<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>

bool cmp(vector<int>&a,vector<int>&b){
    cout<<a.size()<<" "<<b.size()<<endl;
        return a[2]<=b[2];
}
class Solution {
public:
    int find_parent(int a,vector<int>&parent){
        if(a==parent[a]) return a;
        else return parent[a]=find_parent(parent[a],parent); 
    }
    bool union_by_size(int a,int b,vector<int>&size,vector<int>&parent){
        int ua=find_parent(a,parent);
        int ub=find_parent(b,parent);
        if(ua==ub) return false;
        if(size[ua]>=size[ub]){
            parent[ub]=ua;
            size[ua]+=size[ub];
        }
        else{
            parent[ua]=ub;
            size[ub]+=size[ua];
        }
        return true;
    }

    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);
        sort(edges.begin(), edges.end(), [](const vector<int>& a, const vector<int>& b) {
            return a[2] < b[2];
        });
        int mst=0;
        vector<int>size(n,1);
        vector<int>parent(n);
        for(int i=0;i<n;i++) parent[i]=i;
        for(auto e:edges){
            if(union_by_size(e[0],e[1],size,parent)) mst+=e[2];
        }
        vector<int>critical;
        vector<int>pseudoCritical;
        for(auto e1:edges){
            int mst2=0;
            for(int i=0;i<n;i++) size[i]=1;
            for(int i=0;i<n;i++) parent[i]=i;
            for(auto e2:edges){
                if(e2[3]!=e1[3] && union_by_size(e2[0],e2[1],size,parent)){
                     mst2+=e2[2];
                    //  continue;
                }
            }
            // cout<<mst<<" "<<mst2<<endl;
            if(mst<mst2 || (*max_element(size.begin(),size.end()))!=n) {
                critical.push_back(e1[3]);
                continue;
            }
            int mst3=0;
            for(int i=0;i<n;i++) size[i]=1;
            for(int i=0;i<n;i++) parent[i]=i;
            union_by_size(e1[0],e1[1],size,parent);
            mst3+=e1[2];
            for(auto e2:edges){
                if(union_by_size(e2[0],e2[1],size,parent)) mst3+=e2[2];
            }
            if(mst==mst3) pseudoCritical.push_back(e1[3]); 
        }
        return {critical,pseudoCritical};
    }
};
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