class BoryaSolved(object):
def __init__(self):
self.num_cards = raw_input()
cards = raw_input()
#start = time.clock()
self.actual_hand = cards.split(' ')
self.ladder = Ladder(self.actual_hand)
self.construct_clues()
#timeit = time.clock() - start
#print timeit
#print self.clues
self.num_clues_needed = list()
self.solve_ladder()
self.pick_lowest()
#timit = time.clock() - start
#print timeit
def construct_clues(self):
"""
constructs the total number of possible clue
combinations that could yield us with revealing
Borya's hand. We use the list of edges in the ladder
to do this.
"""
self.clues = list()
edges = self.ladder.edges
#print self.ladder.edges
for edge in edges:
ind = edges.index(edge)
edges.remove(edge)
self.construct_clues_recursively([edge.value], edges)
edges.insert(ind, edge)
def construct_clues_recursively(self, clue_seq, edges):
"""
constructs combinations of clues.
helper method for construct_clues
"""
if sorted(clue_seq) not in self.clues:
self.clues.append(sorted(clue_seq))
if len(edges) >= 1:
for edge in edges:
ind = edges.index(edge)
edges.remove(edge)
clues = [clue for clue in clue_seq]
clues.append(edge.value)
self.construct_clues_recursively(clues, edges)
edges.insert(ind, edge)
def solve_ladder(self):
"""
Goes through every possible combination of clues
and checks if the Ladder (constructed by Borya's hand)
can be solved given those clues. if it can, then we append
the number of clues in that clue combination to the
num_clues_needed list.
"""
self.ladder.check_all_but_one()
if not self.ladder.complete:
for clue_seq in self.clues:
if self.num_clues_needed:
if len(clue_seq)<min(self.num_clues_needed):
self.ladder = Ladder(self.actual_hand)
for clue in clue_seq:
self.ladder.give_clue(clue)
if self.ladder.complete:
#print clue_seq
self.num_clues_needed.append(len(clue_seq))
else:
self.ladder = Ladder(self.actual_hand)
for clue in clue_seq:
self.ladder.give_clue(clue)
if self.ladder.complete:
self.num_clues_needed.append(len(clue_seq))
self.ladder.clean_up()
def pick_lowest(self):
"""
out of all the possible clue combinations that can
reveal Borya's hand, the minimum number of num_clues_needed
is printed.
"""
#print self.num_clues_needed
if self.num_clues_needed:
print min(self.num_clues_needed)
else:
print 0
