{ "data": { "question": { "questionId": "1613", "questionFrontendId": "1489", "boundTopicId": null, "title": "Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree", "titleSlug": "find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree", "content": "

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.

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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.

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Note that you can return the indices of the edges in any order.

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Example 1:

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\nInput: n = 5, edges = [[0,1,1],[1,2,1],[2,3,2],[0,3,2],[0,4,3],[3,4,3],[1,4,6]]\nOutput: [[0,1],[2,3,4,5]]\nExplanation: The figure above describes the graph.\nThe following figure shows all the possible MSTs:\n\"\"\nNotice 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.\nThe 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.\n
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Example 2:

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\nInput: n = 4, edges = [[0,1,1],[1,2,1],[2,3,1],[0,3,1]]\nOutput: [[],[0,1,2,3]]\nExplanation: 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.\n
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Constraints:

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