<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> par, siz;
    DSU() {}
    DSU(int n) {
        par.resize(n,0);
        siz.resize(n,1);
        for(int i=0;i<n;i++) par[i]=i;
    }

    int fin(int p) {
        if(par[p]==p) return p;
        return par[p] = fin(par[p]);
    }

    bool uni(int a, int b) {
        int pa = fin(a);
        int pb = fin(b);
        if(pa==pb) return false;
        if(siz[pa]>siz[pb]) {
            siz[pa] += siz[pb];
            par[pb] = pa;
        }
        else {
            siz[pb] += siz[pa];
            par[pa] = pb;
        }
        return true;
    }
};
class Solution {
public:
    static bool comp(vector<int> a, vector<int> b) {
        return a[2]<b[2];
    }
    int mst(vector<vector<int>>& edges, int g, int ni, int n) {
        int c=1,i=0,ms=0;
        DSU dsu = DSU(n);
        if(ni!=-1 && g == 1) {
            dsu.uni(edges[ni][0], edges[ni][1]);
            ms=edges[ni][2];
            c++;
        }
        
        while(c<n&& i<edges.size()) {
            if(i==ni) {
                i++;
                continue;
            }
            int st = edges[i][0];
            int en = edges[i][1];
            int w = edges[i][2];
            if(dsu.uni(st, en)) {
                c++;
                ms +=w;
            }
            i++;
        }
        if(c<n) return INT_MAX;
        return ms;
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<vector<pair<int,int>>> graph(n, vector<pair<int,int>>());
        map<vector<int>, int> moi;
        for(int i=0;i<edges.size();i++) {
            moi[edges[i]]=i;
            graph[edges[i][0]].push_back({edges[i][1], edges[i][2]});
            graph[edges[i][1]].push_back({edges[i][0], edges[i][2]});
        }
        
        sort(edges.begin(), edges.end(), comp);
        map<int,int> taken;
        vector<vector<int>> sol(2, vector<int>());
        int ms = mst(edges, 0, -1, n);
        cout<<ms<<endl;
        for(int i=0;i<edges.size();i++) {
            int vms = mst(edges, 0, i, n);
            if(vms>ms) {
                sol[0].push_back(moi[edges[i]]);
                taken[i]=1;
            }
        }
        for(int i=0;i<edges.size();i++) {
            int vms = mst(edges, 1, i, n);
            if(vms==ms && taken[i]==0) {
                sol[1].push_back(moi[edges[i]]);
            }
        }
        return sol;
    }
};
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