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

Hard

Given a weighted undirected connected graph with n vertices numbered from 0 to n - 1, and an array edges where <code>edgesi = a_i, b_i, weight_i</code> represents a bidirectional and weighted edge between nodes <code>a_i</code> and <code>b_i</code>. 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:

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

• <code>0 <= a_i< b_i< n</code>

• <code>1 <= weight_i<= 1000</code>

• All pairs <code>(a_i, b_i)</code> are distinct.