[s | (1 << bit)] > dp[s] + a[bit][j]) {
dp[s | (1 << bit)] = dp[s] + a[bit][j];
}
int sum = 0, bits = 0, mw = 0;
for (int i = 0; i < n; ++i) {
if (str[i][j] == str[bit][j]) {
sum += a[i][j];
mw = max(mw, a[i][j]);
bits |= 1 << i;
}
}
if (dp[s | bits] == -1 || dp[s | bits] > dp[s] + sum - mw) {
dp[s | bits] = dp[s] + sum - mw;
}
}
}
printf("%d\n", dp[M - 1]);
}
return 0;
}
|
You've got array A, consisting of n integers and a positive integer k. Array A is indexed by integers from 1 to n.
You need to permute the array elements so that value
<image> became minimal possible. In particular, it is allowed not to change order of elements at all.
Input
The first line contains two integers n, k (2 ≤ n ≤ 3·105, 1 ≤ k ≤ min(5000, n - 1)).
The second line contains n integers A[1], A[2], ..., A[n] ( - 109 ≤ A[i] ≤ 109), separate by spaces — elements of the array A.
Output
Print the minimum possible value of the sum described in the statement.
Examples
Input
3 2
1 2 4
Output
1
Input
5 2
3 -5 3 -5 3
Output
0
Input
6 3
4 3 4 3 2 5
Output
3
Note
In the first test one of the optimal permutations is 1 4 2.
In the second test the initial order is optimal.
In the third test one of the optimal permutations is 2 3 4 4 3 5. | #include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const ll inf = 1E17;
const ll mod = 1;
ll a[300010];
int n, k, chnk;
ll dp[5001][5001];
ll solve(int pos, int xtra, int l) {
if (pos == 0) {
if (xtra == 0) return 0;
return inf;
}
ll &ret = dp[pos][xtra];
if (ret != -1) return ret;
ret = a[l + chnk - 1] - a[l] + solve(pos - 1, xtra, l + chnk);
if (xtra)
ret = min(ret, a[l + chnk] - a[l] + solve(pos - 1, xtra - 1, l + chnk + 1));
return ret;
}
int main() {
ios_base::sync_with_stdio(false);
while (cin >> n >> k) {
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
sort(a + 1, a + n + 1);
memset(dp, -1, sizeof dp);
chnk = n / k;
cout << solve(k, n % k, 1) << endl;
}
return 0;
}
|
BCPC stands for Byteforces Collegiate Programming Contest, and is the most famous competition in Byteforces.
BCPC is a team competition. Each team is composed by a coach and three contestants. Blenda is the coach of the Bit State University(BSU), and she is very strict selecting the members of her team.
<image>
In BSU there are n students numbered from 1 to n. Since all BSU students are infinitely smart, the only important parameters for Blenda are their reading and writing speed. After a careful measuring, Blenda have found that the i-th student have a reading speed equal to ri (words per minute), and a writing speed of wi (symbols per minute). Since BSU students are very smart, the measured speeds are sometimes very big and Blenda have decided to subtract some constant value c from all the values of reading speed and some value d from all the values of writing speed. Therefore she considers ri' = ri - c and wi' = wi - d.
The student i is said to overwhelm the student j if and only if ri'·wj' > rj'·wi'. Blenda doesn’t like fights in teams, so she thinks that a team consisting of three distinct students i, j and k is good if i overwhelms j, j overwhelms k, and k overwhelms i. Yes, the relation of overwhelming is not transitive as it often happens in real life.
Since Blenda is busy preparing a training camp in Codeforces, you are given a task to calculate the number of different good teams in BSU. Two teams are considered to be different if there is at least one student that is present in one team but is not present in the other. In other words, two teams are different if the sets of students that form these teams are different.
Input
In the first line of the input three integers n, c and d (3 ≤ n ≤ 345678, 1 ≤ c, d ≤ 109) are written. They denote the number of students Blenda can use to form teams, the value subtracted from all reading speeds and the value subtracted from all writing speeds respectively.
Each of the next n lines contains two integers ri and wi (0 < ri, wi ≤ 109, |ri - c| + |wi - d| > 0). There are no two students, such that both their reading and writing speeds coincide, i.e. for every i ≠ j condition |ri - rj| + |wi - wj| > 0 holds.
Output
Print the number of different teams in BSU, that are good according to Blenda's definition.
Examples
Input
5 2 2
1 1
4 1
2 3
3 2
3 4
Output
4
Input
7 6 6
3 2
1 7
5 7
3 7
6 4
8 9
8 5
Output
11
Note
In the first sample the following teams are good: (i = 1, j = 2, k = 3), (i = 2, j = 5, k = 1), (i = 1, j = 4, k = 3), (i = 5, j = 1, k = 4).
Note, that for example the team (i = 3, j = 1, k = 2) is also good, but is considered to be the same as the team (i = 1, j = 2, k = 3). | import java.util.Arrays;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
/**
* Built using CHelper plug-in
* Actual solution is at the top
* @author Tifuera
*/
public class Main {
public static void main(String[] args) {
InputStream inputStream = System.in;
OutputStream outputStream = System.out;
InputReader in = new InputReader(inputStream);
PrintWriter out = new PrintWriter(outputStream);
TaskE solver = new TaskE();
solver.solve(1, in, out);
out.close();
}
}
class TaskE {
public void solve(int testNumber, InputReader in, PrintWriter out) {
int n = in.nextInt();
long c = in.nextLong();
long d = in.nextLong();
Vector[] vectors = new Vector[2 * n];
for (int i = 0; i < n; i++) {
long x = in.nextInt();
long y = in.nextInt();
vectors[i] = new Vector(x - c, y - d);
}
Arrays.sort(vectors, 0, n);
for (int i = 0; i < n; i++) {
vectors[i + n] = new Vector(vectors[i].x, vectors[i].y, 0, 1);
}
long res = (long) n * (n - 1) * (n - 2) / 6;
int lo = 0;
int hi = 0;
for (int i = 0; i < n; i++) {
while (isLowerThanNegative(i, lo, vectors)) {
lo++;
}
while (isLowerOrEqThanNegative(i, hi + 1, vectors)) {
hi++;
}
res -= (hi - i) * (hi - i - 1L) / 2;
res += (hi - lo + 1) * (hi - lo) / 2;
}
out.println(res);
}
private boolean isLowerThanNegative(int i, int lo, Vector[] vectors) {
int prodSign = vectors[i].vectorProdSign(vectors[lo]);
boolean result;
result = prodSign > 0 || prodSign == 0 && vectors[i].side == vectors[lo].side && vectors[i].partNum == vectors[lo].partNum;
return result;
}
private boolean isLowerOrEqThanNegative(int i, int hi, Vector[] vectors) {
int prodSign = vectors[i].vectorProdSign(vectors[hi]);
boolean result;
result = prodSign > 0 || prodSign == 0 && (vectors[i].side != vectors[hi].side || vectors[i].partNum == vectors[hi].partNum);
return result;
}
private static class Vector implements Comparable<Vector> {
long x;
long y;
int side;
int id;
int partNum;
public Vector(long x, long y) {
this(x, y, 0);
}
public Vector(long x, long y, int id) {
this(x, y, id, 0);
}
public Vector(long x, long y, int id, int partNum) {
this.x = x;
this.y = y;
if (y != 0) {
side = y > 0 ? -1 : 1;
} else {
side = x > 0 ? -1 : 1;
}
this.id = id;
this.partNum = partNum;
}
public int vectorProdSign(Vector o) {
return Long.signum(x * o.y - y * o.x);
}
public boolean isLower(Vector o) {
return x * x + y * y < o.x * o.x + o.y * o.y;
}
public int compareTo(Vector o) {
if (x == o.x && y == o.y) {
return 0;
}
if (side != o.side) {
return Integer.compare(side, o.side);
} else {
int res = -vectorProdSign(o);
if (res != 0) {
return res;
} else if (isLower(o)) {
return -1;
} else if (o.isLower(this)) {
return 1;
} else {
throw new RuntimeException();
}
}
}
}
}
class InputReader {
private BufferedReader reader;
private String[] currentArray;
private int curPointer;
public InputReader(InputStream inputStream) {
reader = new BufferedReader(new InputStreamReader(inputStream));
}
public int nextInt() {
if ((currentArray == null) || (curPointer >= currentArray.length)) {
try {
currentArray = reader.readLine().split(" ");
} catch (IOException e) {
throw new RuntimeException(e);
}
curPointer = 0;
}
return Integer.parseInt(currentArray[curPointer++]);
}
public long nextLong() {
if ((currentArray == null) || (curPointer >= currentArray.length)) {
try {
currentArray = reader.readLine().split(" ");
} catch (IOException e) {
throw new RuntimeException(e);
}
curPointer = 0;
}
return Long.parseLong(currentArray[curPointer++]);
}
}
|
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | import java.awt.*;
import java.awt.geom.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collector;
/**
* Created by ribra on 11/15/2015.
*/
public class Main {
private static InputReader sc = new InputReader(System.in);
private static PrintWriter pw = new PrintWriter(System.out);
public static void main(String [] args) {
int n = sc.nextInt();
Point2D p = new Point2D.Double((double) sc.nextInt(), (double) sc.nextInt());
Point2D[] arr = new Point2D[n];
for (int i = 0; i < n; i++) {
arr[i] = new Point2D.Double((double) sc.nextInt(), (double) sc.nextInt());
}
double min = Double.MAX_VALUE;
double max = Double.MIN_VALUE;
for (int i = 0; i < n; i++) {
int j = (i + 1) % n;
Line2D line = new Line2D.Double(arr[i], arr[j]);
min = Math.min(min, line.ptSegDist(p));
min = Math.min(min, p.distance(arr[i]));
min = Math.min(min, p.distance(arr[j]));
max = Math.max(max, line.ptSegDist(p));
max = Math.max(max, p.distance(arr[i]));
max = Math.max(max, p.distance(arr[j]));
}
pw.print(Math.PI * (max * max - min * min));
terminate();
}
public static void terminate() {
pw.close();
}
static class InputReader {
public BufferedReader reader;
public StringTokenizer tokenizer;
public InputReader(InputStream stream) {
reader = new BufferedReader(new InputStreamReader(stream), 32768);
tokenizer = null;
}
public String next() {
while (tokenizer == null || !tokenizer.hasMoreTokens()) {
try {
tokenizer = new StringTokenizer(reader.readLine());
} catch (IOException e) {
throw new RuntimeException(e);
}
}
return tokenizer.nextToken();
}
public int nextInt() {
return Integer.parseInt(next());
}
}
static class Graph {
private int V;
private int E;
private Set<Integer>[] adj;
public Graph(int V) {
this.V = V;
this.E = 0;
adj = new HashSet[V];
for (int i = 0; i < V; i++)
adj[i] = new HashSet<>();
}
public int V() {
return V;
}
public int E() {
return E;
}
public void addEdge(int v, int w) {
adj[v].add(w);
adj[w].add(v);
E++;
}
public Iterable<Integer> adj(int v) {
return adj[v];
}
public static int degree(Graph g, int v) {
int degree = 0;
for (int w : g.adj(v)) degree++;
return degree;
}
public static int maxDegree(Graph g) {
int max = 0;
for (int i = 0; i < g.V(); i++)
max = Math.max(degree(g, i), max);
return max;
}
public static int avgDegree(Graph g) {
int sum = 0;
for (int i = 0; i < g.V(); i++)
sum += degree(g, i);
return sum / g.V();
}
public static int avgDegreeEfficient(Graph g) {
// g.E = sum degree of every graph
// 2 * g.E - because if v is connected to w, then w is connected to v as well
// and divide by number of vertices
return 2 * g.E() / g.V();
}
public static int numberOfSelfLoops(Graph g) {
int count = 0;
for (int i = 0; i < g.V(); i++)
for (int w : g.adj(i))
if (i == w) count++;
return count / 2;
}
public String toString()
{
String s = V() + " vertices, " + E() + " edges\n";
for (int v = 0; v < V(); v++)
{
s += v + ": ";
for (int w : this.adj(v))
s += w + " ";
s += "\n";
}
return s;
}
}
}
|
Yash is finally tired of computing the length of the longest Fibonacci-ish sequence. He now plays around with more complex things such as Fibonacci-ish potentials.
Fibonacci-ish potential of an array ai is computed as follows:
1. Remove all elements j if there exists i < j such that ai = aj.
2. Sort the remaining elements in ascending order, i.e. a1 < a2 < ... < an.
3. Compute the potential as P(a) = a1·F1 + a2·F2 + ... + an·Fn, where Fi is the i-th Fibonacci number (see notes for clarification).
You are given an array ai of length n and q ranges from lj to rj. For each range j you have to compute the Fibonacci-ish potential of the array bi, composed using all elements of ai from lj to rj inclusive. Find these potentials modulo m.
Input
The first line of the input contains integers of n and m (1 ≤ n, m ≤ 30 000) — the length of the initial array and the modulo, respectively.
The next line contains n integers ai (0 ≤ ai ≤ 109) — elements of the array.
Then follow the number of ranges q (1 ≤ q ≤ 30 000).
Last q lines contain pairs of indices li and ri (1 ≤ li ≤ ri ≤ n) — ranges to compute Fibonacci-ish potentials.
Output
Print q lines, i-th of them must contain the Fibonacci-ish potential of the i-th range modulo m.
Example
Input
5 10
2 1 2 1 2
2
2 4
4 5
Output
3
3
Note
For the purpose of this problem define Fibonacci numbers as follows:
1. F1 = F2 = 1.
2. Fn = Fn - 1 + Fn - 2 for each n > 2.
In the first query, the subarray [1,2,1] can be formed using the minimal set {1,2}. Thus, the potential of this subarray is 1*1+2*1=3. | #include <bits/stdc++.h>
using namespace std;
const int maxn = 3e4 + 50;
int n, m, mod, a[maxn], len, F[maxn << 1];
int sz, bnum, cnt[maxn], belong[maxn], ans[maxn];
vector<int> v;
struct Tree {
int le, ri;
int shift, S1, S2;
} tree[maxn << 2];
void move(int& S1, int& S2, int k) {
int newS1 = (S1 * F[len + k - 1] + S2 * F[len + k]) % mod;
int newS2 = (S1 * F[len + k] + S2 * F[len + k + 1]) % mod;
S1 = newS1;
S2 = newS2;
}
void pushup(int id) {
tree[id].S1 = (tree[id << 1].S1 + tree[id << 1 | 1].S1) % mod;
tree[id].S2 = (tree[id << 1].S2 + tree[id << 1 | 1].S2) % mod;
}
void pushdown(int id) {
if (tree[id].shift) {
tree[id << 1].shift += tree[id].shift;
move(tree[id << 1].S1, tree[id << 1].S2, tree[id].shift);
tree[id << 1 | 1].shift += tree[id].shift;
move(tree[id << 1 | 1].S1, tree[id << 1 | 1].S2, tree[id].shift);
tree[id].shift = 0;
}
}
void build(int id, int le, int ri) {
tree[id].le = le;
tree[id].ri = ri;
tree[id].shift = tree[id].S1 = tree[id].S2 = 0;
if (le == ri) return;
int mid = (le + ri) >> 1;
build(id << 1, le, mid);
build(id << 1 | 1, mid + 1, ri);
}
void Insert(int id, int pos, int val) {
if (tree[id].le == tree[id].ri) {
tree[id].S1 = 1LL * val * F[len + tree[id].shift] % mod;
tree[id].S2 = 1LL * val * F[len + tree[id].shift + 1] % mod;
return;
}
pushdown(id);
int mid = (tree[id].le + tree[id].ri) >> 1;
if (pos <= mid) {
tree[id << 1 | 1].shift += 1;
move(tree[id << 1 | 1].S1, tree[id << 1 | 1].S2, 1);
Insert(id << 1, pos, val);
} else
Insert(id << 1 | 1, pos, val);
pushup(id);
}
void Remove(int id, int pos) {
if (tree[id].le == tree[id].ri) {
tree[id].S1 = tree[id].S2 = 0;
return;
}
pushdown(id);
int mid = (tree[id].le + tree[id].ri) >> 1;
if (pos <= mid) {
tree[id << 1 | 1].shift -= 1;
move(tree[id << 1 | 1].S1, tree[id << 1 | 1].S2, -1);
Remove(id << 1, pos);
} else
Remove(id << 1 | 1, pos);
pushup(id);
}
struct Node {
int id, le, ri;
} q[maxn];
bool cmp(Node x, Node y) {
return (belong[x.le] ^ belong[y.le])
? belong[x.le] < belong[y.le]
: ((belong[x.le] & 1) ? x.ri < y.ri : x.ri > y.ri);
}
void Add(int pos) {
pos = lower_bound(v.begin(), v.end(), a[pos]) - v.begin() + 1;
if (!cnt[pos]++) Insert(1, pos, v[pos - 1]);
}
void Del(int pos) {
pos = lower_bound(v.begin(), v.end(), a[pos]) - v.begin() + 1;
if (!--cnt[pos]) Remove(1, pos);
}
int main() {
scanf("%d%d", &n, &mod);
for (int i = 1; i <= n; ++i) {
scanf("%d", &a[i]);
v.push_back(a[i]);
}
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
len = v.size();
F[len] = 0;
F[len + 1] = 1;
for (int i = 2; i + len < (maxn << 1); ++i)
F[i + len] = (F[i + len - 1] + F[i + len - 2]) % mod;
for (int i = -1; i + len >= 0; --i)
F[i + len] = (F[i + len + 2] - F[i + len + 1] + mod) % mod;
build(1, 1, len);
sz = sqrt(n);
bnum = ceil(double(n / sz));
for (int i = 1; i <= bnum; ++i) {
for (int j = (i - 1) * sz + 1; j <= i * sz && j <= n; ++j) {
belong[j] = i;
}
}
scanf("%d", &m);
for (int i = 0; i < m; ++i) {
scanf("%d%d", &q[i].le, &q[i].ri);
q[i].id = i;
}
sort(q, q + m, cmp);
int L = 1, R = 0;
for (int i = 0; i < m; ++i) {
while (L < q[i].le) Del(L++);
while (L > q[i].le) Add(--L);
while (R < q[i].ri) Add(++R);
while (R > q[i].ri) Del(R--);
ans[q[i].id] = tree[1].S2;
}
for (int i = 0; i < m; ++i) printf("%d\n", ans[i]);
return 0;
}
|
You are given a table consisting of n rows and m columns. Each cell of the table contains either 0 or 1. In one move, you are allowed to pick any row or any column and invert all values, that is, replace 0 by 1 and vice versa.
What is the minimum number of cells with value 1 you can get after applying some number of operations?
Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 20, 1 ≤ m ≤ 100 000) — the number of rows and the number of columns, respectively.
Then n lines follows with the descriptions of the rows. Each line has length m and contains only digits '0' and '1'.
Output
Output a single integer — the minimum possible number of ones you can get after applying some sequence of operations.
Example
Input
3 4
0110
1010
0111
Output
2 | #include <bits/stdc++.h>
const int mod = 1000000007;
const int inf = 1000000009;
const long long INF = 1000000000000000009;
const long long big = 1000000000000000;
const long double eps = 0.0000000001;
using namespace std;
int T[21][100005], C[100005];
long long int DP[(1 << 20)][21];
int main() {
ios::sync_with_stdio(false);
cin.tie();
cout.tie();
int n, m;
cin >> n >> m;
for (int i = 0; i < n; i++)
for (int j = 1; j <= m; j++) {
char c;
cin >> c;
T[i][j] = c - '0';
}
for (int i = 1; i <= m; i++) {
for (int j = 0; j < n; j++) {
if (T[j][i]) C[i] += (1 << j);
}
DP[C[i]][0]++;
}
int wynik = inf;
for (int j = 1; j <= n; j++) {
for (int i = 0; i < (1 << n); i++) {
if (j >= 2) DP[i][j] += (long long int)(j - 2 - n) * DP[i][j - 2];
for (int k = 0; k < n; k++) DP[i][j] += DP[i ^ (1 << k)][j - 1];
DP[i][j] /= j;
}
}
for (int i = 0; i < (1 << n); i++) {
int aktual = 0;
for (int j = 0; j <= n; j++) aktual += DP[i][j] * min(j, n - j);
wynik = min(wynik, aktual);
}
cout << wynik;
return 0;
}
|
Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.
Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).
Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.
They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).
Input
The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.
Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.
Output
If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).
If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.
Examples
Input
4 2
1 2
2 3
Output
1
2
2
1 3
Input
3 3
1 2
2 3
1 3
Output
-1
Note
In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).
In the second sample, there is no way to satisfy both Pari and Arya. | #!/usr/bin/python
from collections import deque
def ir():
return int(raw_input())
def ia():
line = raw_input()
line = line.split()
return map(int, line)
n, m = ia()
adj = [[] for v in range(n)]
for i in range(m):
u, v = ia()
u-=1; v-=1
adj[u].append(v)
adj[v].append(u)
c = [None for u in range(n)]
def bfs(s):
if c[s]!=None: return 1
c[s] = 1; q = [s]
while q:
v = q.pop(0)
for u in adj[v]:
if c[v]==c[u]: return -1
if c[u]!=None: continue
c[u] = -c[v]
q.append(u)
return 1
def solve():
for u in range(n):
rc = bfs(u)
if rc==-1: print -1; return
n1, n2 = 0, 0
for e in c:
if e==1: n1+=1
elif e==-1: n2+=1
print n1
for i, e in enumerate(c):
if e==1: print i+1,
print
print n2
for i, e in enumerate(c):
if e==-1: print i+1,
solve()
|
Tree is a connected acyclic graph. Suppose you are given a tree consisting of n vertices. The vertex of this tree is called centroid if the size of each connected component that appears if this vertex is removed from the tree doesn't exceed <image>.
You are given a tree of size n and can perform no more than one edge replacement. Edge replacement is the operation of removing one edge from the tree (without deleting incident vertices) and inserting one new edge (without adding new vertices) in such a way that the graph remains a tree. For each vertex you have to determine if it's possible to make it centroid by performing no more than one edge replacement.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 400 000) — the number of vertices in the tree. Each of the next n - 1 lines contains a pair of vertex indices ui and vi (1 ≤ ui, vi ≤ n) — endpoints of the corresponding edge.
Output
Print n integers. The i-th of them should be equal to 1 if the i-th vertex can be made centroid by replacing no more than one edge, and should be equal to 0 otherwise.
Examples
Input
3
1 2
2 3
Output
1 1 1
Input
5
1 2
1 3
1 4
1 5
Output
1 0 0 0 0
Note
In the first sample each vertex can be made a centroid. For example, in order to turn vertex 1 to centroid one have to replace the edge (2, 3) with the edge (1, 3). | #include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long INF = 1e18;
const double PI = acos(-1);
const long long tam = 1000100;
const long long MOD = 1e9 + 7;
const long long cmplog = 29;
int hijos[tam];
vector<int> g[tam];
pair<long long, long long> pcen;
int n;
void dfs(int u, int pa) {
hijos[u] = 1;
int maxx = 0;
for (int w : g[u]) {
if (w == pa) continue;
dfs(w, u);
hijos[u] += hijos[w];
maxx = max(maxx, hijos[w]);
}
maxx = max(maxx, n - hijos[u]);
pcen = min(pcen, pair<long long, long long>(maxx, u));
}
vector<pair<long long, long long> > queries[tam];
set<int> sdown[tam];
void dfs2(int u, int pa, int idx) {
hijos[u] = 1;
for (int w : g[u]) {
if (w == pa) continue;
dfs2(w, u, idx);
hijos[u] += hijos[w];
}
int pup = n - hijos[u];
queries[idx].push_back({pup, u});
sdown[idx].insert(hijos[u]);
}
int mejor(multiset<int> &s, int precio) {
auto it = s.upper_bound(precio / 2);
int ans = precio;
if (it != s.end()) {
ans = min(ans, max(precio - *it, *it));
}
if (it != s.begin()) {
it--;
ans = min(ans, max(precio - *it, *it));
}
return ans;
}
bool fans[tam];
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n;
int iz, der;
for (long long i = 0; i < n - 1; i++) {
cin >> iz >> der;
g[iz].push_back(der);
g[der].push_back(iz);
}
pcen = pair<long long, long long>(n, n);
dfs(1, 1);
int ucen = pcen.second;
multiset<int> siz, sder;
for (long long i = 0; i < g[ucen].size(); i++) {
int w = g[ucen][i];
dfs2(w, ucen, i);
}
for (long long idx = 0; idx < g[ucen].size(); idx++) {
for (int xx : sdown[idx]) sder.insert(xx);
}
fans[ucen] = 1;
for (long long idx = 0; idx < g[ucen].size(); idx++) {
for (int xx : sdown[idx]) {
sder.erase(sder.find(xx));
}
for (auto par : queries[idx]) {
int u = par.second;
int pup = par.first;
int bst = min(mejor(siz, pup), mejor(sder, pup));
int otro = n - hijos[g[ucen][idx]];
bst = min(bst, max(pup - otro, otro));
if (bst <= n / 2)
fans[u] = 1;
else
fans[u] = 0;
}
for (int xx : sdown[idx]) {
siz.insert(xx);
}
}
for (long long i = 1; i < n + 1; i++) cout << fans[i] << ' ';
}
|
Polycarp starts his own business. Tomorrow will be the first working day of his car repair shop. For now the car repair shop is very small and only one car can be repaired at a given time.
Polycarp is good at marketing, so he has already collected n requests from clients. The requests are numbered from 1 to n in order they came.
The i-th request is characterized by two values: si — the day when a client wants to start the repair of his car, di — duration (in days) to repair the car. The days are enumerated from 1, the first day is tomorrow, the second day is the day after tomorrow and so on.
Polycarp is making schedule by processing requests in the order from the first to the n-th request. He schedules the i-th request as follows:
* If the car repair shop is idle for di days starting from si (si, si + 1, ..., si + di - 1), then these days are used to repair a car of the i-th client.
* Otherwise, Polycarp finds the first day x (from 1 and further) that there are di subsequent days when no repair is scheduled starting from x. In other words he chooses the smallest positive x that all days x, x + 1, ..., x + di - 1 are not scheduled for repair of any car. So, the car of the i-th client will be repaired in the range [x, x + di - 1]. It is possible that the day x when repair is scheduled to start will be less than si.
Given n requests, you are asked to help Polycarp schedule all of them according to the rules above.
Input
The first line contains integer n (1 ≤ n ≤ 200) — the number of requests from clients.
The following n lines contain requests, one request per line. The i-th request is given as the pair of integers si, di (1 ≤ si ≤ 109, 1 ≤ di ≤ 5·106), where si is the preferred time to start repairing the i-th car, di is the number of days to repair the i-th car.
The requests should be processed in the order they are given in the input.
Output
Print n lines. The i-th line should contain two integers — the start day to repair the i-th car and the finish day to repair the i-th car.
Examples
Input
3
9 2
7 3
2 4
Output
9 10
1 3
4 7
Input
4
1000000000 1000000
1000000000 1000000
100000000 1000000
1000000000 1000000
Output
1000000000 1000999999
1 1000000
100000000 100999999
1000001 2000000 | #include <bits/stdc++.h>
using namespace std;
const int maxn = 209;
struct node {
int l, r;
node() {}
node(int l, int r) : l(l), r(r) {}
bool operator<(const node& R) const { return l < R.l; }
};
set<node> S;
set<node>::iterator it;
int main() {
S.insert(node(1, 2e9));
int n;
scanf("%d", &n);
for (int i = 1; i <= n; i++) {
int l, len, r;
scanf("%d%d", &l, &len);
r = l + len - 1;
int have = 0;
for (it = S.begin(); it != S.end(); it++) {
int L = (*it).l, R = (*it).r;
if (L <= l && R >= r) {
S.erase(it);
printf("%d %d\n", l, r);
if (l != L) {
S.insert(node(L, l - 1));
}
if (r != R) {
S.insert(node(r + 1, R));
}
have = 1;
break;
}
}
if (have) continue;
for (it = S.begin(); it != S.end(); it++) {
int L = (*it).l, R = (*it).r;
if (R - L + 1 >= len) {
l = L, r = L + len - 1;
S.erase(it);
printf("%d %d\n", l, r);
if (l != L) {
S.insert(node(L, l - 1));
}
if (r != R) {
S.insert(node(r + 1, R));
}
break;
}
}
}
}
|
Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not.
The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal).
Input
The tic-tac-toe position is given in four lines.
Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn.
Output
Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise.
Examples
Input
xx..
.oo.
x...
oox.
Output
YES
Input
x.ox
ox..
x.o.
oo.x
Output
NO
Input
x..x
..oo
o...
x.xo
Output
YES
Input
o.x.
o...
.x..
ooxx
Output
NO
Note
In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row.
In the second example it wasn't possible to win by making single turn.
In the third example Ilya could have won by placing X in the last row between two existing Xs.
In the fourth example it wasn't possible to win by making single turn. | #include <bits/stdc++.h>
using namespace std;
char board[4][4];
bool Valid(int x, int y) { return (x >= 0 && x < 4 && y >= 0 && y < 4); }
int main() {
std::ios::sync_with_stdio(false);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
cin >> board[i][j];
}
}
bool valid = false;
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
if (board[i][j] == 'x') {
if (Valid(i - 1, j) && board[i - 1][j] == 'x' && Valid(i - 2, j) &&
board[i - 2][j] == '.' ||
Valid(i - 1, j) && board[i - 1][j] == '.' && Valid(i - 2, j) &&
board[i - 2][j] == 'x') {
valid = true;
break;
} else if (Valid(i + 1, j) && board[i + 1][j] == 'x' &&
Valid(i + 2, j) && board[i + 2][j] == '.' ||
Valid(i + 1, j) && board[i + 1][j] == '.' &&
Valid(i + 2, j) && board[i + 2][j] == 'x') {
valid = true;
break;
} else if (Valid(i, j - 1) && board[i][j - 1] == 'x' &&
Valid(i, j - 2) && board[i][j - 2] == '.' ||
Valid(i, j - 1) && board[i][j - 1] == '.' &&
Valid(i, j - 2) && board[i][j - 2] == 'x') {
valid = true;
break;
} else if (Valid(i, j + 1) && board[i][j + 1] == 'x' &&
Valid(i, j + 2) && board[i][j + 2] == '.' ||
Valid(i, j + 1) && board[i][j + 1] == '.' &&
Valid(i, j + 2) && board[i][j + 2] == 'x') {
valid = true;
break;
} else if (Valid(i + 1, j + 1) && board[i + 1][j + 1] == 'x' &&
Valid(i + 2, j + 2) && board[i + 2][j + 2] == '.' ||
Valid(i + 1, j + 1) && board[i + 1][j + 1] == '.' &&
Valid(i + 2, j + 2) && board[i + 2][j + 2] == 'x') {
valid = true;
break;
} else if (Valid(i - 1, j - 1) && board[i - 1][j - 1] == 'x' &&
Valid(i - 2, j - 2) && board[i - 2][j - 2] == '.' ||
Valid(i - 1, j - 1) && board[i - 1][j - 1] == '.' &&
Valid(i - 2, j - 2) && board[i - 2][j - 2] == 'x') {
valid = true;
break;
} else if (Valid(i - 1, j + 1) && board[i - 1][j + 1] == 'x' &&
Valid(i - 2, j + 2) && board[i - 2][j + 2] == '.' ||
Valid(i - 1, j + 1) && board[i - 1][j + 1] == '.' &&
Valid(i - 2, j + 2) && board[i - 2][j + 2] == 'x') {
valid = true;
break;
} else if (Valid(i + 1, j - 1) && board[i + 1][j - 1] == 'x' &&
Valid(i + 2, j - 2) && board[i + 2][j - 2] == '.' ||
Valid(i + 1, j - 1) && board[i + 1][j - 1] == '.' &&
Valid(i + 2, j - 2) && board[i + 2][j - 2] == 'x') {
valid = true;
break;
}
}
}
}
(valid) ? cout << "YES\n" : cout << "NO\n";
return 0;
}
|
Stepan likes to repeat vowel letters when he writes words. For example, instead of the word "pobeda" he can write "pobeeeedaaaaa".
Sergey does not like such behavior, so he wants to write a program to format the words written by Stepan. This program must combine all consecutive equal vowels to a single vowel. The vowel letters are "a", "e", "i", "o", "u" and "y".
There are exceptions: if letters "e" or "o" repeat in a row exactly 2 times, like in words "feet" and "foot", the program must skip them and do not transform in one vowel. For example, the word "iiiimpleeemeentatiioon" must be converted to the word "implemeentatioon".
Sergey is very busy and asks you to help him and write the required program.
Input
The first line contains the integer n (1 ≤ n ≤ 100 000) — the number of letters in the word written by Stepan.
The second line contains the string s which has length that equals to n and contains only lowercase English letters — the word written by Stepan.
Output
Print the single string — the word written by Stepan converted according to the rules described in the statement.
Examples
Input
13
pobeeeedaaaaa
Output
pobeda
Input
22
iiiimpleeemeentatiioon
Output
implemeentatioon
Input
18
aeiouyaaeeiioouuyy
Output
aeiouyaeeioouy
Input
24
aaaoooiiiuuuyyyeeeggghhh
Output
aoiuyeggghhh | import math
from sys import stdin, stdout
fin = stdin
fout = stdout
n = int(fin.readline().strip())
s = fin.readline().strip()
ans = []
gl = frozenset({'a', 'e', 'i', 'y', 'o', 'u'})
met = False
cdel = False
for i in range(n):
if i > 0:
if s[i] != s[i - 1]:
met = False
cdel = False
ans.append(s[i])
else:
if s[i] in gl:
if s[i] == 'e' or s[i] == 'o':
if not met:
ans.append(s[i])
elif not cdel:
ans.pop()
cdel = True
met = True
else:
ans.append(s[i])
else:
ans.append(s[i])
fout.write(''.join(ans))
|
Finally Fox Ciel arrived in front of her castle!
She have to type a password to enter her castle. An input device attached to her castle is a bit unusual.
The input device is a 1 × n rectangle divided into n square panels. They are numbered 1 to n from left to right. Each panel has a state either ON or OFF. Initially all panels are in the OFF state. She can enter her castle if and only if x1-th, x2-th, ..., xk-th panels are in the ON state and other panels are in the OFF state.
She is given an array a1, ..., al. In each move, she can perform the following operation: choose an index i (1 ≤ i ≤ l), choose consecutive ai panels, and flip the states of those panels (i.e. ON → OFF, OFF → ON).
Unfortunately she forgets how to type the password with only above operations. Determine the minimal number of operations required to enter her castle.
Input
The first line contains three integers n, k and l (1 ≤ n ≤ 10000, 1 ≤ k ≤ 10, 1 ≤ l ≤ 100), separated by single spaces.
The second line contains k integers x1, ..., xk (1 ≤ x1 < x2 < ... < xk ≤ n), separated by single spaces.
The third line contains l integers a1, ..., al (1 ≤ ai ≤ n), separated by single spaces. It is possible that some elements of the array ai are equal value.
Output
Print the minimal number of moves required to type the password. If it's impossible, print -1.
Examples
Input
10 8 2
1 2 3 5 6 7 8 9
3 5
Output
2
Input
3 2 1
1 2
3
Output
-1
Note
One possible way to type the password in the first example is following: In the first move, choose 1st, 2nd, 3rd panels and flip those panels. In the second move, choose 5th, 6th, 7th, 8th, 9th panels and flip those panels. | #include <bits/stdc++.h>
using namespace std;
int n, k, m, x, s, p[10005], c[105], y[30][30], d[10005], q[10005], f, r,
g[1100005];
bool a[10005];
void work(int x, int y) {
if (x > 0 && x <= n && y < d[x]) {
d[x] = y;
q[++r] = x;
}
}
void bfs(int x) {
int i;
memset(d, 1, sizeof(d));
d[x] = 0;
f = 0;
r = 0;
for (q[0] = x; f <= r; f++) {
for (i = 1; i <= m; i++) {
work(q[f] + c[i], d[q[f]] + 1);
work(q[f] - c[i], d[q[f]] + 1);
}
}
for (i = 1; i <= n; i++) {
if (a[i]) y[p[x]][p[i]] = d[i];
}
}
int main() {
int i, j, l;
scanf("%d%d%d", &n, &k, &m);
n++;
for (i = 1; i <= k; i++) {
scanf("%d", &x);
a[x] = 1;
}
for (i = 1; i <= m; i++) scanf("%d", &c[i]);
for (i = n; i >= 1; i--) {
if (a[i] ^= a[i - 1]) p[i] = ++s;
}
for (i = 1; i <= n; i++) {
if (a[i]) bfs(i);
}
memset(g, 80, sizeof(g));
g[0] = 0;
for (i = 1; i <= (1 << s) - 1; i++) {
for (j = 1; j <= s; j++) {
if (i & (1 << j - 1)) {
for (l = j + 1; l <= s; l++) {
if (i & (1 << l - 1))
g[i] = min(g[i], g[i ^ (1 << j - 1) ^ (1 << l - 1)] + y[j][l]);
}
break;
}
}
}
if (g[(1 << s) - 1] > 1 << 20)
puts("-1");
else
printf("%d\n", g[(1 << s) - 1]);
return 0;
}
|
Mister B once received a gift: it was a book about aliens, which he started read immediately. This book had c pages.
At first day Mister B read v0 pages, but after that he started to speed up. Every day, starting from the second, he read a pages more than on the previous day (at first day he read v0 pages, at second — v0 + a pages, at third — v0 + 2a pages, and so on). But Mister B is just a human, so he physically wasn't able to read more than v1 pages per day.
Also, to refresh his memory, every day, starting from the second, Mister B had to reread last l pages he read on the previous day. Mister B finished the book when he read the last page for the first time.
Help Mister B to calculate how many days he needed to finish the book.
Input
First and only line contains five space-separated integers: c, v0, v1, a and l (1 ≤ c ≤ 1000, 0 ≤ l < v0 ≤ v1 ≤ 1000, 0 ≤ a ≤ 1000) — the length of the book in pages, the initial reading speed, the maximum reading speed, the acceleration in reading speed and the number of pages for rereading.
Output
Print one integer — the number of days Mister B needed to finish the book.
Examples
Input
5 5 10 5 4
Output
1
Input
12 4 12 4 1
Output
3
Input
15 1 100 0 0
Output
15
Note
In the first sample test the book contains 5 pages, so Mister B read it right at the first day.
In the second sample test at first day Mister B read pages number 1 - 4, at second day — 4 - 11, at third day — 11 - 12 and finished the book.
In third sample test every day Mister B read 1 page of the book, so he finished in 15 days. | c,v0,v1,a,l = list(map(int, input().split(" ")))
count=1
sum=v0
while sum<c:
sum+=min(v0+count*a-l,v1-l)
count+=1
print(count) |
Polycarp takes part in a math show. He is given n tasks, each consists of k subtasks, numbered 1 through k. It takes him tj minutes to solve the j-th subtask of any task. Thus, time required to solve a subtask depends only on its index, but not on the task itself. Polycarp can solve subtasks in any order.
By solving subtask of arbitrary problem he earns one point. Thus, the number of points for task is equal to the number of solved subtasks in it. Moreover, if Polycarp completely solves the task (solves all k of its subtasks), he recieves one extra point. Thus, total number of points he recieves for the complete solution of the task is k + 1.
Polycarp has M minutes of time. What is the maximum number of points he can earn?
Input
The first line contains three integer numbers n, k and M (1 ≤ n ≤ 45, 1 ≤ k ≤ 45, 0 ≤ M ≤ 2·109).
The second line contains k integer numbers, values tj (1 ≤ tj ≤ 1000000), where tj is the time in minutes required to solve j-th subtask of any task.
Output
Print the maximum amount of points Polycarp can earn in M minutes.
Examples
Input
3 4 11
1 2 3 4
Output
6
Input
5 5 10
1 2 4 8 16
Output
7
Note
In the first example Polycarp can complete the first task and spend 1 + 2 + 3 + 4 = 10 minutes. He also has the time to solve one subtask of the second task in one minute.
In the second example Polycarp can solve the first subtask of all five tasks and spend 5·1 = 5 minutes. Also he can solve the second subtasks of two tasks and spend 2·2 = 4 minutes. Thus, he earns 5 + 2 = 7 points in total. | #include <bits/stdc++.h>
using namespace std;
const int INF = numeric_limits<int>::max();
const long long LLINF = numeric_limits<long long>::max();
const unsigned long long ULLINF = numeric_limits<unsigned long long>::max();
const double PI = acos(-1.0);
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
long long t[50];
long long n, k, M;
cin >> n >> k >> M;
long long sum = 0;
for (int i = 0; i < k; i++) cin >> t[i], sum += t[i];
sort(t, t + k);
long long ans = 0;
for (int s = 0; s <= n; s++) {
if (sum * s > M) break;
long long p = n - s;
long long T = M - sum * s;
long long cur = (k + 1) * s;
for (int i = 0; i < k; i++) {
long long take = min(T / t[i], p);
cur += take;
T -= take * t[i];
}
ans = max(ans, cur);
}
cout << ans;
return 0;
}
|
You're trying to set the record on your favorite video game. The game consists of N levels, which must be completed sequentially in order to beat the game. You usually complete each level as fast as possible, but sometimes finish a level slower. Specifically, you will complete the i-th level in either Fi seconds or Si seconds, where Fi < Si, and there's a Pi percent chance of completing it in Fi seconds. After completing a level, you may decide to either continue the game and play the next level, or reset the game and start again from the first level. Both the decision and the action are instant.
Your goal is to complete all the levels sequentially in at most R total seconds. You want to minimize the expected amount of time playing before achieving that goal. If you continue and reset optimally, how much total time can you expect to spend playing?
Input
The first line of input contains integers N and R <image>, the number of levels and number of seconds you want to complete the game in, respectively. N lines follow. The ith such line contains integers Fi, Si, Pi (1 ≤ Fi < Si ≤ 100, 80 ≤ Pi ≤ 99), the fast time for level i, the slow time for level i, and the probability (as a percentage) of completing level i with the fast time.
Output
Print the total expected time. Your answer must be correct within an absolute or relative error of 10 - 9.
Formally, let your answer be a, and the jury's answer be b. Your answer will be considered correct, if <image>.
Examples
Input
1 8
2 8 81
Output
3.14
Input
2 30
20 30 80
3 9 85
Output
31.4
Input
4 319
63 79 89
79 97 91
75 87 88
75 90 83
Output
314.159265358
Note
In the first example, you never need to reset. There's an 81% chance of completing the level in 2 seconds and a 19% chance of needing 8 seconds, both of which are within the goal time. The expected time is 0.81·2 + 0.19·8 = 3.14.
In the second example, you should reset after the first level if you complete it slowly. On average it will take 0.25 slow attempts before your first fast attempt. Then it doesn't matter whether you complete the second level fast or slow. The expected time is 0.25·30 + 20 + 0.85·3 + 0.15·9 = 31.4. | #include <bits/stdc++.h>
using namespace std;
int n, m, a[55], b[55], x;
long double f[55][5050], c[55], now, res;
void doit() {
for (int i = 0; i <= m; i++) f[n + 1][i] = 0;
for (int i = n; i > 0; i--) {
for (int j = 0; j <= m; j++) {
f[i][j] =
c[i] * (a[i] + (j + a[i] > m ? now : min(f[i + 1][j + a[i]], now)));
f[i][j] += (1 - c[i]) *
(b[i] + (j + b[i] > m ? now : min(f[i + 1][j + b[i]], now)));
}
}
res = f[1][0];
}
int main() {
scanf("%d%d", &n, &m);
for (int i = 1; i <= n; i++) {
scanf("%d%d%d", a + i, b + i, &x);
c[i] = x / 100.0;
}
long double l = 0.0, r = 1000000000.0;
for (int i = 1; i <= 233; i++) {
now = (l + r) / 2.0;
doit();
if (res > now) {
l = now;
} else {
r = now;
}
}
printf("%.233lf", (double)l);
}
|
Alex, Bob and Carl will soon participate in a team chess tournament. Since they are all in the same team, they have decided to practise really hard before the tournament. But it's a bit difficult for them because chess is a game for two players, not three.
So they play with each other according to following rules:
* Alex and Bob play the first game, and Carl is spectating;
* When the game ends, the one who lost the game becomes the spectator in the next game, and the one who was spectating plays against the winner.
Alex, Bob and Carl play in such a way that there are no draws.
Today they have played n games, and for each of these games they remember who was the winner. They decided to make up a log of games describing who won each game. But now they doubt if the information in the log is correct, and they want to know if the situation described in the log they made up was possible (that is, no game is won by someone who is spectating if Alex, Bob and Carl play according to the rules). Help them to check it!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the number of games Alex, Bob and Carl played.
Then n lines follow, describing the game log. i-th line contains one integer ai (1 ≤ ai ≤ 3) which is equal to 1 if Alex won i-th game, to 2 if Bob won i-th game and 3 if Carl won i-th game.
Output
Print YES if the situation described in the log was possible. Otherwise print NO.
Examples
Input
3
1
1
2
Output
YES
Input
2
1
2
Output
NO
Note
In the first example the possible situation is:
1. Alex wins, Carl starts playing instead of Bob;
2. Alex wins, Bob replaces Carl;
3. Bob wins.
The situation in the second example is impossible because Bob loses the first game, so he cannot win the second one. | #include <bits/stdc++.h>
using namespace std;
int a[1005];
int main() {
int n;
while (cin >> n) {
int x = 1, y = 1, z = 0, k = 0;
for (int i = 0; i < n; i++) cin >> a[i];
for (int i = 0; i < n; i++) {
if (a[i] == 1 && x == 1 && y == 1) {
y = 0;
z = 1;
} else if (a[i] == 2 && x == 1 && y == 1) {
x = 0;
z = 1;
} else if (a[i] == 1 && x == 1 && z == 1) {
z = 0;
y = 1;
} else if (a[i] == 3 && x == 1 && z == 1) {
x = 0;
y = 1;
} else if (a[i] == 2 && y == 1 && z == 1) {
z = 0;
x = 1;
} else if (a[i] == 3 && y == 1 && z == 1) {
y = 0;
x = 1;
} else {
k = 1;
break;
}
}
if (k == 1)
cout << "NO" << endl;
else if (k == 0)
cout << "YES" << endl;
}
return 0;
}
|
Given a string s, process q queries, each having one of the following forms:
* 1 i c — Change the i-th character in the string to c.
* 2 l r y — Consider the substring of s starting at position l and ending at position r. Output the number of times y occurs as a substring in it.
Input
The first line of the input contains the string s (1 ≤ |s| ≤ 105) of lowercase English letters.
The second line contains an integer q (1 ≤ q ≤ 105) — the number of queries to process.
The next q lines describe the queries and may have one of the following forms:
* 1 i c (1 ≤ i ≤ |s|)
* 2 l r y (1 ≤ l ≤ r ≤ |s|)
c is a lowercase English letter and y is a non-empty string consisting of only lowercase English letters.
The sum of |y| over all queries of second type is at most 105.
It is guaranteed that there is at least one query of second type.
All strings are 1-indexed.
|s| is the length of the string s.
Output
For each query of type 2, output the required answer in a separate line.
Examples
Input
ababababa
3
2 1 7 aba
1 5 c
2 1 7 aba
Output
3
1
Input
abcdcbc
5
2 1 7 bc
1 4 b
2 4 7 bc
1 2 a
2 1 4 aa
Output
2
2
1
Note
Consider the first sample case. Initially, the string aba occurs 3 times in the range [1, 7]. Note that two occurrences may overlap.
After the update, the string becomes ababcbaba and now aba occurs only once in the range [1, 7]. | #include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
inline int read() {
int x = 0, f = 1;
char c = getchar();
for (; c < '0' || c > '9'; c = getchar())
if (c == '-') f = -1;
for (; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - 48;
return x * f;
}
inline void write(int x) {
if (x < 0) putchar('-'), x = -x;
if (x >= 10) write(x / 10);
putchar((x % 10) + '0');
}
inline void writeln(int x) {
write(x);
puts("");
}
const int oo = 0x3f3f3f3f;
const int inf = oo;
bitset<100005> f[26], ans;
char s[100005], ch[100005];
int n, Q;
int main() {
scanf("%s", s + 1);
n = strlen(s + 1);
for (int i = 1; i <= n; i++) s[i] -= 'a', f[s[i]][i] = 1;
Q = read();
while (Q--) {
int op = read();
if (op == 1) {
int pos = read(), ch = getchar();
f[s[pos]][pos] = 0;
s[pos] = ch - 'a';
f[s[pos]][pos] = 1;
} else {
int l = read(), r = read();
scanf("%s", ch);
int len = strlen(ch);
if (r - l + 1 < len) {
puts("0");
continue;
}
ans.set();
ans <<= (l - 1);
ans ^= (ans << (r - l + 2 - len));
for (int i = 0; i < len; i++) ans = (ans << 1) & f[ch[i] - 'a'];
writeln(ans.count());
}
}
return 0;
}
|
Petya and Vasya arranged a game. The game runs by the following rules. Players have a directed graph consisting of n vertices and m edges. One of the vertices contains a chip. Initially the chip is located at vertex s. Players take turns moving the chip along some edge of the graph. Petya goes first. Player who can't move the chip loses. If the game lasts for 106 turns the draw is announced.
Vasya was performing big laboratory work in "Spelling and parts of speech" at night before the game, so he fell asleep at the very beginning of the game. Petya decided to take the advantage of this situation and make both Petya's and Vasya's moves.
Your task is to help Petya find out if he can win the game or at least draw a tie.
Input
The first line of input contain two integers n and m — the number of vertices and the number of edges in the graph (2 ≤ n ≤ 105, 0 ≤ m ≤ 2·105).
The next n lines contain the information about edges of the graph. i-th line (1 ≤ i ≤ n) contains nonnegative integer ci — number of vertices such that there is an edge from i to these vertices and ci distinct integers ai, j — indices of these vertices (1 ≤ ai, j ≤ n, ai, j ≠ i).
It is guaranteed that the total sum of ci equals to m.
The next line contains index of vertex s — the initial position of the chip (1 ≤ s ≤ n).
Output
If Petya can win print «Win» in the first line. In the next line print numbers v1, v2, ..., vk (1 ≤ k ≤ 106) — the sequence of vertices Petya should visit for the winning. Vertex v1 should coincide with s. For i = 1... k - 1 there should be an edge from vi to vi + 1 in the graph. There must be no possible move from vertex vk. The sequence should be such that Petya wins the game.
If Petya can't win but can draw a tie, print «Draw» in the only line. Otherwise print «Lose».
Examples
Input
5 6
2 2 3
2 4 5
1 4
1 5
0
1
Output
Win
1 2 4 5
Input
3 2
1 3
1 1
0
2
Output
Lose
Input
2 2
1 2
1 1
1
Output
Draw
Note
In the first example the graph is the following:
<image>
Initially the chip is located at vertex 1. In the first move Petya moves the chip to vertex 2, after that he moves it to vertex 4 for Vasya. After that he moves to vertex 5. Now it is Vasya's turn and there is no possible move, so Petya wins.
In the second example the graph is the following:
<image>
Initially the chip is located at vertex 2. The only possible Petya's move is to go to vertex 1. After that he has to go to 3 for Vasya. Now it's Petya's turn but he has no possible move, so Petya loses.
In the third example the graph is the following:
<image>
Petya can't win, but he can move along the cycle, so the players will draw a tie. | #include <bits/stdc++.h>
using namespace std;
int const maxn = 1e5 + 10;
struct bkn {
int to, next;
} e[maxn * 2];
int n, m;
int c[maxn], head[maxn], tot, vis[maxn][2], in[maxn];
int ans[maxn], cnt, h, win;
void add(int a, int b) {
e[++tot].to = b;
e[tot].next = head[a], head[a] = tot;
}
void dfs(int x, int now) {
if (!c[x] && now == 1) {
win = 1;
ans[++cnt] = x;
return;
}
in[x] = 1;
for (int i = head[x]; i; i = e[i].next) {
int y = e[i].to;
if (in[y]) h = 1;
if (vis[y][now ^ 1]) continue;
vis[y][now ^ 1] = 1;
dfs(y, now ^ 1);
if (win) {
ans[++cnt] = x;
return;
}
}
in[x] = 0;
}
int main() {
scanf("%d%d", &n, &m);
int ok = 0;
for (int i = 1; i <= n; i++) {
scanf("%d", &c[i]);
if (!c[i]) ok = 1;
for (int j = 1; j <= c[i]; j++) {
int x;
scanf("%d", &x);
add(i, x);
}
}
int s;
scanf("%d", &s);
if (!ok) {
printf("Draw\n");
return 0;
}
dfs(s, 0);
if (win) {
printf("Win\n");
for (int i = cnt; i >= 1; i--) {
printf("%d ", ans[i]);
}
printf("\n");
} else if (h) {
printf("Draw\n");
} else
printf("Lose\n");
}
|
You are given an undirected graph, consisting of n vertices and m edges. The graph does not necessarily connected. Guaranteed, that the graph does not contain multiple edges (more than one edges between a pair of vertices) or loops (edges from a vertex to itself).
A cycle in a graph is called a simple, if it contains each own vertex exactly once. So simple cycle doesn't allow to visit a vertex more than once in a cycle.
Determine the edges, which belong to exactly on one simple cycle.
Input
The first line contain two integers n and m (1 ≤ n ≤ 100 000, 0 ≤ m ≤ min(n ⋅ (n - 1) / 2, 100 000)) — the number of vertices and the number of edges.
Each of the following m lines contain two integers u and v (1 ≤ u, v ≤ n, u ≠ v) — the description of the edges.
Output
In the first line print the number of edges, which belong to exactly one simple cycle.
In the second line print the indices of edges, which belong to exactly one simple cycle, in increasing order. The edges are numbered from one in the same order as they are given in the input.
Examples
Input
3 3
1 2
2 3
3 1
Output
3
1 2 3
Input
6 7
2 3
3 4
4 2
1 2
1 5
5 6
6 1
Output
6
1 2 3 5 6 7
Input
5 6
1 2
2 3
2 4
4 3
2 5
5 3
Output
0 | #include <bits/stdc++.h>
using namespace std;
const int N = 300005;
struct edge {
int to, next;
} e[N << 1];
int h[N], xb, dfn[N], low[N], n, m, i, j, x, y, w, stx[N], sty[N], ste[N];
vector<int> ans;
bool b[N], cant[N];
inline void addedge(int x, int y) {
e[++xb] = (edge){y, h[x]};
h[x] = xb;
e[++xb] = (edge){x, h[y]};
h[y] = xb;
}
void dfs(int x, int fa) {
dfn[x] = low[x] = ++xb;
int i = h[x], j;
for (; i; i = e[i].next)
if (e[i].to != fa) {
if (!dfn[e[i].to]) {
stx[++w] = x, sty[w] = e[i].to;
ste[w] = i;
dfs(e[i].to, x);
if (low[e[i].to] < low[x]) low[x] = low[e[i].to];
if (low[e[i].to] >= dfn[x]) {
int cnt = 0, ow = w;
for (; stx[w] != x || sty[w] != e[i].to; --w) {
if (!b[stx[w]]) ++cnt, b[stx[w]] = 1;
if (!b[sty[w]]) ++cnt, b[sty[w]] = 1;
}
if (!b[stx[w]]) ++cnt, b[stx[w]] = 1;
if (!b[sty[w]]) ++cnt, b[sty[w]] = 1;
if (ow - w + 1 > cnt || cnt == 2) {
for (j = w; j <= ow; ++j) cant[ste[j] >> 1] = 1;
}
for (j = w; j <= ow; ++j) b[stx[j]] = b[sty[j]] = 0;
--w;
}
} else {
if (dfn[e[i].to] < dfn[x]) stx[++w] = x, sty[w] = e[i].to, ste[w] = i;
if (dfn[e[i].to] < low[x]) low[x] = dfn[e[i].to];
}
}
}
int main() {
cin >> n >> m;
xb = 1;
for (i = 1; i <= m; ++i) {
cin >> x >> y;
addedge(x, y);
}
xb = 0;
for (i = 1; i <= n; ++i)
if (!dfn[i]) dfs(i, 0);
for (i = 1; i <= m; ++i)
if (!cant[i]) ans.push_back(i);
cout << ans.size() << '\n';
for (i = 0; i < int(ans.size()); ++i) cout << ans[i] << ' ';
return 0;
}
|
You have a Petri dish with bacteria and you are preparing to dive into the harsh micro-world. But, unfortunately, you don't have any microscope nearby, so you can't watch them.
You know that you have n bacteria in the Petri dish and size of the i-th bacteria is a_i. Also you know intergalactic positive integer constant K.
The i-th bacteria can swallow the j-th bacteria if and only if a_i > a_j and a_i ≤ a_j + K. The j-th bacteria disappear, but the i-th bacteria doesn't change its size. The bacteria can perform multiple swallows. On each swallow operation any bacteria i can swallow any bacteria j if a_i > a_j and a_i ≤ a_j + K. The swallow operations go one after another.
For example, the sequence of bacteria sizes a=[101, 53, 42, 102, 101, 55, 54] and K=1. The one of possible sequences of swallows is: [101, 53, 42, 102, \underline{101}, 55, 54] → [101, \underline{53}, 42, 102, 55, 54] → [\underline{101}, 42, 102, 55, 54] → [42, 102, 55, \underline{54}] → [42, 102, 55]. In total there are 3 bacteria remained in the Petri dish.
Since you don't have a microscope, you can only guess, what the minimal possible number of bacteria can remain in your Petri dish when you finally will find any microscope.
Input
The first line contains two space separated positive integers n and K (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ K ≤ 10^6) — number of bacteria and intergalactic constant K.
The second line contains n space separated integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — sizes of bacteria you have.
Output
Print the only integer — minimal possible number of bacteria can remain.
Examples
Input
7 1
101 53 42 102 101 55 54
Output
3
Input
6 5
20 15 10 15 20 25
Output
1
Input
7 1000000
1 1 1 1 1 1 1
Output
7
Note
The first example is clarified in the problem statement.
In the second example an optimal possible sequence of swallows is: [20, 15, 10, 15, \underline{20}, 25] → [20, 15, 10, \underline{15}, 25] → [20, 15, \underline{10}, 25] → [20, \underline{15}, 25] → [\underline{20}, 25] → [25].
In the third example no bacteria can swallow any other bacteria. | n, m = map(int, input().split())
l = sorted(map(int, input().split()))
t, b = l[::-1], -m
for a in l:
while b < a:
if a <= b + m:
n -= 1
b = t.pop()
print(n) |
Coach Ankit is forming a team for the Annual Inter Galactic Relay Race. He has N students that train under him and he knows their strengths. The strength of a student is represented by a positive integer.
The coach has to form a team of K students. The strength of a team is defined by the strength of the weakest student in the team. Now he wants to know the sum of strengths of all the teams of size K that can be formed modulo 1000000007. Please help him.
Input
The first line contains the number of test cases T.
Each case begins with a line containing integers N and K. The next line contains N space-separated numbers which describe the strengths of the students.
Output
For test case output a single integer, the answer as described in the problem statement.
Constraints:
1 ≤ T ≤ 100
1 ≤ N ≤ 100000
1 ≤ K ≤ N
0 ≤ Strength of each student ≤ 2000000000
Strength of all the students are different.
SAMPLE INPUT
2
2 1
5 4
3 2
1 0 2
SAMPLE OUTPUT
9
1
Explanation
For first test case: 5+4=9, as team can only consist of 1 student.
For second test case: min(1,0) + min(1,2) + min(0,2) = 0+1+0 =1 | def power(x,m):
global mod
if m==0:
return 1
if m&1==0:
temp=power(x,m/2)%mod
return (temp*temp)%mod
return ((x%mod)*power(x,m-1)%mod)%mod
mod=1000000007
t=input()
for kk in range(0,t):
n,k=(int(i) for i in raw_input().split())
l=[int(i) for i in raw_input().split()]
l.sort()
nCr=[0]*n
nCr[k-1]=1
for i in range(0,n):
if i>=k:
nCr[i]=(((((i%mod)*(nCr[i-1])%mod))%mod)*(power(i-k+1,mod-2)%mod))%mod
ans=0
for i in range(0,n):
if n-i-1<k-1:
break
ans=((ans%mod)+((l[i]%mod)*(nCr[n-i-1]%mod))%mod)%mod
print long(ans)%mod |
Continuing from previous version of codeXplod series i.e. CodeXplod 1.0,Chandu and daspal are still fighting over a matter of MOMO's(they are very fond of Mo Mos of sector 3..:P).This time the fight became so savior that they want to kill each other.As we all know that during a fight it is most probable outcome that both will be injured.As their friend we don`t want that to happen so we devise a method.
We gave them two integers (x,y) as they have to play a game on these values.
Game is defined as follows:-
Players play alternative.
1-During a move they are allowed to subtract gcd(x,y) from both x and y .
2-The player which makes either one of the values to zero or both to zero will win the game and will eat all the MOMO's.
3-If neither of values after 1st step does not equal to zero then the second player gets a chance and play as described by rule 1,2,3.
Now,You are given two integers and you have to find out who will eat all the MOMOs.
Input Format:-
First Line of input will contain an integer T denoting number of test cases.
Each test cases contains 2 integers(x,y) with a strings.
Two integers x,y specify the integers given to them by us and string will specify who will play first i.e. String will be either of values "Chandu" and "Daspal"(Quotes only for clarity).
Output Format:-
Output a string either "Chandu" or "Daspal"(Qoutes for clarity) determinging who will win the game.
Constraints:-
1 ≤ T ≤ 50
1 ≤ x,y ≤ 3000
SAMPLE INPUT
1
2 3 Chandu
SAMPLE OUTPUT
Daspal
Explanation
First gcd(2,3)=1 so Chandu subtract 1 from each so new pair now (1,2) now its Daspal's Turn he has gcd(1,2)=1 so after subtracting (0,1) now daspal have one zero so he is declared as winner of the game.Phew!!! | def gcd(x,y):
if y==0: return x
else: return gcd(y,x%y)
t=int(input())
for zz in range(t):
x,y,win=raw_input().split()
x=int(x);y=int(y)
while True:
k=gcd(x,y)
x-=k;y-=k
if x==0 or y==0:
break
if win=='Chandu': win="Daspal"
else: win="Chandu"
print win |
Bosky is a very curious child who turned 13 yesterday. His parents gifted him a digital watch which he really liked. He was amazed to see how each number can be represented inside one cell only by switching different edges on and off.
Today, while he was in his home alone, getting bored looking at his watch, an idea popped up in his scientific mind. He immediately went to the garage and picked up a long rectangular cardboard, which was 2 units wide and L units long, and lots of thin LED tubes which were 1 unit long.
Bosky wanted to place LED tubes on the rectangular cardboard in such a way that he can represent as many digits as possible using the LED tubes and rectangular board similar to how digits are represented on his watch.
He realized that none of the LED tubes are working so he decided to purchase new LED tubes.
Each LED tube will cost Rs. 7
He has Rs. M with him and he now goes to market and spends all the money purchasing LED tubes.
After he brought all the LED tubes home, he wondered how many different digits he can represent on the rectangular board such that he doesn't have to repeat a number again.
But Bosky is tired now and does not want to try all the possible combinations to figure out how many digits he can represent on the board. He knows that you are a great programmer and you would surely help him. He calls you and tells you the length L and the amount of money M he has. Now, you have to tell him how many different digits he can represent on the rectangular board such that none of the digits is repeated, given:
0 requires -- 6 tubes
1 requires -- 2 tubes
2 requires -- 5 tubes
3 requires -- 5 tubes
4 requires -- 4 tubes
5 requires -- 5 tubes
6 requires -- 6 tubes
7 requires -- 3 tubes
8 requires -- 7 tubes
9 requires -- 6 tubes
[NOTE: Each digit occupies exactly 1 unit length on the board]
Input:
Input will contain a number T denoting the number of test cases.
Then T test cases follow, each one consisting of two space-separated integers L and M .
Output
For each test case, output a single integer - the number of different digits Bosky can represent on the rectangular board such that none of the number is repeated and all the digits fit on the board.
Constraints
1 ≤ T ≤ 100
0 ≤ M ≤ 2000
0 ≤ L ≤ 10
SAMPLE INPUT
4
1 14
1 50
4 28
5 700
SAMPLE OUTPUT
1
10
3
32491
Explanation
Case 1: He has 14 rupees and he can purchase 2 LED tubes using which he can represent only '1' on the board.
Case 2: He can purchase 7 LED tubes using 50 rupees and the number of digits he can represent using 7 tubes are 10. | digits=[6,2,5,5,4,5,6,3,7,6]
valids=[{} for i in xrange(11)]
st0={}
for i in xrange(10):
valids[1][1<<i]=[digits[i],1]
for l in xrange(2,11):
for k in xrange(10):
for prev in valids[l-1]:
if prev&(1<<k)==0:
act=prev|(1<<k)
prevdata=valids[l-1][prev]
if k==0:
st0[act]=st0[act]+prevdata[1] if act in st0 else prevdata[1]
if act in valids[l]:
valids[l][act][1]+=prevdata[1]
else:
valids[l][act]=[prevdata[0]+digits[k],prevdata[1]]
T=int(raw_input())
for iCase in xrange(T):
L,M=map(int,raw_input().split())
M/=7
if L==0: # correction needed because of wrong judgement
L=10
total=0
for i in xrange(1,L+1):
for num in valids[i]:
if valids[i][num][0]<=M:
total+=valids[i][num][1]
if num in st0:
total-=st0[num]
print total |
Professor just has checked all the N students tests. Everything was fine but then he realised that none of the students had signed their papers, so he doesn't know which test belongs to which student.
But it's definitely not professors's job to catch every student and asked him to find his paper! So he will hand out these papers in a random way.
Now he is interested in the following question: what is the probability that X students will receive someone other's test, not their where L ≤ X ≤ R.
Input:
The first line contains 3 space-separated integers: N, L, R.
Output:
Let's suppose the answer is a fraction P / Q where P and Q are coprime. Output P * Q^-1 modulo 10^9 + 7.
Constraints:
1 ≤ N ≤ 100
0 ≤ L ≤ R ≤ N
SAMPLE INPUT
3 1 3
SAMPLE OUTPUT
833333340
Explanation
It's not possible that exactly 1 students doesn't receive his paper.
There are 3 variants when 2 students doesn't receive their tests: {1, 3, 2}, {3, 2, 1}, {2, 1, 3}
There are 2 variants when 3 students doesn't receive their tests: {3, 1, 2}, {2, 3, 1}
There are 5 variants total and 6 overall possible situations. So the answer is (5 / 6) modulo 10^9 + 7 = 833333340 | mod=10**9+7
A=[[0 for i in range(105)] for j in range(105)]
B=[0]*105
for i in range(0,102):
A[i][0]=1
for j in range(1,i+1):
A[i][j]=A[i-1][j]+A[i-1][j-1]
B[0]=1
for i in range(1,102):
B[i]=B[i-1]*i
def ans(n,x):
y=0
for i in range(0,x+1):
y+=((-1)**i)*B[x]/B[i]
return y*A[n][x]
def finalans(n,l,r):
ret=0
for i in range(l,r+1):
ret+=ans(n,i)
return ret
def ANS(n,l,r):
x=finalans(n,l,r)%mod;
y=B[n]
z=pow(y,mod-2,mod);
return (x*z)%mod
N, L, R=map(int,raw_input().split())
print(ANS(N,L,R)) |
Given an integer n and a permutation of numbers 1, 2 ... , n-1, n write a program to print the permutation that lexicographically precedes the given input permutation. If the given permutation is the lexicographically least permutation, then print the input permutation itself.
Input Format:
First line is the test cases and second line contains value of integer n: 1 ≤ n ≤ 1,000,000
third line is a space separated list of integers 1 2 ... n permuted in some random order
Output Format:
Output a single line containing a space separated list of integers which is the lexicographically preceding permutation of the input permutation.
SAMPLE INPUT
1
3
1 3 2
SAMPLE OUTPUT
1 2 3 | for _ in xrange(input()):
n= input()
a=map(int,raw_input().split())
b=[]
flag=0
for x in xrange(n-1,0,-1):
b=a[:x-1]
if a[x]<a[x-1]:
for y in xrange(n-1,x-1,-1):
if a[x-1]>a[y]:
b.append(a[y])
flag=1
c=a[x-1:]
del(c[y-x+1])
c.sort()
c.reverse()
b=b+c
if flag==1:
break
if flag==1:
break
if flag==0:
print ' '.join(str(x) for x in a)
else :
print ' '.join(str(x) for x in b) |
Monk's birthday is coming this weekend! He wants to plan a Birthday party and is preparing an invite list with his friend Puchi. He asks Puchi to tell him names to add to the list.
Puchi is a random guy and keeps coming up with names of people randomly to add to the invite list, even if the name is already on the list! Monk hates redundancy and hence, enlists the names only once.
Find the final invite-list, that contain names without any repetition.
Input:
First line contains an integer T. T test cases follow.
First line of each test contains an integer N, the number of names that Puchi pops up with.
Output:
For each testcase,Output the final invite-list with each name in a new line. The names in the final invite-list are sorted lexicographically.
Constraints:
1 ≤ T ≤ 10
1 ≤ N ≤ 10^5
1 ≤ Length of each name ≤ 10^5
SAMPLE INPUT
1
7
chandu
paro
rahul
mohi
paro
arindam
rahul
SAMPLE OUTPUT
arindam
chandu
mohi
paro
rahul | t = int(raw_input())
for j in range(t):
a = int(raw_input())
c = []
d = []
for i in range(a):
x = raw_input()
c.append(x)
for i in c:
if i not in d:
d.append(i)
d.sort()
for i in d:
print i |
Suppose you have a string S which has length N and is indexed from 0 to N−1. String R is the reverse of the string S. The string S is funny if the condition |Si−Si−1|=|Ri−Ri−1| is true for every i from 1 to N−1.
(Note: Given a string str, stri denotes the ascii value of the ith character (0-indexed) of str. |x| denotes the absolute value of an integer x)
SAMPLE INPUT
2
acxz
bcxz
SAMPLE OUTPUT
Funny
Not Funny
Explanation
Consider the 1st testcase acxz :
c-a
=
x-z
= 2
z-x
=
a-c
= 2
Consider the 2st testcase bcxz
|c-b| != |x-z| | tc=int(raw_input())
for case in range(tc):
s=raw_input()
r=s[::-1]
l=len(s)
flag=1
for i in range(l-1):
t=ord(s[i])-ord(s[i+1])
if t>0:
a=t
else:
a=-1*t
t=ord(r[i])-ord(r[i+1])
if t>0:
b=t
else:
b=-1*t
if not a==b:
flag=0
break
if flag==1:
print "Funny"
else:
print "Not Funny" |
Roy is looking for Wobbly Numbers.
An N-length wobbly number is of the form "ababababab..." and so on of length N, where a != b.
A 3-length wobbly number would be of form "aba".
Eg: 101, 121, 131, 252, 646 etc
But 111, 222, 999 etc are not 3-length wobbly number, because here a != b condition is not satisfied.
Also 010 is not a 3-length wobbly number because it has preceding 0. So 010 equals 10 and 10 is not a 3-length wobbly number.
A 4-length wobbly number would be of form "abab".
Eg: 2323, 3232, 9090, 1414 etc
Similarly we can form a list of N-length wobbly numbers.
Now your task is to find K^th wobbly number from a lexicographically sorted list of N-length wobbly numbers. If the number does not exist print -1 else print the K^th wobbly number. See the sample test case and explanation for more clarity.
Input:
First line contains T - number of test cases
Each of the next T lines contains two space separated integers - N and K.
Output:
For each test case print the required output in a new line.
Constraints:
1 ≤ T ≤ 100
3 ≤ N ≤ 1000
1 ≤ K ≤ 100
SAMPLE INPUT
6
3 1
3 2
3 100
4 3
4 4
5 2
SAMPLE OUTPUT
101
121
-1
1313
1414
12121
Explanation
First 10 terms of 3-length wobbly numbers arranged lexicographically is as follows:
101, 121, 131, 141, 151, 161, 171, 181, 191, 202
1st wobbly number of length 3 is 101.
2nd wobbly number of length 3 is 121.
100th wobbly number of length 3 does not exist, so the output is -1.
First 10 terms of 4-length wobbly numbers arranged lexicographically is as follows:
1010, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020
3rd wobbly number of length 4 is 1313.
4th wobbly number of length 4 is 1414.
Similarly 2nd wobbly number of length 5 is 12121 | combos = []
for i in range(1, 10):
for j in range(0, 10):
if i != j:
combos += [[i, j]]
for i in range(input()):
n, k = map(int, raw_input().rstrip().split())
if k > 81: print -1
else:
numbers = combos[k-1]
ans = ""
for i in range(n):
ans += str(numbers[i % 2])
print ans |
Jack is the most intelligent student in the class.To boost his intelligence,his class teacher gave him a problem named "Substring Count".
Problem :
His Class teacher gave him n strings numbered from 1 to n which consists of only lowercase letters (each having length not more than 10) and then ask Q questions related to the given strings.
Each question is described by the 2 integers L,R and a string str,Now his teacher wants to know how many strings numbered from L to R contains str as a substrings.
As expected, Jack solved this problem with in a minute but he failed to solve it efficiently.Now ,its your turn to teach him.How to do it efficiently?? and save him from punishment.
INPUT
First line of input contains a single integer n denoting the number of strings given by class teacher to jack.Next n lines of input contains n strings (one per line).Next line fo input contains a single integer Q denoting the number of questions asked by his teacher.next Q lines of input contains Q question (one per line) as explained above.
OUTPUT
print the correct answer for each of the question asked by his teacher.
CONSTRAINTS
1 ≤ n ≤ 10000
1 ≤ strlen(str) ≤ 10
1 ≤ Q ≤ 5*10^5
1 ≤ L,R ≤ n
NOTE: strings consist of only lower case characters
SAMPLE INPUT
3
code
coder
coding
2
1 3 code
1 3 co
SAMPLE OUTPUT
2
3
Explanation
Q1:: code coder coding only two out of 3 strings contain cod as substring
Q2:: code coder coding all the 3 strings contain co as substring | t = int(raw_input())
d = {}
for i in range(t):
s = raw_input().strip()
for j in range(len(s)):
for k in range(j, len(s)):
if not d.get(s[j:k+1], 0):
d[s[j:k+1]] = [i]
else:
if i not in d[s[j:k+1]]:
d[s[j:k+1]].append(i)
q = int(raw_input())
while q:
q-=1
l, r, sub = raw_input().strip().split(" ")
l = int(l)
r = int(r)
l-=1
r-=1
if d.get(sub, 0):
f = d[sub]
f.sort()
s = 0
# Use binary search here...
import bisect
print bisect.bisect_right(f, r) - bisect.bisect_left(f, l)
else:
print 0 |
In code world all genders are considered equal ( It means their is nothing like male or female). Now their are N distinct persons living in this hypothetical world. Each person can pair up with any other person or can even remain single. One day Vbhu planned to visit code world. Being a maths guy , he always try to be mathematical. So he started counting the ways in which N persons living in code world can make pairs or remain single. A single person can make pair with at most one other person.Seeing that N can be large , Vibhu ask you for help. Now being a great programmer you need to help Vbhu count the number of ways in which N persons living in code world can make pairs or remain single.
Note : Its not necessary that everyone is required to make pair with someone. Person can remain single also.
Input Format : First line contain number of test cases T. Then next T lines contain a single integer N , denoting the number of persons living in code world.
Output Format : You need to print the number of ways in which N different persons can make their pairs or stay single. As answer can be large so print it modulo 10^9+7.
Constraints :
1 ≤ T ≤10^5
1 ≤ N ≤10^6
Warning: Large Input/Output data, be careful with certain languages
SAMPLE INPUT
2
2
3
SAMPLE OUTPUT
2
4
Explanation
In first test case , For N=2 answer will be 2. Possible ways are :
{1},{2} (It means Person 1 and Person 2 are single)
{1,2} (It means Person 1 and Person 2 had formed a pair)
For second test case , For N=3 , answer will be 4. Possible ways are :
{1},{2},{3} (It means all three Persons are single)
{1,2},{3} (It means Person 1 and Person 2 had formed a pair and Person 3 is single)
{1},{2,3} (It means Person 2 and Person 3 had formed a pair and Person 1 is single)
{1,3},{2} (It means Person 1 and Person 3 had formed a pair and Person 2 is single) | n=int(raw_input())
in_array=[]
for i in xrange(n):
num=int(raw_input())
in_array.append(num)
mx=max(in_array)
arr=[1,1]
for j in xrange(2,mx+1):
arr.append((arr[j-1]+(j-1)*arr[j-2])%(10**9+7))
for i in in_array:
print arr[i] |
We have N camels numbered 1,2,\ldots,N. Snuke has decided to make them line up in a row.
The happiness of Camel i will be L_i if it is among the K_i frontmost camels, and R_i otherwise.
Snuke wants to maximize the total happiness of the camels. Find the maximum possible total happiness of the camel.
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 10^5
* 1 \leq N \leq 2 \times 10^{5}
* 1 \leq K_i \leq N
* 1 \leq L_i, R_i \leq 10^9
* The sum of values of N in each input file is at most 2 \times 10^5.
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
K_1 L_1 R_1
\vdots
K_N L_N R_N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
3
2
1 5 10
2 15 5
3
2 93 78
1 71 59
3 57 96
19
19 23 16
5 90 13
12 85 70
19 67 78
12 16 60
18 48 28
5 4 24
12 97 97
4 57 87
19 91 74
18 100 76
7 86 46
9 100 57
3 76 73
6 84 93
1 6 84
11 75 94
19 15 3
12 11 34
Output
25
221
1354 | import sys
from heapq import heappush, heappop
from operator import itemgetter
sys.setrecursionlimit(10 ** 7)
rl = sys.stdin.readline
def solve():
N = int(rl())
res = 0
camel_left, camel_right = [], []
for _ in range(N):
K, L, R = map(int, rl().split())
res += min(L, R)
if R <= L:
camel_left.append([K, L, R])
elif K != N:
camel_right.append([N - K, L, R])
camel_left.sort(key=itemgetter(0))
camel_right.sort(key=itemgetter(0))
hq = []
i = 0
for j in range(1, N + 1):
while i < len(camel_left) and camel_left[i][0] == j:
heappush(hq, camel_left[i][1] - camel_left[i][2])
i += 1
while j < len(hq):
heappop(hq)
res += sum(hq)
hq = []
i = 0
for j in range(1, N):
while i < len(camel_right) and camel_right[i][0] == j:
heappush(hq, camel_right[i][2] - camel_right[i][1])
i += 1
while j < len(hq):
heappop(hq)
res += sum(hq)
return res
if __name__ == '__main__':
T = int(rl())
ans = []
for _ in range(T):
ans.append(solve())
print(*ans, sep='\n')
|
Print the K-th element of the following sequence of length 32:
1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, 5, 4, 1, 4, 1, 51
Constraints
* 1 \leq K \leq 32
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K
Output
Print the K-th element.
Examples
Input
6
Output
2
Input
27
Output
5 | #include<iostream>
using namespace std;
int main(){
int a[33]={1,1,1,2,1,2,1,5,2,2,1,5,1,2,1,14,1,5,1,5,2,2,1,15,2,2,5,4,1,4,1,51};
int k;
cin >> k;
cout << a[k-1] << endl;
} |
We have N balance beams numbered 1 to N. The length of each beam is 1 meters. Snuke walks on Beam i at a speed of 1/A_i meters per second, and Ringo walks on Beam i at a speed of 1/B_i meters per second.
Snuke and Ringo will play the following game:
* First, Snuke connects the N beams in any order of his choice and makes a long beam of length N meters.
* Then, Snuke starts at the left end of the long beam. At the same time, Ringo starts at a point chosen uniformly at random on the long beam. Both of them walk to the right end of the long beam.
* Snuke wins if and only if he catches up to Ringo before Ringo reaches the right end of the long beam. That is, Snuke wins if there is a moment when Snuke and Ringo stand at the same position, and Ringo wins otherwise.
Find the probability that Snuke wins when Snuke arranges the N beams so that the probability of his winning is maximized.
This probability is a rational number, so we ask you to represent it as an irreducible fraction P/Q (to represent 0, use P=0, Q=1).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
\vdots
A_N B_N
Output
Print the numerator and denominator of the irreducible fraction that represents the maximum probability of Snuke's winning.
Examples
Input
2
3 2
1 2
Output
1 4
Input
4
1 5
4 7
2 1
8 4
Output
1 2
Input
3
4 1
5 2
6 3
Output
0 1
Input
10
866111664 178537096
705445072 318106937
472381277 579910117
353498483 865935868
383133839 231371336
378371075 681212831
304570952 16537461
955719384 267238505
844917655 218662351
550309930 62731178
Output
697461712 2899550585 | #ifndef BZ
#pragma GCC optimize "-O3"
#endif
#include <bits/stdc++.h>
#define ALL(v) (v).begin(), (v).end()
#define rep(i, l, r) for (int i = (l); i < (r); ++i)
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using namespace std;
/*
ll pw(ll a, ll b) {
ll ans = 1; while (b) {
while (!(b & 1)) b >>= 1, a = (a * a) % MOD;
ans = (ans * a) % MOD, --b;
} return ans;
}
*/
struct st {
ll a, b;
};
const int N = 120000;
st a[N];
int n;
ll sm[N];
ll ap = 0;
ll aq = 1;
ll gcd(ll a, ll b) {
while (b) {
ll q = a % b;
a = b;
b = q;
}
return a;
}
using lll = __int128_t;
void upd(ll p, ll q) {
ll g = gcd(p, q);
p /= g, q /= g;
if (lll(ap) * q < lll(p) * aq) {
ap = p;
aq = q;
}
}
int main() {
ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
cout.setf(ios::fixed), cout.precision(20);
cin >> n;
ll sum = 0;
for (int i = 0; i < n; ++i) {
cin >> a[i].a >> a[i].b;
sum += a[i].a;
}
sort(a, a + n, [] (st a, st b) {
return max(a.a, a.b) > max(b.a, b.b);
});
sm[0] = 0;
for (int i = 0; i < n; ++i) {
sm[i + 1] = sm[i] + max(a[i].a, a[i].b);
}
for (int i = 0; i < n; ++i) {
int l = 0;
int r = n + 1;
while (r - l > 1) {
int m = (l + r) >> 1;
ll cur = sum - a[i].b - sm[m];
if (i < m) {
cur += max(a[i].a, a[i].b);
}
if (cur > 0) {
l = m;
} else {
r = m;
}
}
if (r <= n) {
int cnt = r;
if (i >= r) {
++cnt;
}
cnt = n - cnt;
ll cur = sum - sm[r];
if (i < r) {
cur += max(a[i].a, a[i].b);
}
if (cur <= 0) {
upd(cnt + 1, n);
} else {
assert(cur <= a[i].b);
ll p = cnt * a[i].b + a[i].b - cur;
ll q = a[i].b * n;
upd(p, q);
}
}
}
cout << ap << " " << aq << "\n";
return 0;
}
|
Diverta City is a new city consisting of N towns numbered 1, 2, ..., N.
The mayor Ringo is planning to connect every pair of two different towns with a bidirectional road. The length of each road is undecided.
A Hamiltonian path is a path that starts at one of the towns and visits each of the other towns exactly once. The reversal of a Hamiltonian path is considered the same as the original Hamiltonian path.
There are N! / 2 Hamiltonian paths. Ringo wants all these paths to have distinct total lengths (the sum of the lengths of the roads on a path), to make the city diverse.
Find one such set of the lengths of the roads, under the following conditions:
* The length of each road must be a positive integer.
* The maximum total length of a Hamiltonian path must be at most 10^{11}.
Constraints
* N is a integer between 2 and 10 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print a set of the lengths of the roads that meets the objective, in the following format:
w_{1, 1} \ w_{1, 2} \ w_{1, 3} \ ... \ w_{1, N}
w_{2, 1} \ w_{2, 2} \ w_{2, 3} \ ... \ w_{2, N}
: : :
w_{N, 1} \ w_{N, 2} \ w_{N, 3} \ ... \ w_{N, N}
where w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:
* w_{i, i} = 0
* w_{i, j} = w_{j, i} \ (i \neq j)
* 1 \leq w_{i, j} \leq 10^{11} \ (i \neq j)
If there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.
Examples
Input
3
Output
0 6 15
6 0 21
15 21 0
Input
4
Output
0 111 157 193
111 0 224 239
157 224 0 258
193 239 258 0 | #include<bits/stdc++.h>
using namespace std;
long long a1[13]={1,2,4,7,12,20,29,38,52,101},a2[13]={1,2,4,7,12,20,30,39,67,101},n,an[15][15],no=1;
int main(){
cin>>n;
for (int i=1;i<=n;i++)an[i][i]=0;
for (int i=1;i<=n;i++){
for (int j=i+1;j<=n;j++)an[i][j]=an[j][i]=no*a1[j-i-1];
no*=a2[n-i];
}
for (int i=1;i<=n;i++){
for (int j=1;j<=n;j++)cout<<an[i][j]<<' ';
cout<<endl;
}
return 0;
} |
A string is called a KEYENCE string when it can be changed to `keyence` by removing its contiguous substring (possibly empty) only once.
Given a string S consisting of lowercase English letters, determine if S is a KEYENCE string.
Constraints
* The length of S is between 7 and 100 (inclusive).
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If S is a KEYENCE string, print `YES`; otherwise, print `NO`.
Examples
Input
keyofscience
Output
YES
Input
mpyszsbznf
Output
NO
Input
ashlfyha
Output
NO
Input
keyence
Output
YES |
public class Main {
private static void solve() {
char[] s = ns();
int n = s.length;
for (int i = 1; i <= n; i ++) {
for (int j = i; j < n; j ++) {
String a = new String(s, 0, i);
String b = new String(s, j, n - j);
if ((a + b).equals("keyence")) {
System.out.println("YES");
return;
}
}
}
System.out.println("NO");
}
public static void main(String[] args) {
new Thread(null, new Runnable() {
@Override
public void run() {
long start = System.currentTimeMillis();
String debug = args.length > 0 ? args[0] : null;
if (debug != null) {
try {
is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
} catch (Exception e) {
throw new RuntimeException(e);
}
}
reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
solve();
out.flush();
tr((System.currentTimeMillis() - start) + "ms");
}
}, "", 64000000).start();
}
private static java.io.InputStream is = System.in;
private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
private static java.util.StringTokenizer tokenizer = null;
private static java.io.BufferedReader reader;
public static String next() {
while (tokenizer == null || !tokenizer.hasMoreTokens()) {
try {
tokenizer = new java.util.StringTokenizer(reader.readLine());
} catch (Exception e) {
throw new RuntimeException(e);
}
}
return tokenizer.nextToken();
}
private static double nd() {
return Double.parseDouble(next());
}
private static long nl() {
return Long.parseLong(next());
}
private static int[] na(int n) {
int[] a = new int[n];
for (int i = 0; i < n; i++)
a[i] = ni();
return a;
}
private static char[] ns() {
return next().toCharArray();
}
private static long[] nal(int n) {
long[] a = new long[n];
for (int i = 0; i < n; i++)
a[i] = nl();
return a;
}
private static int[][] ntable(int n, int m) {
int[][] table = new int[n][m];
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
table[i][j] = ni();
}
}
return table;
}
private static int[][] nlist(int n, int m) {
int[][] table = new int[m][n];
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
table[j][i] = ni();
}
}
return table;
}
private static int ni() {
return Integer.parseInt(next());
}
private static void tr(Object... o) {
if (is != System.in)
System.out.println(java.util.Arrays.deepToString(o));
}
}
|
You are given N positive integers a_1, a_2, ..., a_N.
For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).
Here, X\ mod\ Y denotes the remainder of the division of X by Y.
Find the maximum value of f.
Constraints
* All values in input are integers.
* 2 \leq N \leq 3000
* 2 \leq a_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
Print the maximum value of f.
Examples
Input
3
3 4 6
Output
10
Input
5
7 46 11 20 11
Output
90
Input
7
994 518 941 851 647 2 581
Output
4527 | #include <bits/stdc++.h>
using namespace std;
int main(){
int n,ans=0;
cin>>n;
for(int i=0,a;i<n;i++){
cin>>a;ans+=a-1;
}
cout<<ans<<endl;
} |
There are N people standing on the x-axis. Let the coordinate of Person i be x_i. For every i, x_i is an integer between 0 and 10^9 (inclusive). It is possible that more than one person is standing at the same coordinate.
You will given M pieces of information regarding the positions of these people. The i-th piece of information has the form (L_i, R_i, D_i). This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.
It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.
Constraints
* 1 \leq N \leq 100 000
* 0 \leq M \leq 200 000
* 1 \leq L_i, R_i \leq N (1 \leq i \leq M)
* 0 \leq D_i \leq 10 000 (1 \leq i \leq M)
* L_i \neq R_i (1 \leq i \leq M)
* If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).
* D_i are integers.
Input
Input is given from Standard Input in the following format:
N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M
Output
If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print `Yes`; if it does not exist, print `No`.
Examples
Input
3 3
1 2 1
2 3 1
1 3 2
Output
Yes
Input
3 3
1 2 1
2 3 1
1 3 5
Output
No
Input
4 3
2 1 1
2 3 5
3 4 2
Output
Yes
Input
10 3
8 7 100
7 9 100
9 8 100
Output
No
Input
100 0
Output
Yes | #include <bits/stdc++.h>
using namespace std;
const int maxn=112345;
typedef pair<int,int> pii;
int n,m,l,r,x,d[maxn],vis[maxn];
vector<pii> G[maxn];
bool dfs(int u,int dep) {
vis[u]=1;
d[u]=dep;
for (int i=0;i<(int)G[u].size();++i) {
int v=G[u][i].first,w=G[u][i].second;
if (vis[v]&&d[u]+w!=d[v]) return false;
if (!vis[v]&&!dfs(v,dep+w)) return false;
}
return true;
}
int main()
{
scanf("%d%d",&n,&m);
for (int i=0;i<m;++i) {
scanf("%d%d%d",&l,&r,&x);
G[l].push_back(pii(r,x));
G[r].push_back(pii(l,-x));
}
for (int i=1;i<=n;++i) if (!vis[i]&&!dfs(i,0))
return 0*puts("No");
return 0*puts("Yes");
}
|
You are given a permutation p_1,p_2,...,p_N consisting of 1,2,..,N. You can perform the following operation any number of times (possibly zero):
Operation: Swap two adjacent elements in the permutation.
You want to have p_i ≠ i for all 1≤i≤N. Find the minimum required number of operations to achieve this.
Constraints
* 2≤N≤10^5
* p_1,p_2,..,p_N is a permutation of 1,2,..,N.
Input
The input is given from Standard Input in the following format:
N
p_1 p_2 .. p_N
Output
Print the minimum required number of operations
Examples
Input
5
1 4 3 5 2
Output
2
Input
2
1 2
Output
1
Input
2
2 1
Output
0
Input
9
1 2 4 9 5 8 7 3 6
Output
3 | #include <iostream>
#include <vector>
using namespace std;
int main() {
int N;
cin >> N;
int S = 0;
int seq = 0;
int p;
for(int i = 1; i <= N; i++) {
cin >> p;
if(i != p) {
S += seq / 2 + seq % 2;
seq = 0;
}
if(i == p) seq++;
}
S += seq / 2 + seq % 2;
cout << S << endl;
return 0;
} |
There are N oases on a number line. The coordinate of the i-th oases from the left is x_i.
Camel hopes to visit all these oases. Initially, the volume of the hump on his back is V. When the volume of the hump is v, water of volume at most v can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.
Camel can travel on the line by either walking or jumping:
* Walking over a distance of d costs water of volume d from the hump. A walk that leads to a negative amount of stored water cannot be done.
* Let v be the amount of water stored at the moment. When v>0, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes v/2 (rounded down to the nearest integer), and the amount of stored water becomes 0.
For each of the oases, determine whether it is possible to start from that oasis and visit all the oases.
Constraints
* 2 ≤ N,V ≤ 2 × 10^5
* -10^9 ≤ x_1 < x_2 < ... < x_N ≤ 10^9
* V and x_i are all integers.
Input
Input is given from Standard Input in the following format:
N V
x_1 x_2 ... x_{N}
Output
Print N lines. The i-th line should contain `Possible` if it is possible to start from the i-th oasis and visit all the oases, and `Impossible` otherwise.
Examples
Input
3 2
1 3 6
Output
Possible
Possible
Possible
Input
7 2
-10 -4 -2 0 2 4 10
Output
Impossible
Possible
Possible
Possible
Possible
Possible
Impossible
Input
16 19
-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84
Output
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Impossible
Impossible
Impossible
Impossible | #include <bits/stdc++.h>
#define rep(i,n) for ((i)=1;(i)<=(n);(i)++)
#define repd(i,n) for ((i)=(n);(i)>=1;(i)--)
using namespace std;
int n,m;
int i,j;
int a[200005],d[200005],lim[25];
int tor[200005][25],tol[200005][25];
int dppre[1<<19],dpsuf[1<<19];
void calc(int x){
int i;
rep(i,n){
tor[i][x]=tor[i-1][x];
if(tor[i][x]<i){
tor[i][x]=i;
while(tor[i][x]<n&&d[tor[i][x]]<=lim[x]){
tor[i][x]++;
}
}
}
tol[n+1][x]=n+1;
repd(i,n){
tol[i][x]=tol[i+1][x];
if(tol[i][x]>i){
tol[i][x]=i;
while(tol[i][x]>1&&d[tol[i][x]-1]<=lim[x]){
tol[i][x]--;
}
}
}
}
int main(){
cin>>n>>lim[m=1];
rep(i,n) cin>>a[i];
rep(i,n-1) d[i]=a[i+1]-a[i];
while(lim[m]>0){
m++;
lim[m]=lim[m-1]/2;
}
rep(i,m){
calc(i);
}
int c=0;
for(i=1;i<=n;i=tor[i][1]+1)c++;
if(c>m+1){
rep(i,n){
puts("Impossible");
return 0;
}
}
for(i=0;i<(1<<(m-1));i++){
dppre[i]=0;dpsuf[i]=n+1;
for(j=0;j<(m-1);j++)if((i>>j)&1){
dppre[i]=max(dppre[i],tor[dppre[i^(1<<j)]+1][j+2]);
dpsuf[i]=min(dpsuf[i],tol[dpsuf[i^(1<<j)]-1][j+2]);
}
}
for(i=1;i<=n;i=tor[i][1]+1){
int f=0;
for(j=0;j<(1<<(m-1));j++){
f|=(dppre[j]>=i-1&&dpsuf[((1<<m-1)-1)^j]<=tor[i][1]+1);
}
if(f){
rep(j,tor[i][1]-i+1) puts("Possible");
}
else{
rep(j,tor[i][1]-i+1) puts("Impossible");
}
}
return 0;
} |
Imagine a game played on a line. Initially, the player is located at position 0 with N candies in his possession, and the exit is at position E. There are also N bears in the game. The i-th bear is located at x_i. The maximum moving speed of the player is 1 while the bears do not move at all.
When the player gives a candy to a bear, it will provide a coin after T units of time. More specifically, if the i-th bear is given a candy at time t, it will put a coin at its position at time t+T. The purpose of this game is to give candies to all the bears, pick up all the coins, and go to the exit. Note that the player can only give a candy to a bear if the player is at the exact same position of the bear. Also, each bear will only produce a coin once. If the player visits the position of a coin after or at the exact same time that the coin is put down, the player can pick up the coin. Coins do not disappear until collected by the player.
Shik is an expert of this game. He can give candies to bears and pick up coins instantly. You are given the configuration of the game. Please calculate the minimum time Shik needs to collect all the coins and go to the exit.
Constraints
* 1 \leq N \leq 100,000
* 1 \leq T, E \leq 10^9
* 0 < x_i < E
* x_i < x_{i+1} for 1 \leq i < N
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N E T
x_1 x_2 ... x_N
Output
Print an integer denoting the answer.
Examples
Input
3 9 1
1 3 8
Output
12
Input
3 9 3
1 3 8
Output
16
Input
2 1000000000 1000000000
1 999999999
Output
2999999996 | //Love and Freedom.
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#define ll long long
#define inf 20021225
#define N 100100
using namespace std;
int read()
{
int s=0,f=1; char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-') f=-1; ch=getchar();}
while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
return f*s;
}
ll f[N],mn; int t,e,n,p[N];
int main()
{
n=read(),e=read(),t=read();
int l=0; mn=1e18;
for(int i=1;i<=n;i++) p[i]=read();
for(int i=1;i<=n;i++)
{
while(l<=i && 2*(p[i]-p[l+1])>t)
mn=min(mn,f[l]-2*p[l+1]), l++;
if(l<i) f[i]=f[l]+t;
f[i]=min(f[i],mn+2*p[i]);
}
printf("%lld\n",f[n]+e);
return 0;
} |
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | #include <iostream>
using namespace std;
int main(void){
int rectangle=0, lozenge=0;
while (true){
int a,b,c;
char e;
cin>>a>>e>>b>>e>>c;
if (cin.eof()) break;
if (a==b) lozenge++;
if (a*a+b*b==c*c) rectangle++;
}
cout<<rectangle<<endl;
cout<<lozenge<<endl;
return 0;
} |
In 20XX, the Aizu Chuo Road, which has a total distance of 58km and 6 sections from Atsushiokanomachi, Kitakata City to Minamiaizucho, is scheduled to be completed and opened.
For half a year after opening, the toll will be halved for vehicles that pass the departure IC or arrival IC between 17:30 and 19:30 and have a mileage of 40km or less. However, the charge will be in units of 50 yen and rounded up. The table below is a list of fares and distances.
<image>
<image>
For example, from Kitakata (2) to Aizuwakamatsu (4), the fare is 450 yen and the distance is 12km. If it is half price time zone, it will be 250 yen.
Create a program that calculates and outputs the charge by inputting the departure IC, departure IC transit time, arrival IC, and arrival IC transit time. However, the time entered will be the value in 24-hour notation. In addition, even if you pass at exactly 17:30 and 19:30, it will be included in the half price time zone.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
d
hd md
a
ha ma
The first line gives the departure IC number d (1 ≤ d ≤ 7), and the second line gives the time hd (0 ≤ hd ≤ 23) and minutes md (0 ≤ md ≤ 59) of the departure IC transit time. ..
The arrival IC number a (1 ≤ a ≤ 7) is given on the third line, and the time ha (0 ≤ ha ≤ 23) and minute ma (0 ≤ ma ≤ 59) of the arrival IC transit time are given on the fourth line. ..
Output
The toll (integer) is output to one line for each data set.
Example
Input
2
17 25
4
17 45
4
17 25
7
19 35
0
Output
250
1300 |
#include<iostream>
using namespace std;
int main()
{
int list[7][7]={
{0,300,500,600,700,1350,1650},
{6,0,350,450,600,1150,1500},
{13,7,0,250,400,1000,1350},
{18,12,5,0,250,850,1300},
{23,17,10,5,0,600,1150},
{43,37,30,25,20,0,500},
{58,52,45,40,35,15,0}
};
int in,out,h,m,start,end,fee;
bool half;
while(cin>>in,in){
cin>>h>>m;
start=100*h+m;
cin>>out>>h>>m;
end=100*h+m;
if(in>out)swap(in,out);
in--;out--;
if( (1730<=start && start<=1930) || (1730<=end && end<=1930) )half=true;
else half=false;
if(list[out][in]>40)half=false;
fee=list[in][out];
if(half){
fee/=2;
fee+=25;
fee/=50;
fee*=50;
}
cout<<fee<<endl;
}
} |
The educational program (AHK Education) of the Aiz Broadcasting Corporation broadcasts a program called "Play with Tsukuro" for children. Today is the time to make a box with drawing paper, but I would like to see if the rectangular drawing paper I prepared can make a rectangular parallelepiped. However, do not cut or fold the drawing paper.
Given six rectangles, write a program to determine if you can make a rectangular parallelepiped using them.
Input
The input is given in the following format.
h1 w1
h2 w2
h3 w3
h4 w4
h5 w5
h6 w6
The input consists of 6 lines, each line given the integer hi (1 ≤ hi ≤ 1000) for the vertical length of each rectangle and the integer wi (1 ≤ wi ≤ 1000) for the horizontal length.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
2 2
2 3
2 3
2 3
2 2
3 2
Output
yes
Input
2 2
2 3
2 3
2 3
2 2
2 2
Output
no | #include <bits/stdc++.h>
using namespace std;
using namespace std::chrono;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<double,double> pdd;
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) _rep2(i,n)
#define _rep2(i,n) _rep3(i,0,n)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) _rrep2(i,n)
#define _rrep2(i,n) _rrep3(i,0,n)
#define _rrep3(i,a,b) for(ll i=b-1;i>=a;i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto&& i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
const ll LINF=0x3fffffffffffffff;
const ll MOD=1000000007;
const ll MODD=0x3b800001;
const int INF=0x3fffffff;
#define yes(i) out(i?"yes":"no")
#define Yes(i) out(i?"Yes":"No")
#define YES(i) out(i?"YES":"NO")
#define Possible(i)out(i?"Possible":"Impossible")
#define unless(a) if(!(a))
//#define START auto start=system_clock::now()
//#define END auto end=system_clock::now();cerr<<duration_cast<milliseconds>(end-start).count()<<" ms\n"
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__);
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define pll pair<ll,ll>
struct SETTINGS{SETTINGS(){cin.tie(0); cout.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);};}SETTINGS;
template<typename T>
inline bool update_min(T& mn,const T& cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;}
template<typename T>
inline bool update_max(T& mx,const T& cnt){if(mx<cnt){mx=cnt;return 1;}else return 0;}
template<typename T>
inline T max(vector<T>& vec){return *max_element(range(vec));}
template<typename T>
inline constexpr T gcd (T a,T b) {if(a==b)return a;else return gcd(b,(a-1)%b+1);}
inline void in() {}
template<typename T>
istream& operator >> (istream& is, vector<T>& vec);
template<typename T,size_t size>
istream& operator >> (istream& is, array<T,size>& vec);
template<typename T,typename L>
istream& operator >> (istream& is, pair<T,L>& p);
template<typename T>
ostream& operator << (ostream& os, vector<T>& vec);
template<typename T,typename L>
ostream& operator << (ostream& os, pair<T,L>& p);
template<typename T>
istream& operator >> (istream& is, vector<T>& vec){for(T& x: vec) is >> x;return is;}
template<typename T,typename L>
istream& operator >> (istream& is, pair<T,L>& p){is >> p.first;is >> p.second;return is;}
template<typename T>
ostream& operator << (ostream& os, vector<T>& vec){os << vec[0];rep(i,1,vec.size()){os << ' ' << vec[i];}return os;}
template<typename T>
ostream& operator << (ostream& os, deque<T>& vec){os << vec[0];rep(i,1,vec.size()){os << ' ' << vec[i];}return os;}
template<typename T,typename L>
ostream& operator << (ostream& os, pair<T,L>& p){os << p.first << " " << p.second;return os;}
template <class Head, class... Tail>
inline void in(Head&& head,Tail&&... tail){cin>>head;in(move(tail)...);}
template <typename T>
inline void out(T t){cout<<t<<endl;}
inline void out(){cout<<'\n';}
template <class Head, class... Tail>
inline void out(Head head,Tail... tail){cout<<head<<' ';out(move(tail)...);}
signed main(){
vv(int,a,6,2);
in(a);
rep(6)sort(range(a[i]));
sort(range(a));
if(a[0]!=a[1]||a[2]!=a[3]||a[4]!=a[5])return puts("no")&0;
rep(2)rep(j,2)if(a[0][0]==a[2][1^i]&&a[2][0^i]==a[4][1^j]&&a[4][0^j]==a[0][1])return puts("yes")&0;
yes(0);
}
|
problem
Chairman K is a regular customer of the JOI pizza shop in the center of JOI city. For some reason, he decided to start a life-saving life this month. So he wanted to order the pizza with the highest calories per dollar among the pizzas he could order at the JOI pizza store. Let's call such a pizza the "best pizza". The "best pizza" is not limited to one type.
At JOI Pizza, you can freely choose from N types of toppings and order the ones placed on the basic dough. You cannot put more than one topping of the same type. You can also order a pizza that doesn't have any toppings on the dough. The price of the dough is $ A and the price of the toppings is $ B. The price of pizza is the sum of the price of the dough and the price of the toppings. That is, the price of a pizza with k types of toppings (0 ≤ k ≤ N) is A + k x B dollars. The total calorie of the pizza is the sum of the calories of the dough and the calories of the toppings placed.
Create a program to find the number of calories per dollar for the "best pizza" given the price of the dough and the price of the toppings, and the calorie value of the dough and each topping.
input
The input consists of N + 3 lines.
On the first line, one integer N (1 ≤ N ≤ 100) representing the number of topping types is written. On the second line, two integers A and B (1 ≤ A ≤ 1000, 1 ≤ B ≤ 1000) are written with a blank as a delimiter. A is the price of the dough and B is the price of the toppings. On the third line, one integer C (1 ≤ C ≤ 10000) representing the number of calories in the dough is written.
On the 3 + i line (1 ≤ i ≤ N), one integer Di (1 ≤ Di ≤ 10000) representing the number of calories in the i-th topping is written.
output
Print the number of calories per dollar for the "best pizza" in one line. However, round down the numbers after the decimal point and output as an integer value.
Input / output example
Input example 1
3
12 2
200
50
300
100
Output example 1
37
In I / O Example 1, with the second and third toppings, 200 + 300 + 100 = 600 calories gives a pizza of $ 12 + 2 x 2 = $ 16.
This pizza has 600/16 = 37.5 calories per dollar. Since this is the "best pizza", we output 37, rounded down to the nearest whole number of 37.5.
Input example 2
Four
20 3
900
300
100
400
1300
Output example 2
100
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
3
12 2
200
50
300
100
Output
37 | import java.util.Scanner;
import java.util.Arrays;
public class Main{
public static void main(String[] args){
new Main().run();
}
public void run(){
Scanner scan = new Scanner(System.in);
int n = scan.nextInt();
int a = scan.nextInt();
int b = scan.nextInt();
int cal = scan.nextInt();
int max = cal / a;
int[] t = new int[n];
for(int i = 0;i < n;i++){
t[i] = scan.nextInt();
}
Arrays.sort(t);
int tc;
for(int k = 1,i = n-1;i >= 0;i--,k++){
cal += t[i];
tc = cal / (k*b + a);
if(max <= tc){
max = tc;
}else{
break;
}
}
System.out.println(max);
}
} |
Problem
KND is a student programmer at the University of Aizu. His chest is known to be very sexy.
<image>
For simplicity, the part of the skin that can be seen from the chest is represented by the isosceles triangle ABC in the figure. However, due to the slack in the clothes, the two sides AC and BC (where these lengths are l), which have the same length, actually have an additional length x minutes. In order to increase the area of the open part, let's make two new triangular ADCs and BECs by pulling the slack part. Points D and E exist outside the triangle ABC. These two new triangles are caused by slack, and the sum of the lengths of side BE and side EC and the sum of the lengths of side AD and side DC must be l + x. You determine the points D and E so that the sum M of the areas of these three triangles is maximized. As KND's neighbor, you decide to write a program to calculate the maximum area of skin (M) to look out of your clothes, using a, l, x as inputs to find out how sexy his chest is. did.
Constraints
The input satisfies the following conditions.
* All inputs are integers.
* 1 ≤ a ≤ 1000
* 1 ≤ l ≤ 1000
* 1 ≤ x ≤ 1000
Input
The input consists of multiple test cases. One test case is given in the following format. The end of input is indicated by EOF.
a l x
here,
* a: Length of side AB of triangle ABC
* l: Length of two sides AC and BC of triangle ABC
* x: Slack on two sides AC, BC
Is.
Output
Output the maximum area for each test case on one line. This value should not differ more than 10-5 from the value of the judge output.
Example
Input
2 2 1
2 3 1
3 2 3
2 3 5
Output
3.9681187851
6.7970540913
6.5668891783
13.9527248554 | #include "bits/stdc++.h"
using namespace std;
//#define int long long
#define DBG 1
#define dump(o) if(DBG){cerr<<#o<<" "<<(o)<<" ";}
#define dumpl(o) if(DBG){cerr<<#o<<" "<<(o)<<endl;}
#define dumpc(o) if(DBG){cerr<<#o; for(auto &e:(o))cerr<<" "<<e;cerr<<endl;}
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9 + 7);
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; }
//Heron's formula
double area(double a, double b, double c) {
double s = (a + b + c) / 2;
return sqrt(s*(s - a)*(s - b)*(s - c));
}
signed main() {
cout << fixed << setprecision(8);
for (double a, l, x; cin >> a >> l >> x&&l;)
cout << area(a, l, l) + area(l, (l + x) / 2, (l + x) / 2) * 2 << endl;
return 0;
} |
The King of a little Kingdom on a little island in the Pacific Ocean frequently has childish ideas. One day he said, “You shall make use of a message relaying game when you inform me of something.” In response to the King’s statement, six servants were selected as messengers whose names were Mr. J, Miss C, Mr. E, Mr. A, Dr. P, and Mr. M. They had to relay a message to the next messenger until the message got to the King.
Messages addressed to the King consist of digits (‘0’-‘9’) and alphabet characters (‘a’-‘z’, ‘A’-‘Z’). Capital and small letters are distinguished in messages. For example, “ke3E9Aa” is a message.
Contrary to King’s expectations, he always received wrong messages, because each messenger changed messages a bit before passing them to the next messenger. Since it irritated the King, he told you who are the Minister of the Science and Technology Agency of the Kingdom, “We don’t want such a wrong message any more. You shall develop software to correct it!” In response to the King’s new statement, you analyzed the messengers’ mistakes with all technologies in the Kingdom, and acquired the following features of mistakes of each messenger. A surprising point was that each messenger made the same mistake whenever relaying a message. The following facts were observed.
Mr. J rotates all characters of the message to the left by one. For example, he transforms “aB23d” to “B23da”.
Miss C rotates all characters of the message to the right by one. For example, she transforms “aB23d” to “daB23”.
Mr. E swaps the left half of the message with the right half. If the message has an odd number of characters, the middle one does not move. For example, he transforms “e3ac” to “ace3”, and “aB23d” to “3d2aB”.
Mr. A reverses the message. For example, he transforms “aB23d” to “d32Ba”.
Dr. P increments by one all the digits in the message. If a digit is ‘9’, it becomes ‘0’. The alphabet characters do not change. For example, he transforms “aB23d” to “aB34d”, and “e9ac” to “e0ac”.
Mr. M decrements by one all the digits in the message. If a digit is ‘0’, it becomes ‘9’. The alphabet characters do not change. For example, he transforms “aB23d” to “aB12d”, and “e0ac” to “e9ac”.
The software you must develop is to infer the original message from the final message, given the order of the messengers. For example, if the order of the messengers is A -> J -> M -> P and the message given to the King is “aB23d”, what is the original message? According to the features of the messengers’ mistakes, the sequence leading to the final message is
A J M P
“32Bad” --> “daB23” --> “aB23d” --> “aB12d” --> “aB23d”.
As a result, the original message should be “32Bad”.
Input
The input format is as follows.
n
The order of messengers
The message given to the King
.
.
.
The order of messengers
The message given to the King
The first line of the input contains a positive integer n, which denotes the number of data sets. Each data set is a pair of the order of messengers and the message given to the King. The number of messengers relaying a message is between 1 and 6 inclusive. The same person may not appear more than once in the order of messengers. The length of a message is between 1 and 25 inclusive.
Output
The inferred messages are printed each on a separate line.
Example
Input
5
AJMP
aB23d
E
86AE
AM
6
JPEM
WaEaETC302Q
CP
rTurnAGundam1isdefferentf
Output
32Bad
AE86
7
EC302QTWaEa
TurnAGundam0isdefferentfr | #include<bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(n); i++)
#define INF 1e8
using namespace std;
bool is_digit(char x){
for(int i=48; i<=57; i++){
if(x == i) return true;
}
return false;
}
int main(){
int n;
cin >> n;
rep(k,n){
string s,t;
cin >> s >> t;
for(int i=s.size()-1; i>=0; i--){
//cout << t << endl;
if(s[i] == 'J') rotate(t.rbegin(),t.rbegin()+1,t.rend());
if(s[i] == 'C') rotate(t.begin(),t.begin()+1,t.end());
if(s[i] == 'E') {
rep(j,t.size()/2){
swap(t[j],t[t.size()-t.size()/2+j]);
}
}
if(s[i] == 'A') reverse(t.begin(),t.end());
if(s[i] == 'P') {
rep(j,t.size()){
if(is_digit(t[j])) {
if(t[j] == 48) t[j] = 57;
else t[j]--;
}
}
}
if(s[i] == 'M') {
rep(j,t.size()){
if(is_digit(t[j])) {
if(t[j] == 57) t[j] = 48;
else t[j]++;
}
}
}
}
cout << t << endl;
}
return 0;
}
|
Example
Input
ACM
Output
0 | #include <bits/stdc++.h>
using namespace std;
typedef pair<string,string> P;
int bnf();
set<P> used;
map<char,int> M;
string S;
int idx,valid;
char ch[8]={'0','1','+','-','*','(',')','='};
int ord[8];
bool check(string a){//??????????????????°???¨???????????????????????¢????
int par=0;
for(char s:a){
par += (s == '(') - (s == ')');
if(s == '=') return 0;
if(par < 0) return 0;
}
return par==0;
}
int getNum(){ //???????????????°????????????
int res = 0;
if(S[idx] == '0' && isdigit(S[idx+1])) valid = 0;
while(isdigit(S[idx]))res = res*2 + S[idx++]-'0';
return res;
}
int cal(){
char ch = S[idx];
int res = 0,sign = 1;
if(ch=='+'||ch=='*'||ch==')'){ valid = 0;return 0;}
while(S[idx] == '-') idx++, sign *= -1;
ch = S[idx];
if(isdigit(ch)){
res = sign*getNum();
if(S[idx] == '*'){idx++; return res * cal();}
return res;
}
else if(ch == '(') {
idx++;res = sign*bnf();idx++;
return res;
}
valid = 0;
return 0;
}
int bnf(){
int res = cal();
while(idx<(int)S.size()){
if(valid == 0) return -1;
char ch = S[idx];
if(ch == '('){valid = 0;}
else if(ch == '*'){idx++;res *= cal();}
else if(ch == '+'){idx++;res += cal();}
else if(ch == '-'){idx++;res -= cal();}
else if(ch != ')') valid = 0;
else break;
}
if(valid ==0) return -1;
return res;
}
string mkS(string a){
string res;
for(char s:a){
if(isalpha(s))res += ch[ ord[ M[s] ] ];
else res += s;
}
return res;
}
int calc(string A,string B){
if(A.size()==0 || B.size()==0) return 0;
if(used.count(P(A,B)))return 0;
used.insert(P(A,B));
valid = check(A) && check(B);
idx = 0;
S = A;
int ra = bnf();
idx = 0;
S = B;
int rb = bnf();
//if(valid)cout<<A<<"="<<B<<" "<<valid<<" "<<ra<<" "<<rb<<endl;
return ra == rb && valid;
}
int calc(string s){
s = mkS(s);
for(int i=0;i<(int)s.size();i++)
if(s[i]=='=') return calc(s.substr(0,i),s.substr(i+1,s.size()-i-1));
return 0;
}
int dfs(int num,string &s){
if(num == 8) return calc(s);
int res = 0;
for(int i=0;i<8;i++){
if(ord[i] != -1)continue;
ord[i] = num;
res +=dfs(num+1,s);
ord[i] = -1;
}
return res;
}
int main(){
string str;
cin>>str;
if(str.size()<3)cout<<0<<endl,exit(0);
map<char,int> cnt;
for(int i=0;i<(int)str.size();i++)if(isalpha(str[i]))cnt[str[i]]++;
if(cnt.size()>8)cout<<0<<endl,exit(0);
int c = 0;
for(pair<char,int> p:cnt)if(isalpha(p.first)) M[p.first] = c++;
memset(ord,-1,sizeof(ord));
cout<<dfs(0,str)<<endl;
return 0;
} |
Story
At UZIA High School in the sky city AIZU, the club activities of competitive programming are very active. N Red Coders and n Blue Coders belong to this club.
One day, during club activities, Red Coder and Blue Coder formed a pair, and from this club activity, n groups participated in a contest called KCP. At this high school, it is customary for paired students to shake hands, so the members decided to find their partner right away.
The members run at full speed, so they can only go straight. In addition, the members want to make the total distance traveled by each member as small as possible.
There are two circular tables in the club room.
Problem
There are two circles, n red dots, and n blue dots on a two-dimensional plane. The center coordinates of the two circles are (x1, y1) and (x2, y2), respectively, and the radii are r1 and r2, respectively. The red point i is at the coordinates (rxi, ryi) and the blue point j is at the coordinates (bxj, by j).
You need to repeat the following operation n times.
Select one red point and one blue point from the points that have not been selected yet, set two common destinations, and move each of the two points straight toward that destination. The destination may be set anywhere as long as it is on a two-dimensional plane. However, since the selected two points cannot pass through the inside of the circle when moving, it is not possible to set the destination where such movement occurs.
Minimize the total distance traveled after n operations. If you cannot perform n operations, output "Impossible" (excluding "") instead.
Constraints
The input satisfies the following conditions.
* 1 ≤ n ≤ 100
* -1000 ≤ xi, yi ≤ 1000
* 1 ≤ ri ≤ 50
* -1000 ≤ rxi, ryi, bxi, byi ≤ 1000
* There can never be more than one point at the same coordinates
* Even if the radius of any circle is changed within the absolute value of 10-9, only the absolute value of 10-3 changes at most.
* Even if the radius of any circle is changed within the absolute value of 10-9, the "Impossible" case remains "Impossible".
* The solution does not exceed 10000
* All points are more than 10-3 away from the circle, and the points are not on the circumference or contained in the circle.
* The two circles do not have a common area and are guaranteed to be at least 10-3 apart.
Input
The input is given in the following format.
n
x1 y1 r1
x2 y2 r2
rx1 ry1
rx2 ry2
...
rxn ryn
bx1 by1
bx2 by2
...
bxn byn
All inputs are given as integers.
N is given on the first line.
The second line is given x1, y1, r1 separated by blanks.
On the third line, x2, y2, r2 are given, separated by blanks.
Lines 4 to 3 + n are given the coordinates of the red points (rxi, ryi) separated by blanks.
The coordinates of the blue points (bxj, byj) are given on the 3 + 2 × n lines from 4 + n, separated by blanks.
Output
Output the minimum value of the total distance traveled when n operations are performed on one line. The output is acceptable if the absolute error from the output of the judge solution is within 10-2.
If you cannot perform n operations, output "Impossible" (excluding "") instead.
Examples
Input
2
3 3 2
8 3 2
0 3
3 7
8 0
8 7
Output
13.8190642862
Input
2
3 3 2
8 3 2
3 0
3 7
8 0
8 7
Output
10.0000000000
Input
2
3 3 2
8 3 2
0 0
0 5
11 0
11 5
Output
22.0000000000
Input
1
10 10 10
31 10 10
15 19
26 1
Output
Impossible | #include <iostream>
#include <iomanip>
#include <complex>
#include <vector>
#include <algorithm>
#include <cmath>
#include <array>
using namespace std;
const double EPS = 1e-5;
const double INF = 1e12;
const double PI = acos(-1);
#define EQ(n,m) (abs((n)-(m)) < EPS)
#define X real()
#define Y imag()
typedef complex<double> P;
typedef vector<P> VP;
struct L : array<P, 2>{
L(const P& a, const P& b){ at(0)=a; at(1)=b; }
L(){}
};
struct C{
P p;
double r;
C(const P& p, const double& r) : p(p), r(r) {}
C(){}
};
namespace std{
bool operator < (const P& a, const P& b){
return !EQ(a.X,b.X) ? a.X<b.X : a.Y+EPS<b.Y;
}
bool operator == (const P& a, const P& b){
return abs(a-b) < EPS;
}
}
double dot(P a, P b){
return (conj(a)*b).X;
}
double cross(P a, P b){
return (conj(a)*b).Y;
}
int ccw(P a, P b, P c){
b -= a;
c -= a;
if(cross(b,c) > EPS) return +1; //ccw
if(cross(b,c) < -EPS) return -1; //cw
if(dot(b,c) < -EPS) return +2; //c-a-b
if(abs(c)-abs(b) > EPS) return -2; //a-b-c
return 0; //a-c-b
}
P unit(const P &p){
return p/abs(p);
}
P rotate(const P &p, double rad){
return p *P(cos(rad), sin(rad));
}
bool intersectSS(const L& a, const L& b){
return ( ccw(a[0],a[1],b[0]) *ccw(a[0],a[1],b[1]) <= 0 ) &&
( ccw(b[0],b[1],a[0]) *ccw(b[0],b[1],a[1]) <= 0 );
}
P projection(const L& l, const P& p) {
double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
return l[0] + t*(l[0]-l[1]);
}
double distanceLP(const L &l, const P &p) {
return abs(cross(l[1]-l[0], p-l[0])) /abs(l[1]-l[0]);
}
double distanceSP(const L &s, const P &p) {
if(dot(s[1]-s[0], p-s[0]) < EPS) return abs(p-s[0]);
if(dot(s[0]-s[1], p-s[1]) < EPS) return abs(p-s[1]);
return distanceLP(s, p);
}
bool isParallel(const P &a, const P &b){
return abs(cross(a,b)) < EPS;
}
bool isParallel(const L &a, const L &b){
return isParallel(a[1]-a[0], b[1]-b[0]);
}
P crosspointLL(const L &l, const L &m) {
double A = cross(l[1]-l[0], m[1]-m[0]);
double B = cross(l[1]-l[0], l[1]-m[0]);
return m[0] + B/A *(m[1]-m[0]);
}
VP crosspointCL(const C &c, const L &l){
VP ret;
P mid = projection(l, c.p);
double d = distanceLP(l, c.p);
if(EQ(d, c.r)){
ret.push_back(mid);
}else if(d < c.r){
double len = sqrt(c.r*c.r -d*d);
ret.push_back(mid +len*unit(l[1]-l[0]));
ret.push_back(mid -len*unit(l[1]-l[0]));
}
return ret;
}
vector<L> getTangentLine(const C &c, const P &p){
vector<L> ret;
P dir = p -c.p;
if(c.r +EPS < abs(dir)){
/*
P a = c.p + c.r*unit(dir);
VP cp = crosspointCL(C(c.p, abs(dir)), L(a, a+dir*P(0,1)));
for(P cpp: cp){
ret.push_back(L(p, c.p +c.r*unit(cpp-c.p)));
}
*/
double a = abs(dir);
double b = sqrt(a*a -c.r*c.r);
double psi = arg(p - c.p);
double phi = PI - acos(b/a);
ret.emplace_back(p, p + b *P(cos(psi+phi), sin(psi+phi)));
ret.emplace_back(p, p + b *P(cos(psi-phi), sin(psi-phi)));
}else if(abs(c.r -abs(dir)) < EPS){
ret.push_back(L(p, p +dir*P(0, 1)));
}
return ret;
}
struct edge{
int to, rev;
int cap;
double cost;
edge(int to, int rev, int cap, double cost)
:to(to),rev(rev),cap(cap),cost(cost){}
edge(){}
};
double min_cost_flow(int s, int g, int f, vector<vector<edge> > &adj){
int n = adj.size();
double res = 0;
while(f > 0){
vector<int> prevv(n), preve(n);
vector<double> mincost(n, INF);
mincost[s] = 0;
while(1){
bool update = false;
for(int i=0; i<n; i++){
if(mincost[i] == INF) continue;
for(int j=0; j<(int)adj[i].size(); j++){
edge &e = adj[i][j];
if(e.cap>0 && mincost[i] +e.cost +EPS < mincost[e.to]){
mincost[e.to] = mincost[i] +e.cost;
prevv[e.to] = i;
preve[e.to] = j;
update = true;
}
}
}
if(!update) break;
}
if(mincost[g] == INF){
return -1;
}
int d = f;
for(int v=g; v!=s; v=prevv[v]){
d = min(d, adj[prevv[v]][preve[v]].cap);
}
f -= d;
res += d*mincost[g];
for(int v=g; v!=s; v=prevv[v]){
edge &e = adj[prevv[v]][preve[v]];
e.cap -= d;
adj[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int n;
cin >> n;
vector<C> c(2);
for(int i=0; i<2; i++){
double x,y,r;
cin >> x >> y >> r;
c[i] = C(P(x, y), r);
}
vector<VP> pos(2, VP(n));
vector<vector<vector<L> > > tangent(2, vector<vector<L> >(n));
for(int d=0; d<2; d++){
for(int i=0; i<n; i++){
double x,y;
cin >> x >> y;
pos[d][i] = P(x, y);
vector<L> ret;
for(int dd=0; dd<2; dd++){
ret = getTangentLine(c[dd], pos[d][i]);
tangent[d][i].insert(tangent[d][i].end(), ret.begin(), ret.end());
}
}
}
//1点経由でのred[i] ~blue[j]の最小距離
vector<vector<double> > dist(n, vector<double>(n, INF));
for(int i=0; i<n; i++){
for(int j=0; j<n; j++){
VP cand;
cand.push_back((pos[0][i] +pos[1][j])/2.0);
for(L t1: tangent[0][i]){
for(L t2: tangent[1][j]){
if(!isParallel(t1, t2)){
cand.push_back(crosspointLL(t1, t2));
}
}
}
for(P cp: cand){
if(distanceSP(L(pos[0][i], cp), c[0].p) +EPS > c[0].r &&
distanceSP(L(pos[0][i], cp), c[1].p) +EPS > c[1].r &&
distanceSP(L(pos[1][j], cp), c[0].p) +EPS > c[0].r &&
distanceSP(L(pos[1][j], cp), c[1].p) +EPS > c[1].r){
dist[i][j] = min(dist[i][j], abs(pos[0][i] -cp) +abs(pos[1][j] -cp));
}
}
}
}
vector<vector<edge> > adj(2*n +2);
for(int i=0; i<n; i++){
for(int j=0; j<n; j++){
if(dist[i][j] == INF) continue;
adj[i+2].emplace_back(j+2+n, adj[j+2+n].size(), 1, dist[i][j]);
adj[j+2+n].emplace_back(i+2, adj[i+2].size()-1, 0, -dist[i][j]);
}
adj[0].emplace_back(i+2, adj[i+2].size(), 1, 0);
adj[i+2].emplace_back(0, adj[0].size()-1, 0, 0);
adj[i+2+n].emplace_back(1, adj[1].size(), 1, 0);
adj[1].emplace_back(i+2+n, adj[i+2+n].size()-1, 0, 0);
}
double ans = min_cost_flow(0, 1, n, adj);
if(ans == -1){
cout << "Impossible" << endl;
}else{
cout << fixed << setprecision(10);
cout << ans << endl;
}
return 0;
}
|
You are working as a private teacher. Since you are giving lessons to many pupils, you are very busy, especially during examination seasons. This season is no exception in that regard.
You know days of the week convenient for each pupil, and also know how many lessons you have to give to him or her. You can give just one lesson only to one pupil on each day. Now, there are only a limited number of weeks left until the end of the examination. Can you finish all needed lessons?
Input
The input consists of multiple data sets. Each data set is given in the following format:
N W
t1 c1
list-of-days-of-the-week
t2 c2
list-of-days-of-the-week
...
tN cN
list-of-days-of-the-week
A data set begins with a line containing two integers N (0 < N ≤ 100) and W (0 < W ≤ 1010 ). N is the number of pupils. W is the number of remaining weeks. The following 2N lines describe information about the pupils. The information for each pupil is given in two lines. The first line contains two integers ti and ci. ti (0 < ti ≤ 1010 ) is the number of lessons that the i-th pupil needs. ci (0 < ci ≤ 7) is the number of days of the week convenient for the i-th pupil. The second line is the list of ci convenient days of the week (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday).
The end of input is indicated by a line that contains two zeros. This line should not be processed.
Output
For each data set, print “Yes” if you can finish all lessons, or “No” otherwise.
Example
Input
2 2
6 3
Monday Tuesday Wednesday
8 4
Thursday Friday Saturday Sunday
2 2
7 3
Monday Tuesday Wednesday
9 4
Thursday Friday Saturday Sunday
0 0
Output
Yes
No | #include<cstdio>
#include<numeric>
#include<algorithm>
#define rep(i,n) for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
const int V_MAX=109;
const int E_MAX=1000;
template<class T>
struct graph{
int n,m,head[V_MAX],next[2*E_MAX],to[2*E_MAX];
T capa[2*E_MAX],flow[2*E_MAX];
void init(int N){
n=N;
m=0;
rep(u,n) head[u]=-1;
}
void add_directed_edge(int u,int v,T ca){
next[m]=head[u]; head[u]=m; to[m]=v; capa[m]=ca; flow[m]=0; m++;
next[m]=head[v]; head[v]=m; to[m]=u; capa[m]= 0; flow[m]=0; m++;
}
void add_undirected_edge(int u,int v,T ca){
next[m]=head[u]; head[u]=m; to[m]=v; capa[m]=ca; flow[m]=0; m++;
next[m]=head[v]; head[v]=m; to[m]=u; capa[m]=ca; flow[m]=0; m++;
}
};
const ll INF=1LL<<61;
int layer[V_MAX],now[V_MAX];
template<class T>
bool make_layer(const graph<T> &G,int s,int t){
int n=G.n;
rep(u,n) layer[u]=(u==s?0:-1);
int head=0,tail=0;
static int Q[V_MAX]; Q[tail++]=s;
while(head<tail && layer[t]==-1){
int u=Q[head++];
for(int e=G.head[u];e!=-1;e=G.next[e]){
int v=G.to[e];
T capa=G.capa[e],flow=G.flow[e];
if(capa-flow>0 && layer[v]==-1){
layer[v]=layer[u]+1;
Q[tail++]=v;
}
}
}
return layer[t]!=-1;
}
template<class T>
T augment(graph<T> &G,int u,int t,T water){
if(u==t) return water;
for(int &e=now[u];e!=-1;e=G.next[e]){
int v=G.to[e];
T capa=G.capa[e],flow=G.flow[e];
if(capa-flow>0 && layer[v]>layer[u]){
T w=augment(G,v,t,min(water,capa-flow));
if(w>0){
G.flow[ e ]+=w;
G.flow[e^1]-=w;
return w;
}
}
}
return 0;
}
template<class T>
T Dinic(graph<T> &G,int s,int t){
int n=G.n;
T ans=0;
while(make_layer(G,s,t)){
rep(u,n) now[u]=G.head[u];
for(T water=1;water>0;ans+=water) water=augment(G,s,t,INF);
}
return ans;
}
int main(){
int n;
for(ll W;scanf("%d%lld",&n,&W),n;){
bool aki[100][7]={};
ll need[100];
rep(i,n){
int m; scanf("%lld%d",need+i,&m);
rep(j,m){
char s[16]; scanf("%s",s);
if(s[0]=='S' && s[1]=='u') aki[i][0]=true;
if(s[0]=='M') aki[i][1]=true;
if(s[0]=='T' && s[1]=='u') aki[i][2]=true;
if(s[0]=='W') aki[i][3]=true;
if(s[0]=='T' && s[1]=='h') aki[i][4]=true;
if(s[0]=='F') aki[i][5]=true;
if(s[0]=='S' && s[1]=='a') aki[i][6]=true;
}
}
int s=n+7,t=s+1;
graph<ll> G;
G.init(n+9);
// source -> left nodes
rep(u,7) G.add_directed_edge(s,u,W);
// right nodes -> sink
rep(i,n){
int v=7+i;
G.add_directed_edge(v,t,need[i]);
}
// left nodes -> right nodes
rep(i,n) rep(j,7) if(aki[i][j]) {
int u=j,v=7+i;
G.add_directed_edge(u,v,W);
}
puts(Dinic(G,s,t)==accumulate(need,need+n,0LL)?"Yes":"No");
}
return 0;
} |
A rabbit is playing a role-playing game. Just before entering the castle, he was ambushed by an enemy!
It was a battle between one hero operated by a rabbit and n enemies. Each character has four stats, health hi, attack power ai, defense power di, and agility si. I = 0 is the information of the main character, 1 ≤ i ≤ n is the information of each enemy.
The battle is turn-based. Each turn, the surviving characters attack in descending order of agility. The enemy always attacks the hero. The hero attacks one enemy, but which enemy to attack Can be selected by the main character every turn. When a character with attack power a attacks a character with defense power d, max {a − d, 0} damage is dealt. The total damage received is greater than or equal to the value of physical strength. The character becomes incapacitated immediately. The battle ends when the main character becomes incapacitated, or when all the enemies become incapacitated.
Input
1 ≤ n ≤ 40 000
1 ≤ hi, ai, di, si ≤ 1 000 000 000 (integer)
si are all different.
Output
When the hero is sure to be incapacitated, output -1. Otherwise, output the minimum total damage to the hero in one line.
Examples
Input
2
10 3 1 2
2 4 1 3
2 2 1 1
Output
4
Input
1
1 1 1 1
10000 10000 10000 10000
Output
-1 | #include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
using namespace std;
using ll = long long;
struct Data {
ll h, a, d, s;
Data() {}
Data(ll h, ll a, ll d, ll s) :
h{h}, a{a}, d{d}, s{s} {}
bool operator < (const Data& d) const {
return s < d.s;
}
};
istream& operator >> (istream& is, Data& d)
{
return is >> d.h >> d.a >> d.d >> d.s;
}
ll solve(Data& M, vector<Data>& ene)
{
vector<pair<double, Data>> v;
for (const Data& e : ene) {
if (M.a <= e.d && M.d < e.a) return -1;
ll turn = ceil((double)e.h / (M.a - e.d));
if (e.a - M.d <= 0) continue;
v.emplace_back((double)turn / (e.a - M.d), e);
}
sort(v.begin(), v.end());
ll res = 0, total_turn = 0;
for (const auto& d : v) {
Data e = d.second;
ll turn = ceil((double)e.h / (M.a - e.d));
total_turn += turn;
ll damage = (total_turn - (M.s > e.s)) * max(0LL, e.a - M.d);
M.h -= damage;
if (M.h <= 0) return -1;
res += damage;
}
return res;
}
int main()
{
int N;
cin >> N;
Data M;
cin >> M;
vector<Data> ene(N);
for (int i = 0; i < N; i++) {
cin >> ene[i];
}
cout << solve(M, ene) << endl;
return 0;
} |
E: Markup language has declined
It's been centuries since we humans have been declining slowly. The earth may already belong to "Progurama". Programa-sans with an average height of 170 cm, 7 heads, high intelligence, and loves Kodingu. I have returned to my hometown of Nibunki, becoming an important international civil servant, "Esui," who is in charge of the relationship between Mr. Programa and people. I chose this job because it's a job that I can do even at my grandfather's age, so I thought it would be easy.
One day, Mr. Programa and his colleagues gave me something like two design documents. According to Mr. Programa, various information can be easily exchanged using texts and scripts.
The first design document was an explanation of the file that represents the sentence structure. The filename of this file ends with .dml and is called a DML file.
In the DML file, the structure of the sentence is expressed by sandwiching it with a character string called a tag. There are start tag and end tag as tags.
<Start tag name> Contents </ end tag name>
It is represented by the element of. At this time, the start tag name and the end tag name are represented by the same character string.
Tags can be nested and can be <tagA> <tagB> </ tagB> </ tagA>. Also, structures like <tagA> <tagB> </ tagA> </ tagB> are not allowed.
The tag name in the DML file is an arbitrary character string except for some special ones. The following five special tags are available.
* Tag name: dml
* Represents the roots of all tags.
* This start tag always appears only once at the beginning of the file, and the end tag of this tag appears only once at the end of the file.
* Tag name: script
* It always appears at the beginning of the dml tag or at the end tag.
* This tag cannot have a nested structure inside.
* Associate the script file enclosed in this tag.
* The character string enclosed in this tag is not output.
* Tag name: br
* A line break will be performed when displaying.
* Does not have an end tag.
* Tag name: link
* This tag cannot have a nested structure inside.
* When the user clicks on the character string enclosed in this tag, the entire current screen is erased and the DML file with the file name represented by that character string is displayed.
* Tag name: button
* This tag cannot have a nested structure inside.
* When the user clicks on the character string enclosed in this tag, the subroutine with the name represented by that character string is executed from the scripts associated with the script tag.
Tag names are represented only in uppercase and lowercase letters. No spaces appear in the tag name. The character strings that appear in the DML file are uppercase and lowercase letters, spaces,'<','>', and'/'. It is also possible that a tag with the same name exists.
Character strings other than tags enclosed by other than script tags are output left-justified from the upper left (0, 0) of the screen, and line breaks do not occur until the screen edge or br tag appears.
The second design document was an explanation of the DS file that shows the operation when the button is pressed in the DML file. Subroutines are arranged in the DS file.
Subroutine name {
formula;
formula;
...;
}
The semicolon marks the end of the expression.
For example, suppose you have a sentence in a DML file that is enclosed in <title>? </ Title>. The possible expressions at that time are the following four substitution expressions.
title.visible = true;
title.visible = false;
title.visible! = true;
title.visible! = false;
Assigning a boolean value to visible changes whether the content of the tag is displayed or not. If it disappears, the text after that will be packed to the left. When the currently displayed DML file is rewritten by clicking the link tag at the beginning, the initial values are all true.
'! ='Represents a negative assignment. In the above example, the 1st and 4th lines and the 2nd and 3rd lines are equivalent, respectively.
The expression can also change multiple values at the same time as shown below.
titleA.visible = titleB.visible = true;
At this time, processing is performed in order from the right. That is,
titleB.visible = true;
titleA.visible = titleB.visible;
Is equivalent to the two lines of. However, this representation is for convenience only, and the tag is not specified on the far right of the statement in the script. Also,
titleA.visible! = titleB.visible = true;
Is
titleB.visible = true;
titleA.visible! = titleB.visible;
Is equivalent to.
The tag is specified by narrowing down with'.'. For example
dml.body.title
Refers to the title tag, which is surrounded by the dml tag and the body tag. However, the script tag and br tag are not used or specified for narrowing down.
At this time, please note that the elements to be narrowed down are not always directly enclosed. For example, when <a> <b> <c> </ c> </ b> </a>, both a.b.c and a.c can point to c.
Also, if there are tags with the same name, the number of specified tags is not limited to one. If the specified tag does not exist, the display will not be affected, but if it appears when changing multiple values at the same time, it will be evaluated as if it existed.
BNF is as follows.
<script_file> :: = <subroutine> | <script_file> <subroutine>
<subroutine> :: = <identifier>'{' <expressions>'}'
<expressions> :: = <expression>';' | <expressions> <expression>';'
<expression> :: = <visible_var>'=' <visible_exp_right>
| <visible_var>'! ='<Visible_exp_right>
| <visible_var>'=' <expression>
| <visible_var>'! ='<Expression>
<visible_exp_right> :: ='true' |'false'
<visible_var> :: = <selector>'.visible'
<selector> :: = <identifier> | <selector>'.' <Identifier>
<identifier> :: = <alphabet> | <identifier> <alphabet>
<alphabet> :: ='a' |'b' |'c' |'d' |'e' |'f' |'g'
|'H' |'i' |'j' |'k' |'l' |'m' |'n'
|'o' |'p' |'q' |'r' |'s' |'t' |'u'
|'v' |'w' |'x' |'y' |'z'
|'A' |'B' |'C' |'D' |'E' |'F' |'G'
|'H' |'I' |'J' |'K' |'L' |'M' |'N'
|'O' |'P' |'Q' |'R' |'S' |'T' |'U'
|'V' |'W' |'X' |'Y' |'Z'
It's going to hurt my head. Isn't it? Is that so.
The user clicks the coordinates (x, y) on the screen after the first DML file is displayed. Then, the screen changes according to the link or button at that location. What if I click anywhere else? Nothing happens. As expected.
What can we do? I will watch over while handing over my favorite food, Enajido Rinku.
Input
The input is given in the following format.
N
filename1
file1
filename2
file2
...
filenameN
fileN
M
w1 h1 s1 startfile1
x11 y11
...
x1s1 y1s1
...
wM hM sM startfileM
xM1 y11
...
xMsM yMsM
...
N (1 <= N <= 20) represents the number of files, after which the file name and the contents of the file are given alternately. filename is represented by any 16 letters of the alphabet plus'.dml' or'.ds'. If it ends with'.dml', it is a DML file, and if it ends with'.ds', it is a DS file. The character string of the file is given in one line and is 500 characters or less.
M (1 <= M <= 50) represents the number of visiting users. For each user, screen width w, height h (1 <= w * h <= 500), number of operations s (0 <= s <= 50), start DML file name, and clicked coordinates of line s x, y (0 <= x <w, 0 <= y <h) is given.
There are no spaces in the DS file. Also, the tags in the given DML file are always closed. The subroutine name with the same name does not appear in the script throughout the input.
Output
Output the final screen with width w and height h for each user. The part beyond the lower right of the screen is not output. If there are no more characters to output on a certain line, output'.' Until the line becomes w characters.
Sample Input 1
1
index.dml
<dml> <title> Markup language has Declined </ title> <br> Programmers world </ dml>
1
15 3 0 index
Sample Output 1
Markup language
has Declined ..
Programmers wor
Sample Input 2
2
hello.dml
<dml> <link> cut </ link> </ dml>
cut.dml
<dml> hello very short </ dml>
1
10 2 1 hello
Ten
Sample Output 2
hello very
short ....
Sample Input 3
2
index.dml
<dml> <script> s </ script> slip <fade> akkariin </ fade> <br> <button> on </ button> <button> off </ button> </ dml>
s.ds
on {fade.visible = true;} off {fade.visible! = true;}
2
15 3 0 index
15 3 3 index
3 1
1 1
3 1
Sample Output 3
slipakkariin ...
on off .........
...............
slip ..........
on off .........
...............
Example
Input
1
index.dml
<dml><title>Markup language has Declined</title><br>Programmers world</dml>
1
15 3 0 index
Output
Markup language
has Declined..
Programmers wor | #include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <iostream>
#include <vector>
#include <map>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
struct Node;
struct Fun;
int h, w, cr, cc;
char scr[512][512];
Node *lnk[512][512];
Fun *evt[512][512];
map<string, vector<pair<string, Fun*> > > scrp;
map<string, Node*> dmls;
map<string, Fun*> funs;
Node *act;
void newline() {
cr++;
cc = 0;
}
void draw(const string& s, Node *hl, Fun *fn) {
rep (i, s.size()) {
if (0 <= cr && cr < h && 0 <= cc && cc < w) {
scr[cr][cc] = s[i];
lnk[cr][cc] = hl;
evt[cr][cc] = fn;
cc++;
}
if (cc == w) newline();
}
}
struct Node {
string tag;
string text;
vector<Node*> cs;
bool visible;
Node(const string& tag) : tag(tag), visible(true) {}
void dump() const { dump(0); }
void dump(int dep) const {
rep (_, dep) cerr << ' ';
cerr << '<' << tag << '>';
cerr << " visi = " << visible;
cerr << " text = " << text << endl;
rep (i, cs.size()) cs[i]->dump(dep+2);
rep (_, dep) cerr << ' ';
cerr << "</" << tag << '>' << endl;;
}
void render() const {
if (!visible) return ;
if (tag == "$text") draw(text, 0, 0);
else if (tag == "script") ;
else if (tag == "link") {
assert(cs.size() == 1 && cs[0]->tag == "$text");
assert(dmls[cs[0]->text]);
draw(cs[0]->text, dmls[cs[0]->text], 0);
}
else if (tag == "button") {
assert(cs.size() == 1 && cs[0]->tag == "$text");
//assert(funs[cs[0]->text]);
draw(cs[0]->text, 0, funs[cs[0]->text]);
}
else if (tag == "br") newline();
else {
rep (i, cs.size()) cs[i]->render();
}
}
void init() {
visible = true;
if (tag == "script") {
assert(cs.size() == 1 && cs[0]->tag == "$text");
string file = cs[0]->text;
vector<pair<string, Fun*> > fs = scrp[file];
rep (i, fs.size()) {
funs[fs[i].first] = fs[i].second;
}
}
rep (i, cs.size()) cs[i]->init();
}
void apply(const vector<string>& vs, int k, bool visi) {
if (vs[k] == tag) {
if (k == (int)vs.size()-1) {
visible = visi;
}
else {
k++;
}
}
rep (i, cs.size()) cs[i]->apply(vs, k, visi);
}
};
struct Fun {
vector<pair<vector<string>, bool> > asn;
void exec() {
rep (i, asn.size()) {
act->apply(asn[i].first, 0, asn[i].second);
}
}
};
vector<string> lex_dml(const string& s) {
vector<string> ts;
int pos = 0;
rep (i, s.size()) {
if (s[i] == '<') {
ts.push_back(s.substr(pos, i-pos));
pos = i;
}
else if (s[i] == '>') {
ts.push_back(s.substr(pos, i+1-pos));
pos = i+1;
}
}
ts.push_back(s.substr(pos));
return ts;
}
bool isbegin(const string& t) {
if (t.size() < 3) return false;
if (t[0] != '<' || t[t.size()-1] != '>') return false;
for (int i = 1; i < (int)t.size()-1; i++) {
assert(t[i] != ' ');
if (!islower(t[i]) && !isupper(t[i])) return false;
}
return true;
}
bool isend(const string& t) {
if (t.size() < 4) return false;
if (t[0] != '<' || t[1] != '/' || t[t.size()-1] != '>') return false;
for (int i = 2; i < (int)t.size()-1; i++) {
assert(t[i] != ' ');
if (!islower(t[i]) && !isupper(t[i])) return false;
}
return true;
}
Node *parse_dml(const vector<string>& ts) {
Node *root = new Node("$root");
vector<Node*> stk;
stk.push_back(root);
rep (i, ts.size()) {
if (ts[i].size() == 0) continue;
if (isbegin(ts[i])) {
Node *node = new Node(ts[i].substr(1, ts[i].size()-2));
stk.back()->cs.push_back(node);
if (ts[i] != "<br>") stk.push_back(node);
}
else if (isend(ts[i])) {
assert(stk.back()->tag == ts[i].substr(2, ts[i].size()-3));
stk.pop_back();
}
else {
Node *node = new Node("$text");
node->text = ts[i];
stk.back()->cs.push_back(node);
}
}
assert(stk.size() == 1);
return root;
}
vector<string> parse_prop(const string& s) {
vector<string> ps;
int pos = 0;
rep (i, s.size()) {
if (s[i] == '.') {
ps.push_back(s.substr(pos, i-pos));
pos = i+1;
}
}
assert(s.substr(pos) == "visible");
return ps;
}
string _s;
unsigned _ix;
vector<pair<vector<string>, bool> > parse_expr() {
unsigned pos = _ix;
vector<string> props;
vector<bool> rev;
while (_s[_ix] != ';') {
if (_s[_ix] == '!' || _s[_ix] == '=') {
props.push_back(_s.substr(pos, _ix-pos));
if (_s[_ix] == '!') {
_ix += 2;
pos = _ix;
rev.push_back(true);
}
else {
_ix += 1;
pos = _ix;
rev.push_back(false);
}
}
else {
_ix++;
}
}
string val = _s.substr(pos, _ix-pos);
bool cur = val == "true";
vector<pair<vector<string>, bool> > rs;
for (int i = (int)props.size()-1; i >= 0; i--) {
if (rev[i]) cur = !cur;
// cerr << props[i] << " = " << cur << endl;
rs.push_back(make_pair(parse_prop(props[i]), cur));
}
_ix++;
return rs;
}
pair<string, Fun*> parse_fun() {
Fun *fun = new Fun();
const unsigned st = _ix;
while (_s[_ix] != '{') _ix++;
const string id = _s.substr(st, _ix-st);
_ix++;
// cerr << id << endl;
while (_s[_ix] != '}') {
vector<pair<vector<string>, bool> > es(parse_expr());
rep (i, es.size()) fun->asn.push_back(es[i]);
}
_ix++;
return make_pair(id, fun);
}
vector<pair<string, Fun*> > parse_ds(const string& s) {
_s = s;
_ix = 0;
vector<pair<string, Fun*> > fs;
while (_ix < _s.size()) {
fs.push_back(parse_fun());
}
return fs;
}
void render(Node *file) {
rep (i, h) rep (j, w) {
scr[i][j] = '.';
lnk[i][j] = 0;
evt[i][j] = 0;
}
cr = cc = 0;
file->render();
act = file;
}
void click(int x, int y) {
if (lnk[y][x]) {
funs.clear();
lnk[y][x]->init();
render(lnk[y][x]);
}
else if (evt[y][x]) {
evt[y][x]->exec();
render(act);
}
}
void getl(string& s) {
getline(cin, s);
assert(s.size() == 0 || s[s.size()-1] != '\r');
}
int main() {
string s;
getl(s);
const int n = atoi(s.c_str());
rep (_, n) {
getl(s);
if (s.substr(s.size()-4) == ".dml") {
const string file = s.substr(0, s.size()-4);;
// cerr << file << endl;
getl(s);
vector<string> ts = lex_dml(s);
// rep (i, ts.size()) cerr << i << ": " << ts[i] << endl;
Node *root = parse_dml(ts);
// root->dump();
dmls[file] = root;
}
else if (s.substr(s.size()-3) == ".ds") {
const string file = s.substr(0, s.size()-3);;
// cerr << file << endl;
getl(s);
vector<pair<string, Fun*> > fs = parse_ds(s);
scrp[file] = fs;
}
else assert(false);
}
getl(s);
const int m = atoi(s.c_str());
rep (_, m) {
int K;
char buf[32];
getl(s);
sscanf(s.c_str(), "%d %d %d %s", &w, &h, &K, buf);
dmls[buf]->init();
render(dmls[buf]);
rep (_, K) {
int x, y;
getl(s);
sscanf(s.c_str(), "%d%d", &x, &y);
click(x, y);
}
rep (i, h) {
rep (j, w) putchar(scr[i][j]);
putchar('\n');
}
}
return 0;
} |
E --Disappear Drive
Story
The person in D likes basketball, but he likes shooting, so other techniques are crazy. I'm not particularly good at dribbling, and when I enter the opponent's defensive range, I always get the ball stolen. So I decided to come up with a deadly dribble that would surely pull out any opponent. After some effort, he finally completed the disappearing drive, "Disapia Drive".
This Apia Drive creates a gap by provoking the opponent to deprive him of his concentration and take his eyes off, and in that gap he goes beyond the wall of dimension and slips through the opponent's defensive range. It's a drive. However, crossing the dimensional wall puts a heavy burden on the body, so there is a limit to the number of times the dimensional wall can be crossed. Also, because he always uses his concentration, he can only change direction once, including normal movements. How do you move on the court to reach the goal in the shortest time without being robbed of the ball?
Problem
Consider a rectangle on a two-dimensional plane with (0,0) at the bottom left and (50,94) at the top right. In addition, there are N circles on this plane, the center position of the i-th circle is (x_i, y_i), and the radius is r_i. There is no overlap between the circles.
Let (25,0) be the point S and (25,94) be the point G, and consider the route from S to G. A "path" consists of (1) a line segment connecting S and G, or (2) a combination of a line segment SP and a line segment GP at any point P inside a rectangle. In the middle of the route from S to G, the period from entering the inside of a circle to exiting the inside of the circle is defined as "the section passing through the inside of the circle". However, it is assumed that the circumferences of the rectangle and the circle are not included in the rectangle and the circle, respectively.
Find the length of the shortest route among the routes where the number of sections passing through the inside of the circle is D or less. If you can't reach the goal, return -1.
Input
The input consists of the following format.
N D
x_1 y_1 r_1
...
x_N y_N r_N
The first line consists of two integers, and the number N of circles and the number of times D that can pass inside the circle are given, separated by one blank character. The following N lines are given circle information. The i + 1 line (1 \ leq i \ leq N) consists of three integers, and the x-coordinate x_i, y-coordinate y_i, and radius r_i of the center of the i-th circle are given by separating them with one blank character.
Constraints:
* 0 \ leq N \ leq 5
* 0 \ leq D \ leq 5
* 0 \ leq x_i \ leq 50
* 0 \ leq y_i \ leq 94
* 1 \ leq r_i \ leq 100
* It can be assumed that any two circles are separated by 10 ^ {-5} or more.
* It can be assumed that S and G are not included inside any circle.
* It can be assumed that S and G are separated from any circle by 10 ^ {-5} or more.
* It can be assumed that the point P in the shortest path is more than 10 ^ {-5} away from the circumference of the rectangle and any circumference.
Output
Output the length of the shortest path on one line. Be sure to start a new line at the end of the line. However, if you cannot reach the goal, return -1. Absolute error or relative error of 10 ^ {-7} or less is allowed for the correct answer.
Sample Input 1
Ten
25 47 10
Sample Output 1
96.2027355887
DisappearDrive_sample1.png
The detour route is the shortest because it cannot disappear.
Sample Input 2
1 1
25 47 10
Sample Output 2
94.0000000000
DisappearDrive_sample2.png
It can disappear, so you just have to go straight through it.
Sample Input 3
Ten
20 47 5
Sample Output 3
94.0000000000
DisappearDrive_sample3.png
Since the circumference is not included in the circle, it can pass through without disappearing.
Sample Input 4
Ten
25 47 40
Sample Output 4
-1
DisappearDrive_sample4.png
You can't reach the goal because you can't disappear or detour.
Sample Input 5
5 2
11 10 16
33 40 18
20 66 10
45 79 14
22 85 8
Sample Output 5
96.1320937224
DisappearDrive_sample5.png
Example
Input
1 0
25 47 10
Output
96.2027355887 | #include <bits/stdc++.h>
using namespace std;
#define dump(...) (cerr<<#__VA_ARGS__<<" = "<<(DUMP(),__VA_ARGS__).str()<<endl)
struct DUMP : stringstream {
template<class T>
DUMP &operator,(const T &t) {
if(this->tellp()) *this << ", ";
*this << t;
return *this;
}
};
constexpr double EPS = 1e-8;
struct point {
double x, y;
point(double x_ = 0, double y_ = 0):x(x_), y(y_) {}
point(const point &p):x(p.x), y(p.y) {}
point operator+(const point &p) const {
return point(x + p.x, y + p.y);
}
point operator-(const point &p) const {
return point(x - p.x, y - p.y);
}
point operator*(double s) const {
return point(x * s, y * s);
}
point operator*(const point &p) const {
return point(x * p.x - y * p.y, x * p.y + y * p.x);
}
point operator/(const double s) const {
return point(x / s, y / s);
}
bool operator<(const point &p) const {
return x + EPS < p.x || (abs(x - p.x) < EPS && y + EPS < p.y);
}
bool operator==(const point &p) const {
return abs(x - p.x) < EPS && abs(y - p.y) < EPS;
}
};
ostream &operator<<(ostream &os, const point &p) {
return os << '(' << p.x << ", " << p.y << ')';
}
point rotate90(const point &p) {
return point(-p.y, p.x);
}
double norm(const point &p) {
return p.x * p.x + p.y * p.y;
}
double abs(const point &p) {
return sqrt(norm(p));
}
double dot(const point &a, const point &b) {
return a.x * b.x + a.y * b.y;
}
double cross(const point &a, const point &b) {
return a.x * b.y - a.y * b.x;
}
struct line {
point a, b;
line(const point &a_, const point &b_):a(a_), b(b_) {}
};
struct segment {
point a, b;
segment(const point &a_, const point &b_):a(a_), b(b_) {}
};
struct circle {
point c;
double r;
circle(const point &c_, double r_):c(c_), r(r_) {}
};
double dist(const point &a, const point &b) {
return abs(a - b);
}
double dist(const line &l, const point &p) {
return abs(cross(l.b - l.a, p - l.a)) / abs(l.b - l.a);
}
double dist(const segment &s, const point &p) {
if(dot(s.b - s.a, p - s.a) < 0) return dist(p, s.a);
if(dot(s.a - s.b, p - s.b) < 0) return dist(p, s.b);
return dist(line(s.a, s.b), p);
}
bool intersect(const circle &c, const point &p) {
return dist(p, c.c) + EPS < c.r;
}
bool intersect(const circle &c, const segment &s) {
return dist(s, c.c) + EPS < c.r;
}
point crosspoint(const line &a, const line &b) {
const double tmp = cross(a.b - a.a, b.b - b.a);
if(abs(tmp) < EPS) return a.a;
return b.a + (b.b - b.a) * cross(a.b - a.a, a.a - b.a) / tmp;
}
vector<point> tangent(const circle &c, const point &p) {
const double x = norm(p - c.c);
double d = x - c.r * c.r;
if(d < -EPS) return vector<point>();
d = max(d, 0.0);
const point p1 = (p - c.c) * (c.r * c.r / x);
const point p2 = rotate90((p - c.c) * (-c.r * sqrt(d) / x));
vector<point> res;
res.push_back(c.c + p1 - p2);
res.push_back(c.c + p1 + p2);
return res;
}
constexpr double W = 50.0;
constexpr double H = 94.0;
constexpr double INF = INT_MAX;
template<class T> inline void chmin(T &a, const T &b) { if(a > b) a = b; }
bool out(const point &p) {
return p.x < EPS || p.y < EPS || p.x + EPS > W || p.y + EPS > H;
}
vector<line> get_line(const circle &c, const point &p) {
const auto ts = tangent(c, p);
vector<line> res;
for(const auto &t : ts) {
if(t == p) {
res.emplace_back(p, p + rotate90(c.c - p));
}
else {
res.emplace_back(p, t);
}
}
return res;
}
int main() {
const point start(W / 2.0, 0);
const point goal(W / 2.0, H);
cout.flags(ios::fixed);
cout.precision(10);
int N, D;
cin >> N >> D;
vector<circle> circles;
circles.reserve(N);
for(int i = 0; i < N; ++i) {
int x, y, r;
cin >> x >> y >> r;
circles.emplace_back(point(x, y), r);
}
int cnt = 0;
for(const auto &c : circles) {
if(intersect(c, segment(start, goal))) ++cnt;
}
if(cnt <= D) {
cout << 94.0 << endl;
return 0;
}
vector<line> s_lines;
vector<line> g_lines;
s_lines.reserve(2 * N);
g_lines.reserve(2 * N);
for(const auto &c : circles) {
auto ls = get_line(c, start);
s_lines.insert(s_lines.end(), ls.begin(), ls.end());
ls = get_line(c, goal);
g_lines.insert(g_lines.end(), ls.begin(), ls.end());
}
double ans = INF;
for(const auto &s_l : s_lines) {
for(const auto &g_l : g_lines) {
const point cp = crosspoint(s_l, g_l);
if(out(cp)) continue;
const segment s1(start, cp);
const segment s2(cp, goal);
cnt = 0;
for(const auto &c : circles) {
const bool i1 = intersect(c, s1);
const bool i2 = intersect(c, s2);
if(i1 && i2 && !intersect(c, cp)) {
cnt += 2;
}
else if(i1 || i2) {
++cnt;
}
}
if(cnt <= D) chmin(ans, dist(start, cp) + dist(cp, goal));
}
}
if(ans == INF) {
puts("-1");
}
else {
cout << ans << endl;
}
return 0;
} |
Example
Input
3 2
3
1 2 1
2 3 2
3 3 1
Output
1 | #include <bits/stdc++.h>
using namespace std;
struct SegmentTree
{
vector< pair< int, int > > seg;
int sz;
SegmentTree(int n)
{
sz = 1;
while(sz < n) sz <<= 1;
seg.assign(2 * sz - 1, make_pair(0, 0));
}
void push(int k)
{
if(k >= sz - 1 || seg[k] == make_pair(0, 0)) return;
if(seg[2 * k + 1] == make_pair(0, 0)) {
seg[2 * k + 1] = seg[k];
} else if(seg[k].first == seg[2 * k + 1].second) {
seg[2 * k + 1].second = seg[k].second;
} else {
seg[2 * k + 1] = {-1, -1};
}
if(seg[2 * k + 2] == make_pair(0, 0)) {
seg[2 * k + 2] = seg[k];
} else if(seg[k].first == seg[2 * k + 2].second) {
seg[2 * k + 2].second = seg[k].second;
} else {
seg[2 * k + 2] = {-1, -1};
}
seg[k] = {0, 0};
}
void update(int a, int b, int x, int k, int l, int r)
{
push(k);
if(a >= r || b <= l) {
} else if(a <= l && r <= b) {
if(seg[k] == make_pair(-1, -1)) return;
if(k >= sz - 1) {
if(seg[k].second == x) seg[k].second++;
else seg[k] = {-1, -1};
} else {
seg[k] = {x, x + 1};
}
push(k);
} else {
update(a, b, x, 2 * k + 1, l, (l + r) >> 1);
update(a, b, x, 2 * k + 2, (l + r) >> 1, r);
}
}
void update(int a, int b, int x)
{
update(a, b, x, 0, 0, sz);
}
int query(int a, int b, int x, int k, int l, int r)
{
push(k);
if(a >= r || b <= l) return (0);
if(a <= l && r <= b) {
return (seg[k] == make_pair(0, x));
}
return (query(a, b, x, 2 * k + 1, l, (l + r) >> 1) +
query(a, b, x, 2 * k + 2, (l + r) >> 1, r));
}
int query(int a, int b, int x)
{
return (query(a, b, x, 0, 0, sz));
}
};
int main()
{
int N, K, T;
scanf("%d %d", &N, &K);
scanf("%d", &T);
SegmentTree tree(N);
while(T--) {
int l, r, x;
scanf("%d %d %d", &l, &r, &x);
tree.update(--l, r, --x);
}
int ret = 0;
for(int i = 0; i < N; i++) ret += tree.query(i, i + 1, K);
printf("%d\n", ret);
} |
D: The Diversity of Prime Factorization
Problem
Ebi-chan has the FACTORIZATION MACHINE, which can factorize natural numbers M (greater than 1) in O ($ \ log $ M) time! But unfortunately, the machine could display only digits and white spaces.
In general, we consider the factorization of M as p_1 ^ {e_1} \ times p_2 ^ {e_2} \ times ... \ times p_K ^ {e_K} where (1) i <j implies p_i <p_j and (2) p_i is prime. Now, she gives M to the machine, and the machine displays according to the following rules in ascending order with respect to i:
* If e_i = 1, then displays p_i,
* otherwise, displays p_i e_i.
For example, if she gives either `22` or` 2048`, then `2 11` is displayed. If either` 24` or `54`, then` 2 3 3`.
Okay, Ebi-chan has written down the output of the machine, but she notices that she has forgotten to write down the input! Now, your task is to count how many natural numbers result in a noted output. Note that Ebi-chan has mistaken writing and no input could result in the output.
The answer could be too large, so, you must output it modulo 10 ^ 9 + 7 (prime number).
Input
N
q_1 q_2 $ \ cdots $ q_N
In the first line, the number of the output of the machine is given. In the second line, the output of the machine is given.
Constraints
* 1 \ leq N \ leq 10 ^ 5
* 2 \ leq q_i \ leq 10 ^ 6 (1 \ leq i \ leq N)
Output
Print the number of the natural numbers that result in the given output of the machine.
Sample Input 1
3
2 3 3
Sample Output for Input 1
2
24 = 2 ^ 3 \ times 3 and 54 = 2 \ times 3 ^ 3 satisfy the condition.
Sample Input 2
3
2 3 4
Sample Output 2 for Input 2
1
Only 162 = 2 \ times 3 ^ 4 satisfies the condition. Note that 4 is not prime.
Sample Input 3
3
3 5 2
Sample Output for Input 3
1
Since 2 <3 <5, only 75 = 3 \ times 5 ^ 2 satisfies the condition.
Sample Input 4
1
Four
Sample Output for Input 4
0
Ebi-chan should have written down it more carefully.
Example
Input
3
2 3 3
Output
2 | #include <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <string>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <stdio.h>
using namespace std;
#define int long long
int MOD = 1000000007;
vector<int> sieve_of_eratosthenes(int n) {
vector<int> primes(n);
for (int i = 2; i < n; ++i)
primes[i] = i;
for (int i = 2; i*i < n; ++i)
if (primes[i])
for (int j = i*i; j < n; j += i)
primes[j] = 0;
return primes;
}
signed main() {
cin.tie(0);
ios::sync_with_stdio(false);
vector<int> primes = sieve_of_eratosthenes(1000005);
int N;
cin >> N;
vector<int> A(N);
int res = 0;
for (int i = 0; i < N; i++) {
cin >> A[i];
}
vector<int> B;
vector<int> C;
bool f1, f2, f3;
for (int i = 0; i < N; i++) {
if (i > 0) {
f1 = (primes[A[i - 1]] != 0);
}
else {
f1 = false;
}
f2 = (primes[A[i]] != 0);
if (i < N - 1) {
f3 = (primes[A[i + 1]] != 0);
}
else {
f3 = true;
}
if (!f2 && !f3) {
cout << 0 << endl;
return 0;
}
if (!f1 && !f2) {
cout << 0 << endl;
return 0;
}
if (f2) {
if (!f1) {
B.push_back(A[i]);
C.push_back(1);
}
else if (!f3) {
B.push_back(A[i]);
C.push_back(1);
}
else {
B.push_back(A[i]);
C.push_back(0);
}
}
}
/*for (int i = 0; i < B.size(); i++) {
cerr << B[i] << " ";
}
cerr << endl;
for (int i = 0; i < C.size(); i++) {
cerr << C[i] << " ";
}
cerr << endl;*/
vector<vector<int> > dp((int)B.size() + 1, vector<int>(3, 0));
dp[0][1] = 1;
for (int i = 1; i < B.size(); i++) {
//for (int k = 0; k < 3; k++) {
if (C[i] == 0) {
if (i > 0 && B[i] > B[i - 1]) {
dp[i][1] = dp[i - 1][1];
}
if (i <= 1 || B[i] > B[i - 2]) {
dp[i][1] = (dp[i][1] + dp[i - 1][0]) % MOD;
}
dp[i][0] = (dp[i][0] + dp[i - 1][1]) % MOD;
}
else {
if (i > 0 && B[i] > B[i - 1]) {
dp[i][1] = dp[i - 1][1];
}
if (i <= 1 || B[i] > B[i - 2]) {
dp[i][1] = (dp[i][1] + dp[i - 1][0]) % MOD;
}
dp[i][0] = 0;
}
//}
}
/*for (int i = 0; i < dp.size(); i++) {
cerr << dp[i][0] << " ";
}
cerr << endl;
for (int i = 0; i < dp.size(); i++) {
cerr << dp[i][1] << " ";
}
cerr << endl;*/
cout << (dp[B.size() - 1][0] + dp[B.size() - 1][1])%MOD << endl;
}
|
Problem
Tomorrow is finally the day of the excursion to Maizu Elementary School. Gatcho, who attends Maizu Elementary School, noticed that he had forgotten to buy tomorrow's sweets because he was so excited. Gaccho wants to stick to sweets so that he can enjoy the excursion to the fullest.
Gaccho gets a $ X $ yen allowance from his mother and goes to buy sweets. However, according to the rules of elementary school, the total amount of sweets to bring for an excursion is limited to $ Y $ yen, and if it exceeds $ Y $ yen, all sweets will be taken up by the teacher.
There are $ N $ towns in the school district where Gaccho lives, and each town has one candy store. Each town is assigned a number from 1 to $ N $, and Gaccho lives in town 1. Each candy store sells several sweets, and the price per one and the satisfaction level that you can get for each purchase are fixed. However, the number of sweets in stock is limited. Also, Gaccho uses public transportation to move between the two towns, so to move directly from town $ i $ to town $ j $, you only have to pay $ d_ {i, j} $ yen. It takes.
At first, Gaccho is in Town 1. Gaccho should make sure that the sum of the total cost of moving and the price of the sweets you bought is within $ X $ yen, and the total price of the sweets you bought is within $ Y $ yen. I'm going to buy sweets. You must have arrived at Town 1 at the end. Gaccho wants to maximize the total satisfaction of the sweets he bought. Find the total satisfaction when you do the best thing.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 14 $
* $ 1 \ leq X \ leq 10000 $
* $ 1 \ leq Y \ leq min (1000, X) $
* $ 1 \ leq K \ leq 300 $
* $ 1 \ leq a_i \ leq 1000 $
* $ 1 \ leq b_i \ leq 1000 $
* $ 1 \ leq c_i \ leq 1000 $
* $ 0 \ leq d_ {i, j} \ leq 10000 $
* $ d_ {i, i} = 0 $
Input
All inputs are given as integers in the following format:
$ N $ $ X $ $ Y $
Information on candy stores in town 1
Information on candy stores in town 2
...
Information on candy stores in town $ N $
$ d_ {1,1} $ $ d_ {1,2} $ ... $ d_ {1, N} $
$ d_ {2,1} $ $ d_ {2,2} $ ... $ d_ {2, N} $
...
$ d_ {N, 1} $ $ d_ {N, 2} $ ... $ d_ {N, N} $
On the first line, the number of towns $ N $, the amount of money you have $ X $, and the maximum amount you can use to buy sweets $ Y $ are given, separated by blanks.
From the second line, information on each $ N $ candy store is given.
In the following $ N $ row and $ N $ column, the amount $ d_ {i, j} $ required to go back and forth between town $ i $ and town $ j $ is given, separated by blanks.
Information on candy stores in each town is given in the following format.
$ K $
$ a_1 $ $ b_1 $ $ c_1 $
$ a_2 $ $ b_2 $ $ c_2 $
...
$ a_K $ $ b_K $ $ c_K $
The first line gives $ K $, the number of types of sweets sold at the candy store. In the following $ K $ line, the price of one candy $ a_i $, the satisfaction level $ b_i $ per candy, and the number of stocks $ c_i $ are given, separated by blanks.
Output
Output the maximum value of the total satisfaction level on one line.
Examples
Input
1 10 10
3
1 10 1
2 20 2
3 30 3
0
Output
100
Input
2 10 10
3
1 10 1
2 20 2
3 30 3
1
5 200 1
0 2
3 0
Output
200
Input
3 10 10
1
1 1 1
1
3 3 3
1
5 5 5
0 1 0
1 0 0
0 1 0
Output
10
Input
4 59 40
1
7 6 3
1
10 3 9
2
9 8 5
7 6 10
4
8 2 9
1 7 1
7 7 9
1 2 3
0 28 7 26
14 0 10 24
9 6 0 21
9 24 14 0
Output
34 | #include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
typedef pair<int,int> P;
typedef pair<int,P> PP;
const int N=14;
int dp1[N][1001],c[N][N],dp2[1<<N][N],dp3[2][1<<(N/2+1)][1001],dp[1<<N][1001],ans;
vector<PP> a[N+1];
int main() {
int A,B,n;
cin >> n >> A >> B;
for(int k=0; k<n; k++) {
fill(dp1[k],dp1[k]+B+1,-(1<<30));
dp1[k][0]=0;
int m;
cin >> m;
for(int i=0; i<m; i++) {
PP p;
cin >> p.S.F >> p.F >> p.S.S;
int t=1;
while(p.S.S) {
do {
for(int j=B; j>=0; j--) {
if(j+p.S.F*t<=B) dp1[k][j+p.S.F*t]=max(dp1[k][j+p.S.F*t],dp1[k][j]+p.F*t);
}
p.S.S-=t;
} while(p.S.S%(t*2));
t*=2;
}
}
for(int i=0; i<B; i++) dp1[k][i+1]=max(dp1[k][i+1],dp1[k][i]);
}
for(int i=0; i<n; i++)for(int j=0; j<n; j++) cin >> c[i][j];
for(int k=0;k<n;k++)for(int i=0;i<n;i++)for(int j=0;j<n;j++)c[i][j]=min(c[i][j],c[i][k]+c[k][j]);
for(int t=0;t<(1<<n);t++)for(int i=0;i<n;i++) dp2[t][i]=1<<30;
for(int i=0; i<n; i++) dp2[1<<i][i]=c[0][i];
for(int t=1; t<(1<<n); t++) {
for(int i=0; i<n; i++) {
if(!(t&(1<<i))) continue;
for(int j=0; j<n; j++) {
if(t&(1<<j)) continue;
dp2[t|(1<<j)][j]=min(dp2[t|(1<<j)][j],dp2[t][i]+c[i][j]);
}
}
}
for(int t=0;t<(1<<(n/2+n%2));t++)for(int i=0;i<=B;i++)dp3[0][t][i]=dp3[1][t][i]=-(1<<30);
for(int l=0; l<2; l++) {
dp3[l][0][0]=0;
for(int t=0; t<(1<<(n/2+n%2*l)); t++) {
for(int i=0; i<n/2+n%2*l; i++) {
if(t&(1<<i)) continue;
for(int j=B; j>=0; j--) {
for(int k=B-j; k>=0; k--) {
dp3[l][t|(1<<i)][j+k]=max(dp3[l][t|(1<<i)][j+k],dp3[l][t][j]+dp1[i+n/2*l][k]);
}
}
}
for(int i=0; i<B; i++) dp3[l][t][i+1]=max(dp3[l][t][i+1],dp3[l][t][i]);
}
}
for(int t=0;t<(1<<n);t++)for(int i=0;i<=B;i++)dp[t][i]=-(1<<30);
for(int t=0;t<(1<<(n/2));t++) {
if(n>1&&t%2==0) continue;
for(int s=0; s<(1<<(n/2+n%2)); s++) {
int C=max(0,A-dp2[t|(s<<(n/2))][0]),D=min(B,C);
for(int i=0; i<=D; i++)ans=max(ans,dp3[0][t][i]+dp3[1][s][D-i]);
}
}
cout << ans << endl;
return 0;
}
|
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | import math
n = int(input())
count = 0
for i in range(n):
t = int(input())
a = int(t ** (1 / 2))
end = 0
for j in range(2, a + 1):
if t % j == 0:
end = 1
break
if end == 0:
count += 1
print(count)
|