<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:
    int parent[100];
    int Size[100];
    static bool cmp(vector<int> x, vector<int> y) { return x[2] < y[2]; }
    void makeSet(int n) {
        for (int i = 0; i < n; i++) {
            parent[i] = i;
            Size[i] = 1;
        }
    }

    int Find(int x) {
        if (parent[x] == x)
            return x;
        return parent[x] = Find(parent[x]);
    }

    bool Union(int a, int b) {
        a = Find(a);
        b = Find(b);
        if (a == b)
            return false;
        if (Size[a] < Size[b])
            swap(a, b);
        parent[b] = a;
        Size[a] += Size[b];
        return true;
    }

    int kruskal1(vector<vector<int>> edges, int n, int pass) {
        int res = 0;
        int index = 0;
        makeSet(n);
        for (int i = 0; i < edges.size(); i++) {
            if (i == pass)
                continue;
            if (index == n - 1)
                break;
            if (Union(edges[i][0], edges[i][1])) {
                // cout<<edges[i][0]<<" "<<edges[i][1]<<endl;
                res += edges[i][2];
                index++;
            }
        }
        return (index == n - 1) ? res : INT_MAX; // Fix: Return INT_MAX if not
                                                 // enough edges to form MST
    }
    int kruskal2(vector<vector<int>> edges, int n, vector<int>& ad) {
        int res = ad[2];
        int index = 1;
        makeSet(n);
        Union(ad[0], ad[1]);
        for (int i = 0; i < edges.size(); i++) {
            if (index == n - 1)
                break;
            if (Union(edges[i][0], edges[i][1])) {
                // cout<<edges[i][0]<<" "<<edges[i][1]<<endl;
                res += edges[i][2];
                index++;
            }
        }
        return (index == n - 1) ? res : INT_MAX; // Fix: Return INT_MAX if not
                                                 // enough edges to form MST
    }

    vector<vector<int>>
    findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        for (int i = 0; i < edges.size(); i++) {
            edges[i].push_back(i);
        }
        sort(edges.begin(), edges.end(), cmp);
        int base = kruskal1(edges, n, -1);
        cout << base << endl;
        vector<int> crit;
        vector<int> pcrit;
        for (int i = 0; i < edges.size(); i++) {
            int res1 = kruskal1(edges, n, i);
            if (res1 > base) {
                crit.push_back(edges[i][3]);
            } else {
                int res2 = kruskal2(edges, n, edges[i]);
                if (res2 == base) {
                    pcrit.push_back(edges[i][3]);
                }
            }
        }
        vector<vector<int>> res;
        res.push_back(crit);
        res.push_back(pcrit);
        return res;
    }
};
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