<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: 

    unordered_map<int,int> parent;
    unordered_map<int,int> rank;

    UnionFind(int n) {
        for(int i=0; i<n; i++) {
            parent[i] = i;
            rank[i] = 1;
        }
    }

    int find(int p) {
        while(p != parent[p]) {
            parent[p] = parent[parent[p]];
            p = parent[p];
        }
        return p;
    }

    bool unite(int p, int q) {

        int x = find(p), y = find(q);

        if(x==y) return false;

        if(rank[x] < rank[y]) {
            parent[x] = y;
            rank[y] += rank[x];
        }
        else {
            parent[y] = x;
            rank[x] += rank[y];
        }
        return true;
    }

    void clear(int n){
        for(int i=0; i<n; i++) {
            parent[i] = i;
            rank[i] = 1;
        }
    }

    int maxRank() {
        int max = 0;
        for(auto p : rank) max = fmax(max, p.second);
        return max;
    }
};

bool f(vector<int>a, vector<int>b){
    return a[2] < b[2];
}

class Solution {
public:

    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {

        map<vector<int>,int>eind;
        for(int i=0; i<edges.size(); i++) eind[edges[i]] = i;
        sort(edges.begin(), edges.end(), f);

        UnionFind u(n);
        int min_wt = 0;
        for(auto e: edges) {
            int a = e[0], b = e[1], w = e[2];
            if(u.unite(a,b)) min_wt += w;
        }

        vector<int> cr;
        vector<int> noncr;
        int wt, a, b, w;

        for(int i=0; i<edges.size(); i++){

            // Try without curr edge
            u.clear(n);
            wt = 0;
            for(int j=0; j<edges.size(); j++){
                auto e = edges[j];
                a = e[0], b = e[1], w = e[2];
                if(i==j) continue;
                if(u.unite(a,b)) wt += w;
            }
            cout<<i<<"\t\t"<<u.maxRank()<<"\t"<<wt<<endl;

            if(u.maxRank() != n || wt > min_wt) {
                cr.push_back(eind[edges[i]]);
                continue;
            }

            // Try with curr edge
            u.clear(n);
            u.unite(edges[i][0], edges[i][1]);
            wt = edges[i][2];
            for(auto e: edges){
                a = e[0], b = e[1], w = e[2];
                if(u.unite(a,b)) wt += w;
            }
            if(wt == min_wt) noncr.push_back(eind[edges[i]]);
        }

        return {cr, noncr};
    }
};
81296