49 lines
1.6 KiB
Markdown
49 lines
1.6 KiB
Markdown
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---
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title: Floyd Warshall Algorithm
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---
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## Floyd Warshall Algorithm
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Floyd Warshall algorithm is a great algorithm for finding shortest distance between all vertices in graph. It has a very concise algorithm and O(V^3) time complexity (where V is number of vertices). It can be used with negative weights, although negative weight cycles must not be present in the graph.
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### Evaluation
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Space Complexity: O(V^2)
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Worse Case Time Complexity: O(V^3)
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### Python implementation
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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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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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<a href='https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md' target='_blank' rel='nofollow'>Graphs</a>
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<a href='https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm' target='_blank' rel='nofollow'>Floyd Warshall - Wikipedia</a>
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