Grokking Graph Algorithms for Coding Interviews
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Reorder Routes to Make All Paths Lead to the City Zero (medium)
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Problem Statement

You are given n cities labeled from 0 to n-1 and n-1 roads, which form a tree structure. Each road is directed, meaning it has a specific direction. These roads are represented by the array connections, where connections[i] = [a, b] indicates a road from city a to city b.

Change the direction of some roads so that every city can reach city 0.

Return the minimum number of edges that need to be reversed.

Examples

Example 1

  • Input: n = 5, connections = [[0, 1], [1, 2], [2, 3], [4, 3]]
Image
  • Expected Output: 3
  • Justification: To make all cities lead to city 0, reverse the roads [0, 1], [1, 2] and [2, 3]. This will make the paths 0 <- 1 <- 2 <- 3 <- 4.

Example 2

  • Input: n = 6, connections = [[0, 1], [2, 0], [3, 2], [4, 3], [5, 3
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  • Expected Output: 1
  • Justification: To make all cities lead to city 0, reverse the road [0, 1].

Example 3

  • Input: n = 4, connections = [[1, 0], [2, 1], [3, 2]]
  • Expected Output: 0
  • Justification: All cities have path from itself to 0. So, we don't need to reverse any edge.

Constraints:

  • 2 <= n <= 5 * 10<sup>4<sup>
  • connections.length == n - 1
  • connections[i].length == 2
  • 0 <= a<sub>i</sub>, b<sub>i</sub> <= n - 1
  • a<sub>i</sub> != b<sub>i</sub>

Try it yourself

Try solving this question here:

Python3
Python3
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