#1489
Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree
expert · 1060 · lc hard +32 · verified · 66.3% accepted · 1,997 likes · top 71%
Description
A weighted undirected connected graph has n vertices (labeled 0 to n-1) and edges edges[i] = [ai, bi, weighti]. Classify each edge as: a critical edge (its removal forces the MST weight to increase), a pseudo-critical edge (it belongs to some but not all MSTs), or neither.
Return two lists — critical edge indices and pseudo-critical edge indices — 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:
Example 2:
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 3:
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.
Code
1
2
3