<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 UnionFind{
    public:
    vector<int> parent;
    vector<int> size;
    int n;
    UnionFind(int a)
    {
        n = a;
        for(int i = 0; i < n; i++)
        {
            parent.push_back(i);
            size.push_back(1);
        }
    }
    int findRoot(int a)
    {
        if(parent[a] != a)
        {
            parent[a] = findRoot(parent[a]);
        }
        return parent[a];
    }
    bool connect(int a, int b)
    {
        int rootA = findRoot(a);
        int rootB = findRoot(b);
        if(rootA == rootB)
            return false;
        if(size[rootA] > size[rootB])
        {
            parent[rootB] = rootA;
            size[rootA] += size[rootB];
        }
        else{
            parent[rootA] = rootB;
            size[rootB] += size[rootA];
        }
        return true;
    }
    int maxx()
    {
        int res = size[0];
        for(auto i : size)
        {
            if(i > res)
                res = i;
        }
        return res;
    }
};

class Solution {
public:
    struct Edge{
        int index;
        vector<int> v;
        bool operator>(const Edge& other){
            return v[2] > other.v[2];
        }
        bool operator<(const Edge& other){
            return v[2] < other.v[2];
        }
    };
    static bool compare(const vector<int>& a, const vector<int>& b){
        return a[2] < b[2];
    }
    int findMST(int n, vector<Edge>& edges)
    {
        UnionFind uf(n);
        int res = 0;
        int cnt = 0;
        for(auto edge : edges)
        {
            if(cnt == n - 1)
                break;
            if(uf.connect(edge.v[0], edge.v[1]) == true)
            {
                res += edge.v[2];
                cnt++;
            }
        }
        return res;
    }

    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<vector<int>> res;
        vector<int> critical;
        vector<int> pseudo;
        vector<Edge> a;
        for(int i = 0; i < edges.size(); i++)
        {
            a.push_back({i, edges[i]});
        }
        sort(a.begin(), a.end());
        int mstLen = findMST(n, a);
        for(int i = 0; i < a.size(); i++)
        {
            auto edge = a[i].v;
            //try without this edge
            UnionFind uf1(n);
            int curRes = 0;
            int cnt = 0;
            for(auto e : a)
            {
                if(e.v[0] == edge[0] && e.v[1] == edge[1])
                    continue;
                if(cnt == n - 1)
                    break;
                if(uf1.connect(e.v[0], e.v[1]) == true)
                {
                    curRes += e.v[2];
                    cnt++;
                }
            }
            if(uf1.maxx() != n || curRes > mstLen)
            {
                critical.push_back(a[i].index);
                continue;
            }

            UnionFind uf2(n);
            curRes = edge[2];
            cnt = 0;
            uf2.connect(edge[0], edge[1]);
            for(auto e : a)
            {
                if(cnt == n - 1)
                    break;
                if(uf2.connect(e.v[0], e.v[1]) == true)
                {
                    curRes += e.v[2];
                    cnt++;
                }
            }
            if(curRes == mstLen)
            {
                pseudo.push_back(a[i].index);
            }
        }
        res.push_back(critical);
        res.push_back(pseudo);
        return res;
    }
};
104290