<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>

struct DSU{
	int n,level[105],pa[105];
	void init(int n){
		this->n = n;
		for(int i=0;i<n;i++){
			level[i]=0;
			pa[i]=i;
		}
	}
	int getpa(int x){
		if(x==pa[x])return x;
		return pa[x]=getpa(pa[x]);
	}
	bool uni(int x,int y){
		x=getpa(x);
		y=getpa(y);
		if(x==y)return false;
		if(level[x]<level[y]){
			int t=x;x=y;y=t;
		}
		pa[y]=x;
		if(level[x]==level[y])level[x]++;
		return true;
	}
} dsu;

int getMST(vector<vector<int>>& edges,int n){
    priority_queue<pair<int,int>,vector<pair<int,int>>, greater<pair<int,int>>> pq;
    dsu.init(n);
    for(int i=0;i<edges.size();i++)
        pq.push({edges[i][2],i});
    int ret=0;
    while(pq.size()){
        auto [w,a]=pq.top();pq.pop();
        if(!dsu.uni(edges[a][0],edges[a][1]))continue;
        ret+=w;
    }
    return ret;
}

class Solution {
public:

    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        int m=edges.size();
        vector<int> critical,rest;
        int val=getMST(edges,n);
        for(int i=0;i<m;i++){
            int t=edges[i][2];
            edges[i][2]=1e7;
            if(getMST(edges,n)>val)
                critical.push_back(i);
            else{
                edges[i][2]=0;
                if(getMST(edges,n)+t==val)
                    rest.push_back(i);
            }
            edges[i][2]=t;
        }
        return {critical,rest};
    }
};
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