48 lines
1.5 KiB
Markdown
48 lines
1.5 KiB
Markdown
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---
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title: Floyd Warshall Algorithm
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localeTitle: Floyd Warshall算法
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---
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## Floyd Warshall算法
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Floyd Warshall算法是一种很好的算法，用于查找图中所有顶点之间的最短距离。它具有非常简洁的算法和O（V ^ 3）时间复杂度（其中V是顶点数）。它可以与负权重一起使用，但图表中不得出现负权重循环。
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### 评估
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空间复杂度：O（V ^ 2）
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更糟糕的案例时间复杂性：O（V ^ 3）
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### Python实现
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```python
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# A large value as infinity
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inf = 1e10
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def floyd_warshall(weights):
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V = len(weights)
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distance_matrix = weights
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for k in range(V):
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next_distance_matrix = [list(row) for row in distance_matrix] # make a copy of distance matrix
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for i in range(V):
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for j in range(V):
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# Choose if the k vertex can work as a path with shorter distance
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next_distance_matrix[i][j] = min(distance_matrix[i][j], distance_matrix[i][k] + distance_matrix[k][j])
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distance_matrix = next_distance_matrix # update
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return distance_matrix
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# A graph represented as Adjacency matrix
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graph = [
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[0, inf, inf, -3],
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[inf, 0, inf, 8],
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[inf, 4, 0, -2],
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[5, inf, 3, 0]
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]
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print(floyd_warshall(graph))
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```
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#### 更多信息：
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[图表](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)
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[Floyd Warshall - 维基百科](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
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