<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>

static const bool Booster = [](){
    std::ios_base::sync_with_stdio(false);
    std::cout.tie(nullptr);
    std::cin.tie(nullptr);
    return true;
}();

struct UnionFindSet {
	vector<int> parent;
	void init(int nn) {
		parent.resize(nn + 1);
		for (int i = 0; i < parent.size(); i++)
			parent[i] = i;
	}

	void merge(int x, int y) {
		parent[find(x)] = find(y);
	}
	int find(int x) {
		return x == parent[x] ? x : parent[x] = find(parent[x]);
	}
	bool together(int x, int y) {
		return find(x) == find(y);
	}
};
bool cmp(const vector<int>& a, const vector<int>& b) {
    return a[2] < b[2];
}

int kruskalls(int n, vector<vector<int>> edges, int forcedEdge = -1, int missedEdge = -1) {
    int mst = 0;
    int totalW = 0;
    UnionFindSet US;
    US.init(n);

    if (forcedEdge != -1) {
        for (const vector<int>& e : edges) {
            if (e[3] == forcedEdge) {
                mst++;
                totalW += e[2];
                US.merge(e[0], e[1]); 
            }
        }
    }

    int i = 0;
    while (mst < n - 1) {
        if (i == edges.size()) break;
        if (edges[i][3] != missedEdge) {
            int u = edges[i][0], v = edges[i][1];
            if (!US.together(u, v)) {
                totalW += edges[i][2];
                mst++;
                US.merge(u, v);
            }
        }
        i++;
    }

    return totalW;
}

class Solution {
public:
    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);
        vector<vector<int>> res = {{}, {}};

        int mst = kruskalls(n, edges); 
        for (int i = 0; i < edges.size(); i++) {
            int newMst = kruskalls(n, edges, i);
            if (newMst == mst) {
                int critEdgeMst = kruskalls(n, edges, -1, i);
                cout << format("critEdgeMst {} i {}\n", critEdgeMst, i);
                if (critEdgeMst == mst) {
                    res[1].push_back(i);
                } else {
                    res[0].push_back(i);
                }
            }
        }

        return res;
    }
};
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