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

https://leetcode.com/problems/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] = [ai, bi, weighti] represents a bidirectional and weighted edge between nodes ai and bi. 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.

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:
![](https://assets.leetcode.com/uploads/2020/06/04/msts.png)
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 <= ai < bi < n

• 1 <= weighti <= 1000

• All pairs (ai, bi) are distinct.

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