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

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

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

    bool findUnion(int x, int y){
        int px=findUltParent(x);
        int py=findUltParent(y);

        if(px==py) return false;

        if(size[px]>size[py]){
            parent[px]=py;
            size[px]+=size[py];
        }
        else{
            parent[py]=px;
            size[py]+=size[px];
        }

        return true;
    }
};

class Solution {
public:

    static bool comp(vector<int>& a, vector<int>& b){
        return a[2]<b[2];
    }
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        disjoint d1(n);
        map<pair<int,int>,int> mp;
        for(int i=0;i<edges.size();i++){
            mp[{edges[i][0],edges[i][1]}]=i;
        }
        sort(edges.begin(),edges.end(),comp);

        int minweight=0;
        for(auto v: edges){
            if(d1.findUnion(v[0],v[1])) minweight+=v[2];
        }
        cout<<"min "<<minweight<<endl;

        map<pair<int,int>, int> mp2;
        vector<int> criticaledges;
        for(auto v:edges){
            disjoint d(n);
            int val=0;
            for(auto u:edges){
                if(u[0]==v[0] && u[1]==v[1]) continue;
                if(d.findUnion(u[0],u[1])) val+=u[2];
            }
            cout<<val<<endl;
            // need to check whether the graph is connected or not as we have ignored v edge completely
            bool connected=true;
            int ultparent= d.findUltParent(0);
            for(int i=1;i<n;i++){
                if(d.findUltParent(i)!=ultparent){
                    connected=false; break;
                } 
            }

            // this edge should be present in every mst, otherwise cost is more.
            if(val>minweight || (connected==false)){
                criticaledges.push_back(mp[{v[0],v[1]}]);
                mp2[{v[0],v[1]}]=1;
            }
        }


        vector<int> pseudocriticaledges;
        for(auto v: edges){
            if(mp2.find({v[0],v[1]})!=mp2.end()) continue;
            disjoint d(n);
            int val=0;
            // must include this edge
            // this edge is not critical and should be part of atleast 1 mst to be pseudocritical
            d.findUnion(v[0],v[1]);
            val+=v[2];
            for(auto u:edges){
                // if(u[0]==v[0] && u[1]==v[1]) continue;
                if(d.findUnion(u[0],u[1])) val+=u[2];
            }
            if(val==minweight){
                pseudocriticaledges.push_back(mp[{v[0],v[1]}]);
            }
        }

        vector<vector<int>> ans;
        ans.push_back(criticaledges);
        ans.push_back(pseudocriticaledges);
        return ans;

    }
};
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