<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> p;
    vector<int> s;
    dsu(int n) {
        p.resize(n);
        s.resize(n, 1);
        for (int i = 0; i < n; i++) {
            p[i] = i;
        }
    }
    int parent(int u) {
        if (u == p[u])
            return u;
        return p[u] = parent(p[u]);
    }
    void un(int u, int v) {
        int x = parent(u);
        int y = parent(v);
        if (x == y)
            return;
        else if (s[x] > s[y]) {
            s[x] += s[y];
            p[y] = x;
        } else {
            s[y] += s[x];
            p[x] = y;
        }
    }
};
class Solution {
public:
    vector<vector<int>>
    findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<vector<int>> sort_e;

        for (auto it : edges) {
            sort_e.push_back({it[2], it[0], it[1]});
        }
        sort(sort_e.begin(), sort_e.end());
        dsu d(n);
        int actual_mst = 0;
        for (auto it : sort_e) {
            int u = it[1];
            int v = it[2];
            if (d.parent(u) != d.parent(v)) {
                actual_mst += it[0];
                d.un(u, v);
            }
        }
        vector<int> critical;
        vector<int> pseudo_critical;
        vector<vector<int>> ans;
        for (int i = 0; i < edges.size(); i++) {
            int exclude_mst=0;
            int include_mst=0;
            // case 1 i will exclude this edge
            dsu a(n);
            
            for (auto it : sort_e) {

                int u = it[1];
                int v = it[2];
                
               if (!(u == edges[i][0] && edges[i][2] == it[0] && edges[i][1] == v))
 {
                    if (a.parent(u) != a.parent(v)) {
                        exclude_mst += it[0];
                        a.un(u, v);
                    }
                }
            }
            bool f=true;
            for(int i=0; i<n; i++)
            {
                if(a.parent(i)!=a.parent(0))
                {
                    f=false;
                    break;
                }
            }
            
            //include in the edge
            dsu b(n);

            b.un(edges[i][0],edges[i][1]);
            include_mst+=edges[i][2];
             for (auto it : sort_e) {

                int u = it[1];
                int v = it[2];
               if (!(u == edges[i][0] && edges[i][2] == it[0] && edges[i][1] == v)) {
                    if (b.parent(u) != b.parent(v)) {
                        include_mst += it[0];
                        b.un(u, v);
                    }
                }
            }
            
             if(!f||exclude_mst>actual_mst)
              {
                    critical.push_back(i);
              }
              else if(include_mst==actual_mst)
              {
                   pseudo_critical.push_back(i);
              }
              
        }
         ans.push_back(critical);
        ans.push_back(pseudo_critical);
        // ans.push_back();
        return ans;
    }
};
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