<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 {
    class DisjointSet{
        public:
        int* parent;
        int* rank;
        DisjointSet(int n){
            parent=new int[n];
            rank=new int[n];
            for(int i=0;i<n;i++){
                parent[i]=i;
                rank[i]=0;
            }
        }

        int find(int v){
            if(parent[v]==v){
                return v;
            }
            int rr=find(parent[v]);
            parent[v]=rr;
            return rr;
        }
        void unite(int a,int b){
            int re1=find(a);
            int re2=find(b);
            if(re1==re2){
                return;
            }
            if(rank[re1]>rank[re2]){
                parent[re2]=re1;
            }
            else if(rank[re1]<rank[re2]){
                parent[re1]=re2;
            }
            else{
                parent[re1]=re2;
                rank[re2]++;
            }
        }
    };
    int mstweight(vector<vector<int> >&edges,int n,int block,int incl){
        DisjointSet ds(n);
        int w=0;
        if(incl!=-1){
            w+=edges[incl][2];
            ds.unite(edges[incl][0],edges[incl][1]);
        }

        for(int i=0;i<edges.size();i++){
            int u=edges[i][0];
            int v=edges[i][1];
            if(i==block || ds.find(u)==ds.find(v)){
                continue;
            }
            w+=edges[i][2];
            ds.unite(u,v);
        }
        for(int i=0;i<n;i++){
            if(ds.find(i)!=ds.find(0)){
                return INT_MAX; // not posible to make mst

            }
        }
        return w;
    }
public:
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        // DisjointSet ds(n);

        vector<int> critical,pseudocritical;
        vector<vector<int> > ans;
        for(int i=0;i<edges.size();i++) {
            edges[i].push_back(i);      //because sprting will change the indices
        }
        auto cmp=[&](vector<int> a,vector<int> b){
            return a[2]<b[2];
        };
        sort(edges.begin(),edges.end(),cmp);    

        int minweight=mstweight(edges,n,-1,-1);

        for(int i=0;i<edges.size();i++){
            if(minweight<mstweight(edges,n,i,-1)){
                critical.push_back(edges[i][3]);
            }
            else if(minweight==mstweight(edges,n,-1,i)){
                pseudocritical.push_back(edges[i][3]);
            }
        }
        ans.push_back(critical);
        ans.push_back(pseudocritical);
        return ans;

    }
};
30003