<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:
 static bool cmp(vector<int> &f,vector<int> &s){
    return f[2]<s[2];
 }
void makeset(vector<int> &par,vector<int> &rank,int n){
    for(int i=0;i<=n;i++){
        par[i]=i;
        rank[i]=0;
    }
   }
   int findparent(int node,vector<int> &parent){
      if(parent[node]==node){
        return node;
      }
      return parent[node]=findparent(parent[node],parent);
   }

   void unionSet(vector<int> &par,vector<int> &rank,int u,int v){
       u=findparent(u,par);
       v=findparent(v,par);

       if(rank[u]<rank[v]){
          par[u]=v;
       }
        else if(rank[u]>rank[v]){
          par[v]=u;
       }
       else{
        par[v]=u;
        rank[u]++;
       }
   }
   int mst_ignore(vector<vector<int>>& edges, 
        int ignore,int n){
            vector<int> parent(n+1);
            vector<int> rank(n+1);
            makeset(parent,rank,n);

            vector<pair<int,pair<int,int> > > v;

            int mt=0;

          for(int i=0;i<edges.size();i++){
            if(i==ignore){
                continue;
            }

            v.push_back({edges[i][2],{edges[i][0],edges[i][1]}});
           }
              sort(v.begin(),v.end());
              int edge = 0;

           for(auto i:v){
            int u=findparent(i.second.first,parent);
            int v=findparent(i.second.second,parent);
            int wt=i.first;

            if(u!=v){
                mt+=wt;
                edge++;
                unionSet(parent,rank,u,v);
            }
           }
     if (edge != n - 1)
        return INT_MAX;
   
           return mt;

           }

    int mst_include(vector<vector<int>>& edges,
         
          int include,int n){
            vector<int> parent(n+1);
            vector<int> rank(n+1);
            makeset(parent,rank,n);

            vector<pair<int,pair<int,int> > > v;  
                int mt=0;
                mt+=edges[include][2];
                unionSet(parent,rank,edges[include][0],edges[include][1]);
         for(int i=0;i<edges.size();i++){
            if(i==include){
                continue;
            }
            v.push_back({edges[i][2],{edges[i][0],edges[i][1]}});
           }
           sort(v.begin(),v.end());

            for(auto i:v){
            int u=findparent(i.second.first,parent);
            int v=findparent(i.second.second,parent);
            int wt=i.first;

            if(u!=v){
                mt+=wt;
                unionSet(parent,rank,u,v);
            }
           }
           return mt;

           }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {

       
           int mst_weight = mst_ignore(edges, -1, n);

           cout<<"MST "<<mst_weight<<endl;
      
            vector<vector<int>> ans;
            vector<int> crit;
            vector<int> non;

            for(int i=0;i<edges.size();i++){

                int include=mst_include(edges,i,n);
                int exclude=mst_ignore(edges,i,n);

                cout<<exclude<<" "<<include<<endl;

                if(exclude>mst_weight){
                    crit.push_back(i);
                }
               else if(include==mst_weight){
                    non.push_back(i);
                }
            }
            
       ans.push_back(crit);
       ans.push_back(non);

           return ans;




    }
};
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