<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:
    class DSU {
    public:
        vector<int> parent, size;
        DSU(int n) {
            parent.resize(n + 1);
            size.resize(n + 1);
            for (int i = 0; i <= n; i++) {
                parent[i] = i;
                size[i] = 1;
            }
        }

        int findUpperPar(int node) {
            if (node == parent[node])
                return node;

            return parent[node] = findUpperPar(parent[node]);
        }

        void unionBySize(int u, int v) {
            int ultimate_par_u = findUpperPar(u);
            int ultimate_par_v = findUpperPar(v);

            if (size[ultimate_par_u] > size[ultimate_par_v]) {
                parent[ultimate_par_v] = ultimate_par_u;
                size[ultimate_par_u] += size[ultimate_par_v];

            } else {
                parent[ultimate_par_u] = ultimate_par_v;
                size[ultimate_par_v] += size[ultimate_par_u];
            }
        }
    };
    int mst(int n, vector<vector<int>> edges) {
         sort(edges.begin(), edges.end());
        DSU ds(n + 1);
        int weight = 0;
        for (int i = 0; i < edges.size(); i++) {
            if (ds.findUpperPar(edges[i][1]) != ds.findUpperPar(edges[i][2])) {
                ds.unionBySize(edges[i][1], edges[i][2]);
                weight += edges[i][0];
            }
        }
        return weight;
    }

    int find_critic_or_psedo(int n, int mstvalue, int wei, int u, int v,
                             set<pair<int, pair<int, int>>>& st) {

        int weight_without = 0;
        st.erase({wei, {u, v}});
         //  cout<<wei<<u<<v<<endl;
        DSU ds1(n + 1);
        for (auto it : st) {
            if (ds1.findUpperPar(it.second.first) !=
                ds1.findUpperPar(it.second.second)) {
             //   cout <<it.first<< it.second.first << it.second.second << endl;
                ds1.unionBySize(it.second.first, it.second.second);
                weight_without += it.first;
            }
        }
        
        if (mstvalue != weight_without || ds1.size[ds1.findUpperPar(0)] != n ) {
            st.insert({wei, {u, v}});
            return 1;
        }

        DSU ds2(n + 1);
        ds2.unionBySize(u, v);
        int weight_with = wei;
        for (auto it : st) {
            if (ds2.findUpperPar(it.second.first) !=
                ds2.findUpperPar(it.second.second)) {
                ds2.unionBySize(it.second.first, it.second.second);
                weight_with += it.first;
            }
        }
        st.insert({wei, {u, v}});
          // cout<<weight_without<<" "<<weight_with<<endl;
        if (weight_without == mstvalue && weight_with == mstvalue &&
            ds2.size[ds2.findUpperPar(0)] == n)
            return 2;

        return 0;
    }
    vector<vector<int>>
    findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<vector<int>> cricAndPsedoedge(2);

        set<pair<int, pair<int, int>>> st;

        for (int i = 0; i < edges.size(); i++) {
            swap(edges[i][0], edges[i][2]);
            st.insert({edges[i][0], {edges[i][1], edges[i][2]}});
        }

       

        int mstvalue = mst(n, edges);

        for (int i = 0; i < edges.size(); i++) {

            int value = find_critic_or_psedo(n, mstvalue, edges[i][0],
                                             edges[i][1], edges[i][2], st);
            if (value == 1) {
                cricAndPsedoedge[0].push_back(i);
            }else if (value == 2) {
                cricAndPsedoedge[1].push_back(i);
            }
        }

        return cricAndPsedoedge;
    }
};
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