def MaximumAntichain(G):
"""
Find a maximum antichain in the given directed acyclic graph.
"""
if not isAcyclic(G):
raise ValueError("MaximumAntichain: input is not acyclic.")
TC = TransitiveClosure(G)
M, A, B = BipartiteMatching.matching(TransitiveClosure(G))
return set(A).intersection(B)
def MaximumAntichain(G):
"""
Find a maximum antichain in the given directed acyclic graph.
"""
if not isAcyclic(G):
raise ValueError("MaximumAntichain: input is not acyclic.")
TC = TransitiveClosure(G)
M,A,B = BipartiteMatching.matching(TransitiveClosure(G))
return set(A).intersection(B)
def MinimumPathDecomposition(G):
"""
Cover a directed acyclic graph with a minimum number of paths.
"""
M, A, B = BipartiteMatching.matching(G)
H = dict([(v, []) for v in G])
for v in G:
if v in M:
H[M[v]] = (v, )
return TracePaths(H)
def MinimumPathDecomposition(G):
"""
Cover a directed acyclic graph with a minimum number of paths.
"""
M,A,B = BipartiteMatching.matching(G)
H = dict([(v,[]) for v in G])
for v in G:
if v in M:
H[M[v]] = (v,)
return TracePaths(H)
import sys
#http://www.ics.uci.edu/~eppstein/PADS/
#David Eppstein's python library
sys.path.append("pads")
from collections import defaultdict
import BipartiteMatching
for case in range(1, input() + 1):
print "Case #%s:" % (case),
topics = []
for topic in range(1, input() + 1):
topics.append(raw_input().split())
#print topics
g = defaultdict(list)
h = defaultdict(list)
for first, second in topics:
g["l_%s" % first].append("r_%s" % second)
h["r_%s" % second].append("l_%s" % first)
#print g
matching = BipartiteMatching.matching(g)[0]
#print matching
remainder = len(g) + len(h) - 2 * len(matching)
#print len(topics), len(matching), len(g), remainder
print len(topics) - len(matching) - remainder