<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>

bool comp(vector<int>& a, vector<int>& b){
    return a[2]<b[2];
}

class Solution {
public:
    vector<int> parent, ranks;
    void make_set(int v){
        parent[v]=v;
        ranks[v]=0;
    }
    int find_set(int v){
        if(v==parent[v]){
            return v;
        }
        else return parent[v]=find_set(parent[v]);
    }
    void union_set(int a, int b){
        a=find_set(a);
        b=find_set(b);
        if(a!=b){
            if(ranks[a]<ranks[b]){
                swap(a,b);
            }
            parent[b]=a;
            if(ranks[a]==ranks[b]){
                ranks[a]++;
            }
        }
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edgeList) {
        parent.resize(n);
        ranks.resize(n);
        int mincost=0;
        for(int i=0;i<n;i++){
            make_set(i);
        }
        auto edges=edgeList;
        sort(edges.begin(),edges.end(),comp);

        for(auto ed:edges){
            int u=ed[0];
            int v=ed[1];
            int w=ed[2];
            if(find_set(u)!=find_set(v)){
                mincost+=w;
                union_set(u,v);
            }
        }

        unordered_set<int> crit;
        vector<int> pseudo;
        unordered_set<int> noncrit;
        for(int i=0;i<edgeList.size();i++){
            edges=edgeList;
            edges[i][2]=1e9;
            int cost=0;
            for(int k=0;k<n;k++){
                make_set(k);
            }
            sort(edges.begin(),edges.end(),comp);

            for(auto ed:edges){
                int u=ed[0];
                int v=ed[1];
                int w=ed[2];
                if(find_set(u)!=find_set(v)){
                    cost+=w;
                    union_set(u,v);
                }
            }

            if(cost>mincost){
                crit.insert(i);
            }
        }

        for(int i=0;i<edgeList.size();i++){
            edges=edgeList;
            int cost=edges[i][2];
            for(int k=0;k<n;k++){
                make_set(k);
            }
            union_set(edges[i][0],edges[i][1]);
            edges[i][2]=1e9;
            sort(edges.begin(),edges.end(),comp);

            for(auto ed:edges){
                int u=ed[0];
                int v=ed[1];
                int w=ed[2];
                if(find_set(u)!=find_set(v)){
                    cost+=w;
                    union_set(u,v);
                }
            }

            if(cost>mincost){
                noncrit.insert(i);
            }
        }

        for(int i=0;i<edgeList.size();i++){
            if(crit.count(i)==0 and noncrit.count(i)==0){
                pseudo.push_back(i);
            }
        }

        vector<vector<int>> ans;
        ans.push_back(vector<int>(crit.begin(),crit.end()));
        ans.push_back(pseudo);
        return ans;
    }
};
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