<p>Given a weighted undirected connected graph with <code>n</code>&nbsp;vertices numbered from <code>0</code> to <code>n - 1</code>,&nbsp;and an array <code>edges</code>&nbsp;where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, weight<sub>i</sub>]</code> represents a bidirectional and weighted edge between nodes&nbsp;<code>a<sub>i</sub></code>&nbsp;and <code>b<sub>i</sub></code>. A minimum spanning tree (MST) is a subset of the graph&#39;s edges that connects all vertices without cycles&nbsp;and with the minimum possible total edge weight.</p>

<p>Find <em>all the critical and pseudo-critical edges in the given graph&#39;s minimum spanning tree (MST)</em>. An MST edge whose deletion from the graph would cause the MST weight to increase is called a&nbsp;<em>critical edge</em>. On&nbsp;the other hand, a pseudo-critical edge is that which can appear in some MSTs but not all.</p>

<p>Note that you can return the indices of the edges in any order.</p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/06/04/ex1.png" style="width: 259px; height: 262px;" /></p>

<pre>
<strong>Input:</strong> n = 5, edges = [[0,1,1],[1,2,1],[2,3,2],[0,3,2],[0,4,3],[3,4,3],[1,4,6]]
<strong>Output:</strong> [[0,1],[2,3,4,5]]
<strong>Explanation:</strong> The figure above describes the graph.
The following figure shows all the possible MSTs:
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/04/msts.png" style="width: 540px; height: 553px;" />
Notice that the two edges 0 and 1 appear in all MSTs, therefore they are critical edges, so we return them in the first list of the output.
The edges 2, 3, 4, and 5 are only part of some MSTs, therefore they are considered pseudo-critical edges. We add them to the second list of the output.
</pre>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/06/04/ex2.png" style="width: 247px; height: 253px;" /></p>

<pre>
<strong>Input:</strong> n = 4, edges = [[0,1,1],[1,2,1],[2,3,1],[0,3,1]]
<strong>Output:</strong> [[],[0,1,2,3]]
<strong>Explanation:</strong> We can observe that since all 4 edges have equal weight, choosing any 3 edges from the given 4 will yield an MST. Therefore all 4 edges are pseudo-critical.
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= edges.length &lt;= min(200, n * (n - 1) / 2)</code></li>
	<li><code>edges[i].length == 3</code></li>
	<li><code>0 &lt;= a<sub>i</sub> &lt; b<sub>i</sub> &lt; n</code></li>
	<li><code>1 &lt;= weight<sub>i</sub>&nbsp;&lt;= 1000</code></li>
	<li>All pairs <code>(a<sub>i</sub>, b<sub>i</sub>)</code> are <strong>distinct</strong>.</li>
</ul>

class Solution {
public:
    int spanning(vector<pair<int,int>>adj[], vector<vector<int>>&edges, int n, int block, int comp){
        int start = 0;

        vector<int>vis(n,0);
        int wt = 0;
        priority_queue<pair<pair<int,int>,int>,vector<pair<pair<int,int>,int>>,
                                                        greater<pair<pair<int,int>,int>>>pq;
        if(comp!=-1){
            vis[edges[comp][0]] = 1;
            vis[edges[comp][1]] = 1;
            start = edges[comp][0];
            int en = edges[comp][1];
            wt = edges[comp][2];
            for(auto it: adj[start]){
                if(it.first==edges[comp][1]){
                    continue;
                }
                pq.push({{it.second, it.first},start});
            }
            for(auto it: adj[en]){
                if(it.first==start){
                    continue;
                }
                pq.push({{it.second, it.first},en});
            }
        }
        else
            pq.push({{0,start},-1});
        // vis[start] = 1;
        while(!pq.empty()){
            int dis = pq.top().first.first;
            int node = pq.top().first.second;
            int income = pq.top().second;
            pq.pop();
            if(vis[node])continue;
            if(block!=-1){
                int nd = edges[block][0];
                int go = edges[block][1];
                if((income==nd and node==go) or (income==go and node==nd)){
                    continue;
                }
            }
            vis[node] = 1;
            wt = wt+dis;
            // cout<<dis<<endl;
            // if(node!=start){
            //     mp[{node,income}]++;
            //     mp[{income,node}]++;
            // }
            for(auto it: adj[node]){
                if(!vis[it.first]){
                    // vis[it.first] = 1;
                    pq.push({{it.second, it.first},node});
                }
            }
        }
        for(auto it: vis){
            if(it==0){
                return INT_MAX;
            }
        }
        return wt;
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<pair<int,int>>adj[n];
        for(auto it:edges){
            adj[it[0]].push_back({it[1],it[2]});
            adj[it[1]].push_back({it[0],it[2]});
        }
        int mst = spanning(adj,edges,n, -1,-1);
        vector<vector<int>>ans(2);
        for(int i=0;i<edges.size();i++){
            int mst1 = spanning(adj,edges,n,i,-1);
            int mst2 = spanning(adj,edges,n,-1,i);
            if(mst1>mst){
                ans[0].push_back(i);
            }
            else if(mst2==mst){
                ans[1].push_back(i);
            }
        }
        return ans;
    }
};
60071