"""
 Floyd's algorithm

 find all minimum path distances
 between pairs of vertices

 Runs in O(n**3)
"""

inf = float('inf')
vertices = range(5)

# adjacency matrix
a = [[0,   1, inf, 4, inf],
     [1,   0, 1,   1, 5],
     [inf, 1, 0,   6, 1],
     [4,   1, 6,   0, inf],
     [inf, 5, 1, inf, 0]]

for x in vertices:
    for v1 in vertices:
        for v2 in vertices:
            dis = a[v1][x] + a[x][v2]
            if dis < a[v1][v2]:
                a[v1][v2] = a[v2][v1] = dis

print a