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115 lines
3.9 KiB
Python
115 lines
3.9 KiB
Python
from typing import NamedTuple
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class Edge(NamedTuple):
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src: int
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dst: int
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weight: int
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def print_distance_and_paths(distance: list[float], paths: list[list[int]], src: int):
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"""
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Prints the shortest distance and paths from the source vertex to each vertex.
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"""
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print(f"Vertex\tShortest Distance from Vertex {src}\tPath")
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for vertex, (dist, path) in enumerate(zip(distance, paths)):
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path_str = " -> ".join(map(str, path)) if path else "No path"
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print(f"{vertex}\t\t{dist}\t\t\t\t{path_str}")
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def check_negative_cycle(graph: list[Edge], distance: list[float],
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predecessor: list[int]) -> bool:
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"""
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Checks if there is a negative weight cycle reachable from the source vertex.
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If found, return True, indicating a negative cycle.
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"""
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for edge in graph:
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if (distance[edge.src] != float("inf") and
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distance[edge.src] + edge.weight
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< distance[edge.dst]):
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# Update predecessors to indicate a cycle for affected paths
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# Use -1 as a marker for negative cycle detection
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predecessor[edge.dst] = -1
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return True
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return False
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def reconstruct_paths(predecessor: list[int],
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vertex_count: int, src: int) -> list[list[int]]:
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"""
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Reconstructs the shortest paths from the source vertex to
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each vertex using the predecessor list.
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"""
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paths = [[] for _ in range(vertex_count)]
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for vertex in range(vertex_count):
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if predecessor[vertex] == -1:
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paths[vertex] = ["Negative cycle detected"]
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elif predecessor[vertex] is not None:
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path = []
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current = vertex
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while current is not None:
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path.insert(0, current)
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if current == src:
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break
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current = predecessor[current]
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paths[vertex] = path
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return paths
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def bellman_ford(graph: list[Edge],
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vertex_count: int, src: int) -> tuple[list[float], list[list[int]]]:
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"""
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Returns the shortest paths from a vertex src to all other vertices,
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including path reconstruction.
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"""
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distance = [float("inf")] * vertex_count
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predecessor = [None] * vertex_count # Keeps track of the path predecessors
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distance[src] = 0.0
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# Step 1: Relax edges repeatedly
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for _ in range(vertex_count - 1):
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for edge in graph:
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if (distance[edge.src] != float("inf") and
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distance[edge.src] + edge.weight < distance[edge.dst]):
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distance[edge.dst] = distance[edge.src] + edge.weight
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predecessor[edge.dst] = edge.src
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# Step 2: Check for negative weight cycles
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if check_negative_cycle(graph, distance, predecessor):
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raise Exception("Negative cycle found")
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# Step 3: Reconstruct paths from predecessor list
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paths = reconstruct_paths(predecessor, vertex_count, src)
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return distance, paths
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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try:
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V = int(input("Enter number of vertices: ").strip())
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E = int(input("Enter number of edges: ").strip())
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graph: list[Edge] = []
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for i in range(E):
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print(f"Edge {i + 1}")
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src, dest, weight = map(int,
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input("Enter source, destination, weight: ").strip().split())
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if src < 0 or src >= V or dest < 0 or dest >= V:
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print(f"Invalid vertices: src and dest should be between 0 and {V - 1}")
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continue
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graph.append(Edge(src, dest, weight))
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source = int(input("\nEnter shortest path source vertex: ").strip())
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if source < 0 or source >= V:
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print(f"Invalid source: source should be between 0 and {V - 1}")
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else:
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shortest_distance, paths = bellman_ford(graph, V, source)
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print_distance_and_paths(shortest_distance, paths, source)
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except ValueError:
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print("Invalid input. Please enter valid integers.")
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