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86 lines
2.2 KiB
Python
86 lines
2.2 KiB
Python
import math
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class Graph:
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def __init__(self, n=0): # a graph with Node 0,1,...,N-1
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self.n = n
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self.w = [
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[math.inf for j in range(n)] for i in range(n)
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] # adjacency matrix for weight
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self.dp = [
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[math.inf for j in range(n)] for i in range(n)
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] # dp[i][j] stores minimum distance from i to j
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def add_edge(self, u, v, w):
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"""
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Adds a directed edge from node u
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to node v with weight w.
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>>> g = Graph(3)
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>>> g.add_edge(0, 1, 5)
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>>> g.dp[0][1]
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5
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"""
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self.dp[u][v] = w
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def floyd_warshall(self):
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"""
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Computes the shortest paths between all pairs of
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nodes using the Floyd-Warshall algorithm.
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>>> g = Graph(3)
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>>> g.add_edge(0, 1, 1)
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>>> g.add_edge(1, 2, 2)
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>>> g.floyd_warshall()
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>>> g.show_min(0, 2)
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3
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>>> g.show_min(2, 0)
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inf
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"""
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for k in range(self.n):
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for i in range(self.n):
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for j in range(self.n):
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self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j])
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def show_min(self, u, v):
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"""
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Returns the minimum distance from node u to node v.
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>>> g = Graph(3)
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>>> g.add_edge(0, 1, 3)
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>>> g.add_edge(1, 2, 4)
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>>> g.floyd_warshall()
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>>> g.show_min(0, 2)
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7
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>>> g.show_min(1, 0)
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inf
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"""
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return self.dp[u][v]
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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# Example usage
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graph = Graph(5)
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graph.add_edge(0, 2, 9)
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graph.add_edge(0, 4, 10)
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graph.add_edge(1, 3, 5)
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graph.add_edge(2, 3, 7)
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graph.add_edge(3, 0, 10)
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graph.add_edge(3, 1, 2)
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graph.add_edge(3, 2, 1)
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graph.add_edge(3, 4, 6)
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graph.add_edge(4, 1, 3)
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graph.add_edge(4, 2, 4)
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graph.add_edge(4, 3, 9)
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graph.floyd_warshall()
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print(
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graph.show_min(1, 4)
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) # Should output the minimum distance from node 1 to node 4
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print(
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graph.show_min(0, 3)
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) # Should output the minimum distance from node 0 to node 3
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