<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 DisjointSet{

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

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

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

    void unionBySize(int u , int v){
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if(ulp_u==ulp_v){
            return ;
        }
        if(size[ulp_v]>size[ulp_v]){
            parent[ulp_u] = ulp_v;
            size[ulp_v] += size[ulp_u];
        }
        else{
            parent[ulp_v] = ulp_u;
            size[ulp_u] += size[ulp_v];
        }
    }

};

class Solution {
public:
int N;

int kruskal(vector<vector<int>> vec , int skip_edge , int add_edge){
    int sum = 0;
    DisjointSet ds(N);

    if(add_edge!=-1){
        ds.unionBySize(vec[add_edge][0],vec[add_edge][1]);
        sum += vec[add_edge][2];
    }

    
    for(int i =0;i<vec.size();i++){
        if(i==skip_edge){
            continue;
        }

        int u = vec[i][0];
        int v = vec[i][1];
        int paru = ds.findUPar(u);
        int parv = ds.findUPar(v);
        if(paru!=parv){
            ds.unionBySize(u,v);
            sum += vec[i][2];
        }
        
    }

    for(int i =0;i<N;i++){
        if(ds.findUPar(i)!=ds.findUPar(0)){
            return INT_MAX;
        }
    }

    return sum;

    
}
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        N = n;
        for(int i = 0;i<edges.size();i++){
            edges[i].push_back(i);
        }

        sort(edges.begin(),edges.end(),[](vector<int> a , vector<int>b){
            return a[2]<b[2];
        });


        vector<int> critical;
        vector<int> psuedo_critical;
        int mst_weight = kruskal(edges,-1,-1);
        for(int i =0;i<edges.size();i++){
            if(kruskal(edges,i,-1)>mst_weight){
                critical.push_back(edges[i][3]);
            }
            else if(kruskal(edges,-1,i)==mst_weight){
                psuedo_critical.push_back(edges[i][3]);
            }
        }

        return {critical,psuedo_critical};
        
    }
};
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