<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>

#include <iostream>
#include <vector>
#include <algorithm>
#include <climits>

using namespace std;

class UnionFind {
public:
    vector<int> parent;

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

    int findParent(int p) {
        return parent[p] == p ? p : parent[p] = findParent(parent[p]);
    }

    void Union(int u, int v) {
        int pu = findParent(u), pv = findParent(v);
        parent[pu] = pv;
    }
};

class Solution {
private:
    int MST(int n, vector<vector<int>> &edges, int block, int e) {
        UnionFind uf(n);
        int w = 0;

        //include the excluded edge if required (find initial weight of MST to compare for crit edge)
        if (e != -1) {
            w += edges[e][2];
            uf.Union(edges[e][0], edges[e][1]);
        }

        // build mst
        for (int i = 0; i < edges.size(); i++) {
            if (i == block) continue;
            if (uf.findParent(edges[i][0]) == uf.findParent(edges[i][1])) continue;

            uf.Union(edges[i][0], edges[i][1]);
            w += edges[i][2];
        }

        for (int i = 0; i < n; i++) {
            if (uf.findParent(i) != uf.findParent(0)) return INT_MAX;
        }

        return w;
    }

public:
    // comparator function for sorting on weight
    static bool cmp(vector<int> &a, vector<int> &b) {
        return a[2] < b[2];
    }

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

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

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

        //first to find the weight of the mst
        int mst = MST(n, edges, -1, -1);

        for (int i = 0; i < edges.size(); i++) {
            if (mst < MST(n, edges, i, -1)) {
                critical.push_back(edges[i][3]);
            } else if (mst == MST(n, edges, -1, i)) {
                pseudoCritical.push_back(edges[i][3]);
            }
        }

        return {critical, pseudoCritical};
    }
};

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