1.5 KiB
1.5 KiB
| title | localeTitle |
|---|---|
| Floyd Warshall Algorithm | Floyd Warshall算法 |
Floyd Warshall算法
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。
评估
空间复杂度：O（V ^ 2）
更糟糕的案例时间复杂性：O（V ^ 3）
Python实现
# 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))