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126 lines
3.7 KiB
Python
126 lines
3.7 KiB
Python
# floyd_warshall.py
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"""
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The problem is to find the shortest distance between all pairs of vertices in a
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weighted directed graph that can have negative edge weights.
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"""
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def _print_dist(dist, v):
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print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
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for i in range(v):
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for j in range(v):
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if dist[i][j] != float("inf"):
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print(int(dist[i][j]), end="\t")
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else:
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print("INF", end="\t")
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print()
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def floyd_warshall(graph, v):
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"""
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:param graph: 2D array calculated from weight[edge[i, j]]
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:type graph: List[List[float]]
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:param v: number of vertices
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:type v: int
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:return: shortest distance between all vertex pairs
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distance[u][v] will contain the shortest distance from vertex u to v.
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1. For all edges from v to n, distance[i][j] = weight(edge(i, j)).
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3. The algorithm then performs distance[i][j] = min(distance[i][j], distance[i][k] +
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distance[k][j]) for each possible pair i, j of vertices.
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4. The above is repeated for each vertex k in the graph.
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5. Whenever distance[i][j] is given a new minimum value, next vertex[i][j] is
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updated to the next vertex[i][k].
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>>> num_vertices = 3
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>>> graph = [
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... [float('inf'), float('inf'), float('inf')],
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... [float('inf'), float('inf'), float('inf')],
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... [float('inf'), float('inf'), float('inf')]
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... ]
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>>> expected = [
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... [0, 2, float('inf')],
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... [1, 0, float('inf')],
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... [float('inf'), float('inf'), 0]
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... ]
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>>> dist, _ = floyd_warshall(graph, num_vertices)
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<BLANKLINE>
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The shortest path matrix using Floyd Warshall algorithm
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<BLANKLINE>
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0 2 INF
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1 0 INF
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INF INF 0
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>>> dist == expected
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True
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"""
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dist = [[float("inf") for _ in range(v)] for _ in range(v)]
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for i in range(v):
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for j in range(v):
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dist[i][j] = graph[i][j]
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# check vertex k against all other vertices (i, j)
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for k in range(v):
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# looping through rows of graph array
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for i in range(v):
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# looping through columns of graph array
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for j in range(v):
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if (
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dist[i][k] != float("inf")
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and dist[k][j] != float("inf")
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and dist[i][k] + dist[k][j] < dist[i][j]
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):
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dist[i][j] = dist[i][k] + dist[k][j]
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_print_dist(dist, v)
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return dist, v
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if __name__ == "__main__":
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v = int(input("Enter number of vertices: "))
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e = int(input("Enter number of edges: "))
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graph = [[float("inf") for i in range(v)] for j in range(v)]
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for i in range(v):
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graph[i][i] = 0.0
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# src and dst are indices that must be within the array size graph[e][v]
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# failure to follow this will result in an error
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for i in range(e):
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print("\nEdge ", i + 1)
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src = int(input("Enter source:"))
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dst = int(input("Enter destination:"))
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weight = float(input("Enter weight:"))
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graph[src][dst] = weight
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floyd_warshall(graph, v)
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# Example Input
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# Enter number of vertices: 3
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# Enter number of edges: 2
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# # generated graph from vertex and edge inputs
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# [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
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# [[0.0, inf, inf], [inf, 0.0, inf], [inf, inf, 0.0]]
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# specify source, destination and weight for edge #1
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# Edge 1
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# Enter source:1
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# Enter destination:2
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# Enter weight:2
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# specify source, destination and weight for edge #2
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# Edge 2
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# Enter source:2
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# Enter destination:1
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# Enter weight:1
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# # Expected Output from the vertice, edge and src, dst, weight inputs!!
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# 0 INF INF
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# INF 0 2
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# INF 1 0
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