48 lines
1.6 KiB
Markdown
48 lines
1.6 KiB
Markdown
|
---
|
||
|
|
title: Floyd Warshall Algorithm
|
||
|
|
localeTitle: Floyd Warshall Algorithm
|
||
|
|
---
|
||
|
|
## Floyd Warshall Algorithm
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
### Evaluación
|
||
|
|
|
||
|
|
Complejidad del espacio: O (V ^ 2)
|
||
|
|
|
||
|
|
Peor complejidad de tiempo del caso: O (V ^ 3)
|
||
|
|
|
||
|
|
### Implementacion Python
|
||
|
|
|
||
|
|
```python
|
||
|
|
# A large value as infinity
|
||
|
|
inf = 1e10
|
||
|
|
|
||
|
|
def floyd_warshall(weights):
|
||
|
|
V = len(weights)
|
||
|
|
distance_matrix = weights
|
||
|
|
for k in range(V):
|
||
|
|
next_distance_matrix = [list(row) for row in distance_matrix] # make a copy of distance matrix
|
||
|
|
for i in range(V):
|
||
|
|
for j in range(V):
|
||
|
|
# Choose if the k vertex can work as a path with shorter distance
|
||
|
|
next_distance_matrix[i][j] = min(distance_matrix[i][j], distance_matrix[i][k] + distance_matrix[k][j])
|
||
|
|
distance_matrix = next_distance_matrix # update
|
||
|
|
return distance_matrix
|
||
|
|
|
||
|
|
# A graph represented as Adjacency matrix
|
||
|
|
graph = [
|
||
|
|
[0, inf, inf, -3],
|
||
|
|
[inf, 0, inf, 8],
|
||
|
|
[inf, 4, 0, -2],
|
||
|
|
[5, inf, 3, 0]
|
||
|
|
]
|
||
|
|
|
||
|
|
print(floyd_warshall(graph))
|
||
|
|
```
|
||
|
|
|
||
|
|
#### Más información:
|
||
|
|
|
||
|
|
[Graficas](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)
|
||
|
|
|
||
|
|
[Floyd Warshall - Wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
|