<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{
    vector<int> parent;
    int n;
public:
    Dsu(int _n){
        n = _n;
        parent.resize(n, -1);
    }

    int findParent(int a)
    {
        if(parent[a]<0)
            return a;
        return parent[a] = findParent(parent[a]);
    }

    void unionNodes(int a, int b)
    {
        int para = findParent(a);
        int parb = findParent(b);
        if(para==parb)
            return;
        if(para<parb)
            parent[parb] = para;
        else
            parent[para] = parb;
        return;
    }

};


int findMSTWeight(vector<vector<int>> &edges, int skipIndex, int addIndex, int n)
{
    int mstWeight = 0;
    Dsu d = Dsu(n);
    if(addIndex!=-1)
    {
        d.unionNodes(edges[addIndex][0], edges[addIndex][1]);
        mstWeight += edges[addIndex][2];
    }

    for(int i=0;i<edges.size();i++)
    {
        if(i==addIndex || i==skipIndex)
            continue;
        
        int u = edges[i][0];
        int v = edges[i][1];
        int w = edges[i][2];

        if(d.findParent(u)==d.findParent(v))
            continue;
        
        d.unionNodes(u, v);
        mstWeight+=w;
    }
        
    return mstWeight;



}


class Solution {
public:

    static bool comperator(vector<int> &a, vector<int> &b)
    {
        return a[2]<b[2];
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {

        for(int i=0;i<edges.size();i++)
            edges[i].push_back(i);

        sort(edges.begin(), edges.end(), comperator);

        int finalMstWeight = findMSTWeight(edges, -1, -1, n);

        vector<int> critical, pseudoCritical;

        for(int i=0;i<edges.size();i++)
        {
            // check for critical edge
            if(findMSTWeight(edges, i, -1, n)!=finalMstWeight)
                critical.push_back(edges[i][3]);
            else if(findMSTWeight(edges, -1, i, n)==finalMstWeight)
                pseudoCritical.push_back(edges[i][3]);
        }

        return {critical, pseudoCritical};
    }
};
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