<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>


#include <bits/stdc++.h>
using namespace std;

static const int _ = []()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 0;
}();

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

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

    void unionNodes(int u, int v)
    {
        int uroot = find(u);
        int vroot = find(v);
        if (uroot != vroot)
        {
            if (size[uroot] > size[vroot])
            {
                parent[vroot] = uroot;
                size[uroot] += size[vroot];
            }
            else
            {
                parent[uroot] = vroot;
                size[vroot] += size[uroot];
            }
        }
    }

    bool validate()
    {
        // cout<<"parent: ";
        // for(auto it : parent){
        //     cout<<it<<" ";
        // }
        // cout<<"\n";
        for (int i = 0; i < parent.size() - 1; ++i)
        {
            if (find(i) != find(i + 1))
            {
                return false;
            }
        }
        return true;
    }
};

class Solution
{
public:
    int kruskals(int n, vector<vector<int>> &edges, int skip, int inc = -1)
    {
        UnionFind *obj = new UnionFind(n);
        int total = 0, size = edges.size();
        if (inc != -1)
        {
            total += edges[inc][0];
            obj->unionNodes(edges[inc][1], edges[inc][2]);
        }
        for (int i = 0; i < size; ++i)
        {
            if (i != skip && i != inc)
            {
                if (obj->find(edges[i][1]) != obj->find(edges[i][2]))
                {
                    obj->unionNodes(edges[i][1], edges[i][2]);
                    total += edges[i][0];
                }
            }
        }

        return obj->validate() ? total : INT_MIN;
    }

    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>> &edges)
    {
        vector<vector<int>> result(2);
        set<int> st;
        for (int i = 0; i < edges.size(); ++i)
        {
            // swap(edges[i][2], edges[i][1]);
            // swap(edges[i][0], edges[i][1]);
            // edges[i].push_back(i);
            edges[i] = {edges[i][2], edges[i][0], edges[i][1], i};
        }
        sort(edges.begin(), edges.end());
        for(auto it : edges){
            cout<<it[0]<<" "<<it[1]<<" "<<it[2]<<" "<<it[3]<<"\n";
        }
        int mst = kruskals(n, edges, -1, -1);
        cout << mst << "\n";
        for (int i = 0; i < edges.size(); ++i)
        {
            int temp = kruskals(n, edges, i, -1);
            if (temp > mst || temp == INT_MIN)
            {
                result[0].push_back(edges[i][3]);
            }
            temp = kruskals(n, edges, -1, i);
            if (temp == mst)
            {
                st.insert(edges[i][3]);
            }
        }
        // remove the critical edges from pseudo critical edges
        for (auto it : result[0])
        {
            st.erase(it);
        }
        for (auto it : st)
        {
            result[1].push_back(it);
        }
        return result;
    }
};
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