输入4个数字, 输出所有用加减乘除结果为24的表达式. 代码如下:
def isEqual(num1, num2):
return abs(num1 - num2) < 1e-5;
# End of isEqual().
def expressionsFromExpOpSeq(expSeq, opSeq):
assert(len(expSeq) == len(opSeq) + 1)
if 1 == len(expSeq):
yield expSeq[0]
return
# End of if.
for idx in range(len(opSeq)):
newExp = "(%s %s %s)" % (
expSeq[idx], opSeq[idx], expSeq[idx+1])
newExpSeq = expSeq[:idx] + [newExp] + expSeq[idx+2:]
newOpSeq = opSeq[:idx] + opSeq[idx+1:]
for exp in expressionsFromExpOpSeq(newExpSeq, newOpSeq):
yield exp
# End of for.
# End of expressionsFromExpOpSeq().
def expressionsFromExpSeq(expSeq):
for opSeq in selections("+-*/", len(expSeq) - 1):
for exp in expressionsFromExpOpSeq(expSeq, opSeq):
yield exp
# End of expressionsFromExpSeq().
def expressions(numList):
'''Generate expressions.
'''
if (0 == len(numList)): return;
for numPerm in permutations(numList):
expSeq = [str(n) for n in numPerm]
for exp in expressionsFromExpSeq(expSeq):
yield exp
# End of expressions().
numTuple=input("Please input 4 numbers to computer 24:(use ',' to divide them)")
numList=[float(i) for i in numTuple]
# numList = [1.0,4.0,5.0,6.0]
TARGET = 24.0
print("Your input is: %s" % numList)
for exp in expressions(numList):
try:
if isEqual(TARGET, eval(exp)):
print("%s = %s" % (exp, TARGET))
except ZeroDivisionError:
pass
# End of try.
# End of for.
其中计算排列组合的代码来自Cookbook:
# Recipe 19.15. Generating Permutations, Combinations, and Selections
def _combinators(_handle, items, n):
''' factored-out common structure of all following combinators '''
if n==0:
yield [ ]
return
for i, item in enumerate(items):
this_one = [ item ]
for cc in _combinators(_handle, _handle(items, i), n-1):
yield this_one + cc
def combinations(items, n):
''' take n distinct items, order matters '''
def skipIthItem(items, i):
return items[:i] + items[i+1:]
return _combinators(skipIthItem, items, n)
def selections(items, n):
''' take n (not necessarily distinct) items, order matters '''
def keepAllItems(items, i):
return items
return _combinators(keepAllItems, items, n)
def permutations(items):
''' take all items, order matters '''
return combinations(items, len(items))
示例:
Please input 4 numbers to computer 24:(use ',' to divide them)1,4,5,6
Your input is: [1.0, 4.0, 5.0, 6.0]
(4.0 / (1.0 - (5.0 / 6.0))) = 24.0
(6.0 / ((5.0 / 4.0) - 1.0)) = 24.0
也可以输入多个数字:
Please input 4 numbers to computer 24:(use ',' to divide them)2,3,4,5.5,6
Your input is: [2.0, 3.0, 4.0, 5.5, 6.0]
((2.0 - (3.0 / (4.0 - 5.5))) * 6.0) = 24.0
(2.0 * (3.0 - ((4.0 - 5.5) * 6.0))) = 24.0
((2.0 + (3.0 / (5.5 - 4.0))) * 6.0) = 24.0
......
参考:
* 一个 Lua 的凑24程序 ( http://blog.csdn.net/shell_picker/archive/2010/11/25/6034158.aspx )
* python 算24的题目 ( http://zhidao.baidu.com/question/207378450.html )