<p>You are given an undirected graph (the <strong>&quot;original graph&quot;</strong>) with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. You decide to <strong>subdivide</strong> each edge in the graph into a chain of nodes, with the number of new nodes varying between each edge.</p>

<p>The graph is given as a 2D array of <code>edges</code> where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>, cnt<sub>i</sub>]</code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the original graph, and <code>cnt<sub>i</sub></code> is the total number of new nodes that you will <strong>subdivide</strong> the edge into. Note that <code>cnt<sub>i</sub> == 0</code> means you will not subdivide the edge.</p>

<p>To <strong>subdivide</strong> the edge <code>[u<sub>i</sub>, v<sub>i</sub>]</code>, replace it with <code>(cnt<sub>i</sub> + 1)</code> new edges and <code>cnt<sub>i</sub></code> new nodes. The new nodes are <code>x<sub>1</sub></code>, <code>x<sub>2</sub></code>, ..., <code>x<sub>cnt<sub>i</sub></sub></code>, and the new edges are <code>[u<sub>i</sub>, x<sub>1</sub>]</code>, <code>[x<sub>1</sub>, x<sub>2</sub>]</code>, <code>[x<sub>2</sub>, x<sub>3</sub>]</code>, ..., <code>[x<sub>cnt<sub>i</sub>-1</sub>, x<sub>cnt<sub>i</sub></sub>]</code>, <code>[x<sub>cnt<sub>i</sub></sub>, v<sub>i</sub>]</code>.</p>

<p>In this <strong>new graph</strong>, you want to know how many nodes are <strong>reachable</strong> from the node <code>0</code>, where a node is <strong>reachable</strong> if the distance is <code>maxMoves</code> or less.</p>

<p>Given the original graph and <code>maxMoves</code>, return <em>the number of nodes that are <strong>reachable</strong> from node </em><code>0</code><em> in the new graph</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/01/origfinal.png" style="width: 600px; height: 247px;" />
<pre>
<strong>Input:</strong> edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3
<strong>Output:</strong> 13
<strong>Explanation:</strong> The edge subdivisions are shown in the image above.
The nodes that are reachable are highlighted in yellow.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4
<strong>Output:</strong> 23
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5
<strong>Output:</strong> 1
<strong>Explanation:</strong> Node 0 is disconnected from the rest of the graph, so only node 0 is reachable.
</pre>

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

<ul>
	<li><code>0 &lt;= edges.length &lt;= min(n * (n - 1) / 2, 10<sup>4</sup>)</code></li>
	<li><code>edges[i].length == 3</code></li>
	<li><code>0 &lt;= u<sub>i</sub> &lt; v<sub>i</sub> &lt; n</code></li>
	<li>There are <strong>no multiple edges</strong> in the graph.</li>
	<li><code>0 &lt;= cnt<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= maxMoves &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= n &lt;= 3000</code></li>
</ul>

#include <bits/stdc++.h>
#include <iomanip>
using namespace std;

#define fi first
#define endl '\n'
#define se second
//#define up unordered_map
#define us unordered_set
typedef vector<int> vi;
typedef long long ll;
typedef vector<vi> vvi;
typedef vector<ll> vll;
typedef vector<vll> vvl;

typedef pair<int,int> ii;
typedef vector<ii> vii;
typedef pair<ll,ll> pll;
typedef vector<pll> vpl;
typedef vector<pair<int,ll>> vil;

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,
        tree_order_statistics_node_update> indexed_set;
//s.find_by_order(ele)--for it of target
//s.order_of_key(ele)--for lower bound index of target
ll m1=1000000007;
// ll m2=998244353;
int inf=1e9+10000;


vi dist(3001,inf);

class Solution {
public:
void bellman(vector<vvi> &adj){
    multiset<ii> s;
    s.insert({0,0});
    int n=(int)adj.size();
    vi marked(n,0);

    while(!s.empty()){


        auto i=*s.begin();
        s.erase(s.begin());
        int node=i.se;

        if(marked[node]) continue;
        marked[node]=1;

        for(auto child:adj[node]){
            int ch=child[0];
            int edge=child[1];
            if(marked[ch]) continue;
            if(dist[ch] <= dist[node]+edge) continue;
            dist[ch]=dist[node]+edge;
            s.insert({dist[ch],ch});

        }
    }
}

    int reachableNodes(vvi& edges, int rng, int n) {
        for(int i=0;i<n;i++) dist[i]=inf;


        vector<vvi> adj(n);
   

        for(auto edge:edges){
            int a=edge[0];
            int b=edge[1];
            int c=edge[2]+1;
            adj[a].push_back({b,c});
            adj[b].push_back({a,c});
        }

        dist[0]=0;
        bellman(adj);

        vi nodes(n,0);
        int snodes=0;

        cout<<endl;
        for(auto edge:edges){
            int par=edge[0];
            int ch=edge[1];
            int sub=edge[2];
            if(par > ch) continue;
            if(dist[par] > rng && dist[ch] > rng) continue;

        
            int all=0;
            if(dist[par] <= rng) all+=rng-dist[par];
            if(dist[ch] <= rng)all+=rng-dist[ch];

            snodes+=min(sub,all);
        }
        for(int i=0;i<n;i++){
            snodes+=(dist[i] <= rng);
        }
         return snodes;
    }

};
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