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Cycle Detection in Loyalty Graphs

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Your question is Cycle Detection in Loyalty Graphs. Start with the requirements on the right.

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Problem

CRED models loyalty reward dependencies as a directed graph: an edge u -> v means reward rule u depends on reward rule v. A circular dependency can prevent reward evaluation from completing.

Given the number of reward rules and a list of directed edges, determine whether the graph contains at least one cycle.

Formal Specification

Implement has_cycle(n, edges), where n is an integer representing reward rules labeled 0 through n - 1, and edges is a list of two-element lists [u, v] representing a directed edge from u to v. Return True if any directed cycle exists, otherwise return False.

The graph may be disconnected and may contain multiple edges between the same pair of vertices. A self-loop, such as [2, 2], is a cycle.

Constraints

  • 1 <= n <= 10^5
  • 0 <= len(edges) <= 2 * 10^5
  • Each edge contains exactly two integers
  • 0 <= u, v < n for every edge [u, v]

Function Signature

def has_cycle(n, edges):
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