{ "data": { "question": { "questionId": "3105", "questionFrontendId": "2858", "boundTopicId": null, "title": "Minimum Edge Reversals So Every Node Is Reachable", "titleSlug": "minimum-edge-reversals-so-every-node-is-reachable", "content": "

There is a simple directed graph with n nodes labeled from 0 to n - 1. The graph would form a tree if its edges were bi-directional.

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You are given an integer n and a 2D integer array edges, where edges[i] = [ui, vi] represents a directed edge going from node ui to node vi.

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An edge reversal changes the direction of an edge, i.e., a directed edge going from node ui to node vi becomes a directed edge going from node vi to node ui.

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For every node i in the range [0, n - 1], your task is to independently calculate the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

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Return an integer array answer, where answer[i] is the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

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Example 1:

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\nInput: n = 4, edges = [[2,0],[2,1],[1,3]]\nOutput: [1,1,0,2]\nExplanation: The image above shows the graph formed by the edges.\nFor node 0: after reversing the edge [2,0], it is possible to reach any other node starting from node 0.\nSo, answer[0] = 1.\nFor node 1: after reversing the edge [2,1], it is possible to reach any other node starting from node 1.\nSo, answer[1] = 1.\nFor node 2: it is already possible to reach any other node starting from node 2.\nSo, answer[2] = 0.\nFor node 3: after reversing the edges [1,3] and [2,1], it is possible to reach any other node starting from node 3.\nSo, answer[3] = 2.\n
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Example 2:

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\nInput: n = 3, edges = [[1,2],[2,0]]\nOutput: [2,0,1]\nExplanation: The image above shows the graph formed by the edges.\nFor node 0: after reversing the edges [2,0] and [1,2], it is possible to reach any other node starting from node 0.\nSo, answer[0] = 2.\nFor node 1: it is already possible to reach any other node starting from node 1.\nSo, answer[1] = 0.\nFor node 2: after reversing the edge [1, 2], it is possible to reach any other node starting from node 2.\nSo, answer[2] = 1.\n
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Constraints:

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\r\ndp[x] = dp[y] + (1 if the edge between x and y is going from y to x; 0 otherwise), where x is the parent of y.", "Let answer[x] be the minimum number of edge reversals so it is possible to reach any other node starting from node x.", "Using another DFS starting from node 0 and traversing the edges bidirectionally, we can compute answer.
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