Package g1401_1500.s1489_find_critical_and_pseudo_critical_edges_in_minimum_spanning_tree

Class Solution

java.lang.Object

g1401_1500.s1489_find_critical_and_pseudo_critical_edges_in_minimum_spanning_tree.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 Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
List<List<Integer>>	findCriticalAndPseudoCriticalEdges(int n, int[][] edges)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

findCriticalAndPseudoCriticalEdges

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