<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:

    class UnionFind:
        def __init__(self, n):
            self.parent = list(range(n))
            self.size = [1] * n
            self.max_size = 1

        def find(self, x):
            # Finds the root of x
            if x != self.parent[x]:
                self.parent[x] = self.find(self.parent[x])
            return self.parent[x]

        def union(self, x, y):
            # Connects x and y
            root_x = self.find(x)
            root_y = self.find(y)
            if root_x != root_y:
                if self.size[root_x] < self.size[root_y]:
                    root_x, root_y = root_y, root_x
                self.parent[root_y] = root_x
                self.size[root_x] += self.size[root_y]
                self.max_size = max(self.max_size, self.size[root_x])
                return True
            return False

    def findCriticalAndPseudoCriticalEdges(self, n, edges):
        new_edges = [edge.copy() for edge in edges]
        # Add index to edges for tracking
        for i, edge in enumerate(new_edges):
            edge.append(i)
        # Sort edges based on weight
        new_edges.sort(key=lambda x: x[2])
        print(new_edges)
        # Find MST weight using union-find
        uf_std = self.UnionFind(n)
        std_weight = 0
        for u, v, w, _ in new_edges:
            if uf_std.union(u, v):
                std_weight += w
                        
        # Check each edge for critical and pseudo-critical
        critical = []
        pseudo_critical = []
        for (u, v, w, i) in new_edges:
            # Ignore this edge and calculate MST weight
            uf_ignore = self.UnionFind(n)
            ignore_weight = 0
            for (x, y, w_ignore, j) in new_edges:
                if i != j and uf_ignore.union(x, y):
                    ignore_weight += w_ignore
            # If the graph is disconnected or the total weight is greater,
            # the edge is critical
            if uf_ignore.max_size < n or ignore_weight > std_weight:
                critical.append(i)
                continue

            # Force this edge and calculate MST weight
            uf_force = self.UnionFind(n)
            force_weight = w
            uf_force.union(u, v)
            for (x, y, w_force, j) in new_edges:
                if i != j and uf_force.union(x, y):
                    force_weight += w_force
            # If total weight is the same, the edge is pseudo-critical
            if force_weight == std_weight:
                pseudo_critical.append(i)

        return [critical, pseudo_critical]
696