Package g1401_1500.s1489_find_critical_and_pseudo_critical_edges_in_minimum_spanning_tree

Class Solution

  • public class Solution
extends Object
    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 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:

    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.

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • findCriticalAndPseudoCriticalEdges

        public List<List<Integer>> findCriticalAndPseudoCriticalEdges​(int n,
                                                              int[][] edges)