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@christianp christianp/4cards.py
Created Sep 25, 2012

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Given a set of cards, can you make 24 by combining all of them, using +,-,÷,×?
from itertools import permutations,product
from operator import itemgetter
from sys import argv
from fractions import Fraction as f
def add(ap,bp):
(ae,a),(be,b)=ap,bp
return ('(%s+%s)' % (ae if len(ae) else str(a),be if len(be) else str(b)),a+b)
def sub(ap,bp):
(ae,a),(be,b)=ap,bp
return ('(%s-%s)' % (ae if len(ae) else str(a),be if len(be) else str(b)),a-b)
def mul(ap,bp):
(ae,a),(be,b)=ap,bp
return ('%s*%s' % (ae if len(ae) else str(a),be if len(be) else str(b)),a*b)
def div(ap,bp):
((ae,a),(be,b))=(ap,bp)
return ('%s/%s' % (ae if len(ae) else str(a),be if len(be) else str(b)),a/b)
ops = [add,sub,mul,div]
def comb(nums,ops):
if len(nums)==1:
yield nums[0]
return
for perm in permutations(nums):
for i in range(1,len(nums)):
As = set(comb(perm[:i],ops))
Bs = set(comb(perm[i:],ops))
for a,b in product(As,Bs):
for op in ops:
try:
yield op(a,b)
except Exception:
pass
if len(argv)>1:
nums = [int(x) for x in argv[1:]]
else:
nums = [3,3,8,8]
nums = [f(n) for n in nums]
results = set(comb([('',i) for i in nums],ops))
results = sorted(results,key=itemgetter(1))
poss = [a for ae,a in results]
if 24 in poss:
for ae,a in results:
if a==24:
print('24 = %s' % ae)
print('You can make 24 with these cards.')
else:
print('You can\'t make 24 with these cards.')
best = min(poss,key=lambda a: abs(24-a))
print('Closest is %g' % best)
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