<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(vector<int>&parent, int x){
        //TC=log*n (log star n)
        if(parent[x]==x) return x;
        return parent[x]=find(parent, parent[x]);
    }
    void unionof(vector<int>&parent, vector<int>&rank, int a, int b){
        a=find(parent,a);
        b=find(parent,b);
        if(a==b) return;
        if(rank[a]>=rank[b]){
            rank[a]++;
            parent[b]=a;
        }
        else{
            rank[b]++;
            parent[a]=b;
        
        }
    }
    struct Edge{
        int src;
        int dest;
        int wt;
        int idx;
    };
    static bool cmp(Edge e1, Edge e2){
        return e1.wt<e2.wt;
    }
    int kruskal(vector<Edge>input, int n, int skipping_edge , int adding_edge){
        vector<int>parent(n+1);
        vector<int>rank(n+1,1);
        for(int i=1;i<=n;i++){
            parent[i]=i;
        }
        int total_count=0;
        int result=0;
        if(adding_edge!=-1){
            Edge curr=input[adding_edge];
            int src2=find(parent,curr.src);
            int dest2=find(parent,curr.dest);
            if(src2!=dest2) {
                unionof(parent,rank,src2,dest2);
                result+=curr.wt;
                total_count++;
            }
        }
        for(int i=0;i<input.size();i++){
            if(i==skipping_edge) continue;
            Edge curr=input[i];
            int src2=find(parent,curr.src);
            int dest2=find(parent,curr.dest);
            if(src2!=dest2) {
                unionof(parent,rank,src2,dest2);
                result+=curr.wt;
                total_count++;
            }
        }
        return total_count==n-1 ? result : INT_MAX;  
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<Edge>edgeList;
        for(int i=0;i<edges.size();i++){
            edgeList.push_back(Edge(edges[i][0], edges[i][1], edges[i][2], i));
        }
        sort(edgeList.begin(),edgeList.end(),cmp);
        vector<int>critical;
        vector<int>psedo_critical;
        int mstWeight=kruskal(edgeList,n,-1,-1);
        for(int i=0;i<edgeList.size();i++){
            if(kruskal(edgeList,n,i,-1)>mstWeight) critical.push_back(edgeList[i].idx);
            else if(kruskal(edgeList,n,-1,i)==mstWeight) psedo_critical.push_back(edgeList[i].idx);    
        }
        return{critical,psedo_critical};
    }
};
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