LeetCode 1489: Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree

Explanation

To find the critical and pseudo-critical edges in a minimum spanning tree (MST) of a given graph, we can use the Kruskal's algorithm with some modifications. The main idea is to iterate through all the edges in the graph and determine whether an edge is critical or pseudo-critical based on the following criteria:

1. If an edge is not included in the MST, and adding that edge results in a higher MST weight, then it is a critical edge.
2. If an edge is included in all possible MSTs, then it is a critical edge.
3. If an edge is included in some but not all MSTs, then it is a pseudo-critical edge.

We start by sorting all the edges based on their weights. Then, we perform two rounds of MST construction:

1. First, we find the weight of the MST without considering any specific edge. This can be done by applying Kruskal's algorithm without including any edges.
2. Next, we iterate through each edge and check if it is a critical or pseudo-critical edge by temporarily excluding that edge from the graph, constructing the MST, and comparing the MST weight with the weight obtained in the first step.

The time complexity of this approach is O(E log E + E^2), where E is the number of edges in the graph. The space complexity is O(E).

class Solution {
    public List<List<Integer>> findCriticalAndPseudoCriticalEdges(int n, int[][] edges) {
        // Implementation in Java
    }
}