<p>You are given an integer <code>n</code> and an array of <strong>unique</strong> integers <code>blacklist</code>. Design an algorithm to pick a random integer in the range <code>[0, n - 1]</code> that is <strong>not</strong> in <code>blacklist</code>. Any integer that is in the mentioned range and not in <code>blacklist</code> should be <strong>equally likely</strong> to be returned.</p>

<p>Optimize your algorithm such that it minimizes the number of calls to the <strong>built-in</strong> random function of your language.</p>

<p>Implement the <code>Solution</code> class:</p>

<ul>
	<li><code>Solution(int n, int[] blacklist)</code> Initializes the object with the integer <code>n</code> and the blacklisted integers <code>blacklist</code>.</li>
	<li><code>int pick()</code> Returns a random integer in the range <code>[0, n - 1]</code> and not in <code>blacklist</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Solution&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;]
[[7, [2, 3, 5]], [], [], [], [], [], [], []]
<strong>Output</strong>
[null, 0, 4, 1, 6, 1, 0, 4]

<strong>Explanation</strong>
Solution solution = new Solution(7, [2, 3, 5]);
solution.pick(); // return 0, any integer from [0,1,4,6] should be ok. Note that for every call of pick,
                 // 0, 1, 4, and 6 must be equally likely to be returned (i.e., with probability 1/4).
solution.pick(); // return 4
solution.pick(); // return 1
solution.pick(); // return 6
solution.pick(); // return 1
solution.pick(); // return 0
solution.pick(); // return 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= blacklist.length &lt;= min(10<sup>5</sup>, n - 1)</code></li>
	<li><code>0 &lt;= blacklist[i] &lt; n</code></li>
	<li>All the values of <code>blacklist</code> are <strong>unique</strong>.</li>
	<li>At most <code>2 * 10<sup>4</sup></code> calls will be made to <code>pick</code>.</li>
</ul>

class Solution {
public:
    unordered_map<int, int> mp;
    int valid_range;
    Solution(int n, vector<int>& blacklist) {
        // set le liya h toh sort karne ki need ni, iske andar automatically
        // sorted hi milega
        set<int> st;
        for (auto numbers : blacklist) {
            st.insert(numbers);
        }

        // kis range tak hi number niklege ki kitne non-blacklist h
        valid_range = n - blacklist.size();

        int lastNum = valid_range;

        for (auto number : st) {
            // jo range ke andar ho aur blacklist ho, toh aise number se map
            // karunga jo range ke bahar ho par non-blacklist ho
            // sabse pehle check karunga ki range ke andar hai vo blacklist
            // number...then range ke bahar ka number mapk karwaunga jo st ke
            // andar na ho bole toh blacklist na ho
            if (number < valid_range) {
                while (st.count(lastNum)) {
                    lastNum++;
                }
                mp[number] = lastNum;
                lastNum++;
            }
        }
    }

    int pick() {
        int random = rand() % valid_range;
        if (mp.count(random)) {
            return mp[random];
        }
        return random;
    }
};
/*
trick ye hai manle ki 20 numbers hai aur unme se 5 tere blacklist number h toh
non-backlist tere hue 20 - 5 = 15 toh 15 non-blacklist ho gaye. m kya karunga 0
- 15 numbers tak jaunga, ab 15 ke baad toh 5 number bachege. m kya karunga ki
uss 15 numbers ke andar jo blacklist number h usko m 15 ke baad wale
non-blacklist number se map karwa dunga. ye m map lekr karunga toh kya hoga ki
random number toh tu non-blacklit ke liye hi nikalega kyuki tujhe chahiye toh
non blacklist hi, bole toh 0 - 15 ke beech toh agr jo tunne random number nikala
agr ye tera blacklist h toh m kya karunga ki uske corresponding jo non blacklist
h vo return kardunga ni toh jo number generate kiya that will be a non-blacklist
toh I'll return that.

*/
77900