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Detect Circular Dependencies
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Detect Circular Dependencies

MediumPython

Problem

IDFC FIRST Bank operates microservices whose dependencies form a directed graph. Given each service and the services it calls, detect whether any circular dependency exists and return one cycle if found.

Formal Specification

Implement detect_circular_dependencies(dependencies), where dependencies is a dictionary mapping a service name to a list of services it directly depends on. Return a list of service names representing any directed cycle, without repeating the first service. Return an empty list when the dependency graph is acyclic.

All service names are non-empty strings. A dependency may appear only in a list and should still be treated as a graph vertex with no outgoing dependencies. The order of a valid cycle is not important, and any one cycle is acceptable.

Constraints

  • 1 <= number of distinct services <= 10^5
  • 0 <= number of dependency edges <= 2 * 10^5
  • Service names are non-empty strings
  • The graph may be disconnected
  • A self-dependency counts as a cycle

Function Signature

def detect_circular_dependencies(dependencies):
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