def find_negative_cycle(
graph: Graph, source: str) -> Tuple[bool, Optional[List[Graph.Edge]]]:
"""
Finds a negative cycle starting at source in graph.
:param graph: the graph where source is
:param source: the starting node of the cycle to find
:return:
found: True if a negative cycle exists, False otherwise
cycle: the list of edges representing the cycle. It is None if found is False.
"""
# Step 1: Find all neighbors outgoing from source
neighbors = {
edge.opposite(source): edge
for edge in graph.incident_edges(source, outgoing=True)
}
# Step 2: Find minimum edge weight in the graph
minimum_edge_weight = min(edge.element() for edge in graph.edges())
# Step 3: Make all edges positive
for edge in graph.edges():
edge._element += abs(minimum_edge_weight)
# Step 4: Call compute_shortest_path from each vertex in neighbors to source
paths = {
vertex: compute_shortest_path(graph, vertex, source)
for vertex in neighbors
}
# Step 5: Restore all edges weights
for edge in graph.edges():
edge._element -= abs(minimum_edge_weight)
# Step 6: Close cycles
for vertex, path in paths.items():
if len(path) == 0:
continue
path_weight = sum(edge.element() for edge in path)
first_edge = neighbors[vertex]
first_weight = first_edge.element()
cycle_weight = first_weight + path_weight
cycle = [first_edge] + path
if cycle_weight < 0:
return True, cycle
return False, None
