<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 Solution {
public:
    class UnionFind{
        public:
        UnionFind(int n) : n(n), link(n), size(n) {
            for(int i = 0; i < n; i++){
                link[i] = i;
                size[i] = 1;
            }

        };

        int find(int x){

            while(x != link[x])
                x = link[x];

            return x;
        }

        bool isSame(int a, int b){
            return find(a) == find(b);
        }

        void unite(int a, int b){
            a = find(a);
            b = find(b);

            if(size[a] < size[b]) swap(a, b);

            size[a] += size[b];
            link[b] = a;
        }


        int n;
        vector<int> link;
        vector<int> size;
    };
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        
        UnionFind uf(n);

        vector<vector<int>> ogEdges(edges);

        sort(edges.begin(), edges.end(), [](const vector<int> & a, const vector<int> & b){
            return a[2] < b[2];
        });


        int minCost = 0;
        for(const vector<int> & edge : edges){
            int a = edge[0];
            int b = edge[1];
            int c = edge[2];
            if(!uf.isSame(a, b)){


                uf.unite(a, b);
                minCost += c;
            }
            
        }

        set<vector<int>> critical;

        for(int i = 0; i < edges.size(); i++){
            
            UnionFind criticalUf(n);
            int criticalMinCost = 0;
            for(int j = 0; j < edges.size(); j++){
                
                if(j == i)
                    continue;
                
                vector<int>& edge = edges[j];
                int a = edge[0];
                int b = edge[1];
                int c = edge[2];
                if(!criticalUf.isSame(a, b)){
                    criticalUf.unite(a, b);
                    criticalMinCost += c;
                }

            }

            if(!criticalUf.isSame(edges[i][0], edges[i][1]) || criticalMinCost > minCost)
                critical.insert(edges[i]);
        }


        set<vector<int>> pseudocritical;
        for(int i = 0; i < edges.size(); i++){
            
            UnionFind pseudocriticalUf(n);
            
            int pseudocriticalMinCost = edges[i][2];
            pseudocriticalUf.unite(edges[i][0], edges[i][1]);


            for(int j = 0; j < edges.size(); j++){
                
                
                vector<int>& edge = edges[j];
                int a = edge[0];
                int b = edge[1];
                int c = edge[2];
                if(!pseudocriticalUf.isSame(a, b)){
                    pseudocriticalUf.unite(a, b);
                    pseudocriticalMinCost += c;
                }

            }

            if(pseudocriticalMinCost == minCost)
                pseudocritical.insert(edges[i]);
        }



        vector<vector<int>> res(2);

        for(int i = 0; i < ogEdges.size(); i++){
            if(critical.contains(ogEdges[i])){
                res[0].push_back(i);
            }
            else if(pseudocritical.contains(ogEdges[i])){
                res[1].push_back(i);
            }

        }
        return res;
    }
};
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