How should I practice Minimum Direction Violations?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Google onsite interview problems in FastPrep.

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FastPrep tags this as a Google onsite interview coding practice problem when the problem catalog has that company and stage context.

Problem · Graph

Minimum Direction Violations

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Problem statement

You are given a directed graph with n vertices numbered from 0 to n - 1. Each pair [u, v] in edges is an original directed edge from u to v.

You may traverse every listed edge in either direction:

Traversing from u to v, the original direction, costs 0 violations.
Traversing from v to u, against the original direction, costs 1 violation.

Return the minimum total number of direction violations needed to travel from start to end.

Function

minimumDirectionViolations(n: int, edges: int[][], start: int, end: int) → int

Examples

Example 1

n = 5edges = [[0,1],[2,1],[2,3],[4,3]]start = 0end = 4return = 2

Follow 0 -> 1, reverse 2 -> 1 to move 1 -> 2, follow 2 -> 3, and reverse 4 -> 3 to move 3 -> 4. Exactly two traversals oppose their original directions, and no path uses fewer violations.

Example 2

n = 4edges = [[0,1],[1,2],[2,3]]start = 0end = 3return = 0

The path 0 -> 1 -> 2 -> 3 follows every original edge direction, so its total violation cost is 0.

Example 3

n = 3edges = [[1,0],[0,2],[2,1]]start = 0end = 1return = 0

Reversing the direct edge 1 -> 0 would cost 1, but the longer path 0 -> 2 -> 1 follows original directions and costs 0.

Constraints

1 <= n <= 100000
0 <= edges.length <= 200000
Every entry in edges contains exactly two valid vertex indices.
0 <= start, end < n
end is reachable from start when all edge directions are ignored.