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# N is the set of nodes {a,b,c..}
# A is the set of arcs with costs {(a,b,1),(a,c,2)..}
#
# Use: Kruskal (N,A)
def find (u, C):
i = 0
for c in C:
if (u in c): return (c,i)
i += 1
def merge (C, ucomp, vcomp):
return [ucomp[0] + vcomp[0]] + [i for j, i in enumerate(C) if j not in [ucomp[1], vcomp[1]]]
def Kruskal (N, A):
A = sorted(A, key= lambda A: A[2])
C = [[u] for u in N]
T = []
n = len(N)
for shortestA in A:
u, v = shortestA[0], shortestA[1]
ucomp, vcomp = find(u, C), find(v, C)
if (ucomp != vcomp):
print u, v, ":",C
C = merge (C, ucomp, vcomp)
T.append((u,v))
if (len(T) == (n-1)): break
print "\nMinimum spanning tree:\n", T
return T
# My experiment
N = ["a1","a2","a3", "a4", "a5", "a6", "a7"]
A = [("a1","a2",1), ("a1","a4",4),
("a2","a4",6), ("a2","a5",4), ("a2","a3",2),
("a3","a5",5), ("a3","a6",6),
("a4","a5",3), ("a4","a7",4),
("a5","a6",8), ("a5","a7",7),
("a6","a7",3)]
Kruskal(N, A)
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