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Improved Bellman-Ford Algorithm : Added Path Reconstruction With Better Output Representation

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unknown 2024-10-11 05:40:11 +05:30
parent f8a94a8b00
commit 4a30fcd84d
1 changed files with 20 additions and 12 deletions
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32
graphs/bellman_ford.py
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@ -17,22 +17,28 @@ def print_distance_and_paths(distance: list[float], paths: list[list[int]], src:
print(f"{vertex}\t\t{dist}\t\t\t\t{path_str}")
def check_negative_cycle(graph: list[Edge], distance: list[float], predecessor: list[int]) -> bool:
def check_negative_cycle(graph: list[Edge], distance: list[float],
predecessor: list[int]) -> bool:
"""
Checks if there is a negative weight cycle reachable from the source vertex.
If found, return True, indicating a negative cycle.
"""
for edge in graph:
if distance[edge.src] != float("inf") and distance[edge.src] + edge.weight < distance[edge.dst]:
if (distance[edge.src] != float("inf") and
distance[edge.src] + edge.weight
< distance[edge.dst]):
# Update predecessors to indicate a cycle for affected paths
predecessor[edge.dst] = -1 # Use -1 as a marker for negative cycle detection
# Use -1 as a marker for negative cycle detection
predecessor[edge.dst] = -1
return True
return False
def reconstruct_paths(predecessor: list[int], vertex_count: int, src: int) -> list[list[int]]:
def reconstruct_paths(predecessor: list[int],
vertex_count: int, src: int) -> list[list[int]]:
"""
Reconstructs the shortest paths from the source vertex to each vertex using the predecessor list.
Reconstructs the shortest paths from the source vertex to
each vertex using the predecessor list.
"""
paths = [[] for _ in range(vertex_count)]
for vertex in range(vertex_count):
@ -50,9 +56,11 @@ def reconstruct_paths(predecessor: list[int], vertex_count: int, src: int) -> li
return paths
def bellman_ford(graph: list[Edge], vertex_count: int, src: int) -> tuple[list[float], list[list[int]]]:
def bellman_ford(graph: list[Edge],
vertex_count: int, src: int) -> tuple[list[float], list[list[int]]]:
"""
Returns the shortest paths from a vertex src to all other vertices, including path reconstruction.
Returns the shortest paths from a vertex src to all other vertices,
including path reconstruction.
"""
distance = [float("inf")] * vertex_count
predecessor = [None] * vertex_count # Keeps track of the path predecessors
@ -61,7 +69,8 @@ def bellman_ford(graph: list[Edge], vertex_count: int, src: int) -> tuple[list[f
# Step 1: Relax edges repeatedly
for _ in range(vertex_count - 1):
for edge in graph:
if distance[edge.src] != float("inf") and distance[edge.src] + edge.weight < distance[edge.dst]:
if (distance[edge.src] != float("inf") and
distance[edge.src] + edge.weight < distance[edge.dst]):
distance[edge.dst] = distance[edge.src] + edge.weight
predecessor[edge.dst] = edge.src
@ -88,7 +97,8 @@ if __name__ == "__main__":
for i in range(E):
print(f"Edge {i + 1}")
src, dest, weight = map(int, input("Enter source, destination, weight: ").strip().split())
src, dest, weight = map(int,
input("Enter source, destination, weight: ").strip().split())
if src < 0 or src >= V or dest < 0 or dest >= V:
print(f"Invalid vertices: src and dest should be between 0 and {V - 1}")
continue
@ -101,6 +111,4 @@ if __name__ == "__main__":
shortest_distance, paths = bellman_ford(graph, V, source)
print_distance_and_paths(shortest_distance, paths, source)
except ValueError:
print("Please enter valid integer inputs.")
except Exception as e:
print(e)
print("Invalid input. Please enter valid integers.")