<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 find(int u, vector<int>& parent) {
        if (parent[u] < 0) return u;
        return parent[u] = find(parent[u], parent);  
    }

    vector<pair<int, pair<int, int>>> create_mst(vector<pair<int, pair<int, int>>>& v, int& dis, int s) {
        vector<pair<int, pair<int, int>>> temp;
        int l = v.size();
        vector<int> parent(s, -1);
        
        dis = 0;  // Reset distance for each MST calculation
        for (int i = 0; i < l; i++) {
            int u = find(v[i].second.first, parent);
            int b = find(v[i].second.second, parent);
            if (u != b) {
                dis += v[i].first;
                temp.push_back(v[i]);
                
                if (abs(parent[u]) <= abs(parent[b])) {
                    parent[b] += parent[u];
                    parent[u] = b;
                } else {
                    parent[u] += parent[b];
                    parent[b] = u;
                }
            }
        }

        // Check if the MST is valid
        if (temp.size() != s - 1) {
            dis = INT_MAX;  // Set to a very high value if MST is not spanning all nodes
        }

        return temp;
    }

    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<pair<int, pair<int, int>>> a;
        int s = edges.size();
        vector<int> ans1, ans2;
        vector<vector<int>> ans;

        for (int i = 0; i < s; i++) {
            a.push_back({edges[i][2], {edges[i][0], edges[i][1]}});
        }

        sort(a.begin(), a.end());
        int dis1 = 0;
        vector<pair<int, pair<int, int>>> temp = create_mst(a, dis1, n);

        for (int i = 0; i < edges.size(); i++) {
            // Exclude edge i and create MST
            vector<pair<int, pair<int, int>>> modifiedEdges;
            for (int j = 0; j < edges.size(); ++j) {
                if (i != j) {
                    modifiedEdges.push_back({edges[j][2], {edges[j][0], edges[j][1]}});
                }
            }

            int dis = 0;
            sort(modifiedEdges.begin(), modifiedEdges.end());
            create_mst(modifiedEdges, dis, n);

            if (dis > dis1) {
                ans1.push_back(i);
            } else {
                // Check if edge i is pseudo-critical
                vector<pair<int, pair<int, int>>> forcedEdges = {{edges[i][2], {edges[i][0], edges[i][1]}}};
                forcedEdges.insert(forcedEdges.end(), modifiedEdges.begin(), modifiedEdges.end());

                dis = 0;
                auto forcedMST = create_mst(forcedEdges, dis, n);
                if (dis == dis1) {
                    ans2.push_back(i);  
                }
            }
        }

        ans.push_back(ans1);
        ans.push_back(ans2);
        return ans;
    }
};

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