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Minimum Union of Two Routes

Google● MediumINTERNONSITE INTERVIEW

Problem statement

You are given an undirected, unweighted graph with n vertices numbered from 0 to n - 1. Alice starts at vertex a, Bob starts at vertex b, and both must reach destination d.

Alice chooses one path from a to d, and Bob chooses one path from b to d. The cost of their two routes is the number of distinct undirected edges that appear in the union of both paths.

Return the minimum possible cost. Return -1 when either traveler cannot reach d.

The problem statement continues

Pro

Examples

Example 1

n = 7edges = [[0,2],[1,2],[2,3],[3,6],[0,4],[1,4],[4,5],[5,6]]a = 0b = 1d = 6return = 4

The travelers can meet at vertex 2. The edges from 0 and 1 to 2 contribute two edges, and the shared suffix 2 - 3 - 6 contributes two more.

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