<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 DSU{
    public:
    vector<int> size;
    vector<int> parent;
    public:
    DSU(int n){
        size.resize(n,1);
        parent.resize(n);
        for(int i =0;i<n;i++) parent[i]=i;
    }
    
    int find(int node){
        if(parent[node]==node) return node;
        return parent[node]= find(parent[node]);
    }
    
    void merge(int u ,int v){
        int up_u=find(u);
        int up_v=find(v);
        if(up_u==up_v) return;
        if(size[up_u]<size[up_v]){
            parent[up_u]=up_v;
            size[up_v]+=size[up_u];
        }
        else{
            parent[up_v]=up_u;
            size[up_u]+=size[up_v];
        }
        return;
    }
};

class Solution {
public:
    bool  static compare(vector<int> v1,vector<int> v2){
        return (v1[2]<v2[2]);
    }
    int findMST(vector<vector<int>>& edges,int n,int inc,int exc){
        DSU dsu(n);
        int wt=0;
        if(inc!=-1){
            wt+=edges[inc][2];
            dsu.merge(edges[inc][0],edges[inc][1]);
        }
        for(int i =0;i<edges.size();i++){
            int u = edges[i][0];
            int v = edges[i][1];
            if(i==exc) continue;
            if(dsu.find(u)!=dsu.find(v)){
                wt+=edges[i][2];
                dsu.merge(u,v);
            }
        }
        int n_c=0;
        for(int i =0;i<n;i++){
            if(dsu.parent[i]==i) n_c++;
        }
        if(n_c>1) return -1;
        return wt;
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        int weight = 0;
        vector<vector<int>> edgelist;
        int index=0;
        for(auto it : edges) edgelist.push_back({it[0],it[1],it[2],index++});
        sort(edgelist.begin(),edgelist.end(),compare);
        vector<vector<int>> ans(2);
        int mst = findMST(edgelist,n,-1,-1);
        for(int i =0 ;i<edgelist.size();i++){
            int mst_exc=findMST(edgelist,n,-1,i);
            if(mst_exc==-1) {
                ans[0].push_back(edgelist[i][3]);
                continue;
            }
            if(mst_exc>mst) {
                ans[0].push_back(edgelist[i][3]);
                continue;
            }
            int mst_inc = findMST(edgelist,n,i,-1);
            if(mst==mst_inc) ans[1].push_back(edgelist[i][3]);
        }

        return ans;
    }
};
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