48 lines
1.6 KiB
Markdown
48 lines
1.6 KiB
Markdown
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---
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title: Floyd Warshall Algorithm
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localeTitle: Floyd Warshall Algorithm
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---
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## Floyd Warshall Algorithm
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El algoritmo Floyd Warshall es un gran algoritmo para encontrar la distancia más corta entre todos los vértices en la gráfica. Tiene un algoritmo muy conciso y complejidad de tiempo O (V ^ 3) (donde V es el número de vértices). Puede utilizarse con pesos negativos, aunque los ciclos de peso negativos no deben estar presentes en el gráfico.
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### Evaluación
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Complejidad del espacio: O (V ^ 2)
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Peor complejidad de tiempo del caso: O (V ^ 3)
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### Implementacion Python
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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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#### Más información:
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[Graficas](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)
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[Floyd Warshall - Wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
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