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# 1489. Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree

## Description

Given a weighted undirected connected graph with `n`

vertices numbered from `0`

to `n - 1`

, and an array `edges`

where `edges[i] = [a`

represents a bidirectional and weighted edge between nodes _{i}, b_{i}, weight_{i}]`a`

and _{i}`b`

. A minimum spanning tree (MST) is a subset of the graph's edges that connects all vertices without cycles and with the minimum possible total edge weight._{i}

Find *all the critical and pseudo-critical edges in the given graph's minimum spanning tree (MST)*. An MST edge whose deletion from the graph would cause the MST weight to increase is called a *critical edge*. On the other hand, a pseudo-critical edge is that which can appear in some MSTs but not all.

Note that you can return the indices of the edges in any order.

**Example 1:**

Input:n = 5, edges = [[0,1,1],[1,2,1],[2,3,2],[0,3,2],[0,4,3],[3,4,3],[1,4,6]]Output:[[0,1],[2,3,4,5]]Explanation:The figure above describes the graph. The following figure shows all the possible MSTs: 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.

**Example 2:**

Input:n = 4, edges = [[0,1,1],[1,2,1],[2,3,1],[0,3,1]]Output:[[],[0,1,2,3]]Explanation: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.

**Constraints:**

`2 <= n <= 100`

`1 <= edges.length <= min(200, n * (n - 1) / 2)`

`edges[i].length == 3`

`0 <= a`

_{i}< b_{i}< n`1 <= weight`

_{i}<= 1000- All pairs
`(a`

are_{i}, b_{i})**distinct**.