<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>

struct DisjoinSetUnion {
public:
    DisjoinSetUnion(int _size): size(_size){
        for (int i = 0; i < _size; ++i)
            parent.emplace_back(i);
    }
    bool isUnion(const int &a, const int &b) {
        return getParent(a) == getParent(b); 
    }
    void unionSets(int a, int b){
        a = getParent(a);
        b = getParent(b);
        if (a != b){
            if (size[a] < size[b])
                std::swap(a, b);
            parent[b] = a;
            size[a] += size[b];
        }
    }
private:
    std::vector<int> parent, size;
    int getParent(int s){
        if (parent[s] == s)
            return s;
        return parent[s] = getParent(parent[s]);
    }
};
class Solution {
public:
    std::vector<std::vector<int>> findCriticalAndPseudoCriticalEdges(int n, std::vector<std::vector<int>>& edges) {
        
        const int NOF_EDGES = edges.size();

        // Make elements in edges array have struct {ai, bi, weighti, i}.
        for (int i = 0; i < edges.size(); ++i){
            edges[i].emplace_back(i);
        }
        
        // Sort edges array in order of weight.
        auto customComp = [](const std::vector<int>&a, const std::vector<int>&b)->bool const {
            if (a[2] < b[2])
                return true;
            return false;
        };
        std::sort(edges.begin(), edges.end(), customComp);
        
        int minMSTLength = INT_MAX;
        std::vector<int> lenMSTExcludeEdge(NOF_EDGES);
        std::vector<int> lenMSTIncludeEdge(NOF_EDGES);

        // Exclude one edge a time.
        std::vector<int> uselessEdge{0, 0, 0, -1};
        for (int i = 0; i < edges.size(); ++i){
            DisjoinSetUnion dsu(n);
            int length = 0;
            int unionedTimes = 0;

            std::swap(edges[i], uselessEdge);
            kruskal(length, unionedTimes, n, edges, dsu);
            std::swap(edges[i], uselessEdge);
            lenMSTExcludeEdge[edges[i][3]] = length;
        }

        // Include one edge a time.
        for (int i = 0; i < edges.size(); ++i){
            DisjoinSetUnion dsu(n);
            int length = edges[i][2];
            int unionedTimes = 1;
            dsu.unionSets(edges[i][0], edges[i][1]);
            
            kruskal(length, unionedTimes, n, edges, dsu);
            lenMSTIncludeEdge[edges[i][3]] = length;
            
            minMSTLength = std::min(minMSTLength, length);
        }


        std::vector<std::vector<int>> result(2);
        for (int i = 0; i < NOF_EDGES; ++i){
            if (lenMSTExcludeEdge[i] > minMSTLength)
                result[0].emplace_back(i);
            else if (lenMSTIncludeEdge[i] == minMSTLength)
                result[1].emplace_back(i);
        }
        
        return result;
    }
private:
    void kruskal(int &length, int &unionedTimes,
        const int &n, const std::vector<std::vector<int>> &edges, DisjoinSetUnion &dsu){
        
        for (const auto &edge : edges){
            if (!dsu.isUnion(edge[0], edge[1])){
                length += edge[2];
                dsu.unionSets(edge[0], edge[1]);
                if (++unionedTimes == n - 1)
                    return;
            }
        }
        
        if (unionedTimes != n - 1)
            length = INT_MAX;
    }
};
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