<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 find_parent(int x,vector<int>&parent){
	    if(x==parent[x])return x;
	    return parent[x]=find_parent(parent[x],parent);
	}
	bool union_set(int a, int b,vector<int>&parent,vector<int>&rank){
	    int pa=find_parent(a,parent);
	    int pb=find_parent(b,parent);
	    if(pa==pb){
	        return false;
	    }
	    else{
	        if(rank[pa]<rank[pb]){
	            swap(pa,pb);
	        }
	        parent[pb]=pa;
	        if(rank[pa]==rank[pb]){
	            rank[pa]++;
	        }
	        return true;
	    }
	}
    int spanningTree(int V, vector<vector<int>> adj[], int skip, int compulsory)
    {
        vector<int>parent(V);
        for(int i=0;i<V;i++){
            parent[i]=i;
        }
        vector<int>rank(V,0);
        vector<pair<int,pair<int,int>>>v;
        int ans=0;
        for(int i=0;i<V;i++){
            for(auto &it:adj[i]){
                if(it[2]!=skip){//skip edge
                    v.push_back({it[1],{i,it[0]}});
                }
                if(it[2]==compulsory){
                    ans+=it[1];
                    union_set(i,it[0],parent,rank);
                }
            }
        }
        sort(v.begin(),v.end());
        for(int i=0;i<v.size();i++){
            int x=v[i].second.first;
            int y=v[i].second.second;
            int w=v[i].first;
            if(union_set(x,y,parent,rank)){
                ans+=w;
            }
        }
        for(int i=1;i<V;i++){
            if(find_parent(i,parent)!=find_parent(i-1,parent)){
                return INT_MAX;
            }
        }
        return ans;
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<vector<int>> adj[n];
        int m=edges.size();
        for(int i=0;i<m;i++){
            int u=edges[i][0];
            int v=edges[i][1];
            int w=edges[i][2];
            adj[u].push_back({v,w,i});
        }
        int mst=spanningTree(n,adj,-1,-1);
        vector<int>critical;
        vector<int>pseudo_critical;
        for(int i=0;i<m;i++){
            // critical
            if(spanningTree(n,adj,i,-1)>mst){
                critical.push_back(i);
            }
            else{
                // pseudo critical
                if(spanningTree(n,adj,-1,i)==mst){
                    pseudo_critical.push_back(i);
                }
            }
        }
        return {critical,pseudo_critical};
    }
};
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