<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(int x,vector<int>&parent){
    if(parent[x]==x)return x;

    return parent[x]=find(parent[x],parent);
}
void unionn(vector<int>&rank,vector<int>&parent,int &x,int &y){
    int x_parent=find(x,parent);
    int y_parent=find(y,parent);

    if(x_parent!=y_parent){
        if(rank[x_parent]>rank[y_parent]){
            parent[y_parent]=x_parent;   
        }
        else if(rank[x_parent]<rank[y_parent]){
            parent[x_parent]=y_parent;      
        }
        else{
            parent[x_parent]=y_parent;
            rank[y_parent]++;
        }
    }

}

void Krushkal(vector<vector<int>>& edges,vector<int>& x,int &mstsize,int &mstweight,int &n,bool whattodo){
    vector<int>rank(n,0);
    vector<int>parent(n);
    for(int i=0;i<n;i++)parent[i]=i;
       
       if(whattodo){
        unionn(rank,parent,x[0],x[1]);
          mstweight += x[2];
          mstsize++;
       }
       
       for(auto v: edges){
        if(whattodo==false && x[3]==v[3])continue;

        int x=v[0]; int y=v[1];
        int x_parent=find(x,parent);
        int y_parent=find(y,parent);

        if(x_parent!=y_parent){
            unionn(rank,parent,x,y);
            mstweight+=v[2];
            mstsize++;
        }

       }

}
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        for(int i=0;i<edges.size();i++){
            edges[i].push_back(i);
        }

auto cmp=[&](vector<int>&a,vector<int>&b){
    return a[2]<b[2];
};
       sort(edges.begin(),edges.end(),cmp);
         
         int mstsize=0;
         int mstweight=0;

         Krushkal(edges,edges[0],mstsize,mstweight,n,true);

vector<int>critical;
vector<int>psduocritical;
         for(auto v: edges){
         
         int mstsize1=0;
         int mstweight1=0;

         Krushkal(edges,v,mstsize1,mstweight1,n,false);

         if(mstsize1!=mstsize || mstweight!=mstweight1){
            critical.push_back(v[3]);
         }
         else{
            int mstsize2=0;
         int mstweight2=0;

         Krushkal(edges,v,mstsize2,mstweight2,n,true);
         if(mstsize2==mstsize1 && mstweight1==mstweight2){
            psduocritical.push_back(v[3]);
         }
         }

         }
         vector<vector<int>>ans{critical,psduocritical};
         return ans;


       
      
    }
};
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