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How to Solve Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree Problem
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LeetCode ProblemFind Critical and Pseudo-Critical Edges in Minimum Spanning Tree
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.
Union FindGraphSortingMinimum Spanning TreeStrongly Connected Component
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Problem Breakdown
Understanding the Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree Problem
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Problem Statement
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.
HardProblem #1489
LeetCodeFind Critical and Pseudo-Critical Edges in Minimum Spanning Tree
Related Topics
Union FindGraphSortingMinimum Spanning TreeStrongly Connected Component
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Examples
# 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]]
# Example 2
Input
n = 4, edges = [[0,1,1],[1,2,1],[2,3,1],[0,3,1]]
Output
[[],[0,1,2,3]]
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.
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Solve Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree — Given a weighted undirected connected graph with n vertices numbered from 0 to n...
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Frequently Asked Questions
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The AI provides structured guidance: first the approach (what algorithm/data structure to use and why), then the implementation with clean code, and finally complexity analysis. This helps you think clearly even under pressure.
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