<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:
    vector<int> parent; 
   
    static bool cmp(vector<int>&a , vector<int>&b) {
        return a[2] < b[2]; 
    }
	void union_(int u,int v){
	    if(abs(parent[u])<abs(parent[v])){
	        parent[v]+=parent[u];
	        parent[u]=v;
	    }
	    else{
	        parent[u]+=parent[v];
	        parent[v]=u;
	    }
	}
	int find_parent(int node){
	    if(parent[node]<0) return node;
	    return find_parent(parent[node]);
	}
    int spanningTree(int n, vector<vector<int>> edges,int skip,int add)
    {
        int ans=0;
        parent.resize(n);
        for(int i=0;i<n;i++)
            parent[i] = -1;
        if(add!=-1){
            int u_ptr=find_parent(edges[add][0]);
            int v_ptr=find_parent(edges[add][1]);
            union_(u_ptr,v_ptr);
            ans+=edges[add][2];
            
        }
        for(int i=0;i<edges.size();i++){
            if(i==skip) continue;
            int u=edges[i][0],v=edges[i][1];
            int u_ptr=find_parent(u);
            int v_ptr=find_parent(v);
            if(u_ptr!=v_ptr){
                union_(u_ptr,v_ptr);
                ans+=edges[i][2];
            }
        }
        //check whether all nodes are connected or not
        for(int i=0;i<n;i++){
            if(find_parent(i)!=find_parent(0)) return INT_MAX;
        }
        return ans;
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        vector<int> critical,pseudo;
        
        for(int i=0;i<edges.size();i++)   edges[i].push_back(i); 
        sort(edges.begin(),edges.end(),cmp);
        int mst_wt=spanningTree(n,edges,-1,-1);
        for(int i=0;i<edges.size();i++){
            if(spanningTree(n,edges,i,-1)>mst_wt) critical.push_back(edges[i][3]);
            else if(spanningTree(n,edges,-1,i)==mst_wt)  pseudo.push_back(edges[i][3]);
        }
        return {critical,pseudo};
    }
};
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