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a99acae32d
I've added comments to make understanding this method a little easier for those that are not familiar. This should close out #727 . Other changes: 1. added if __name__ == '__main__' rather than the "# MAIN" comment 2. put in return for distances and vertices. Previously everything was just printed out, but someone may find it useful to have the algorithm return something. 3. Other PEP8 changes 4. Added example input and expected output as a check to make sure any future changes will give the same output.
103 lines
2.8 KiB
Python
103 lines
2.8 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 weighted directed graph that can
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have negative edge weights.
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"""
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from __future__ import print_function
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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] + distance[k][j]) for each
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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 updated to the next vertex[i][k].
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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 dist[i][k]!=float('inf') and dist[k][j]!=float('inf') and dist[i][k]+dist[k][j] < dist[i][j]:
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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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