本來想用回溯法實現 算24點。題目都擬好了，就是《python 回溯法 子集樹模板 系列 —— 7、24點》。無奈想了一天，沒有頭緒。只好改用暴力窮舉法。
思路說明
根據四個數，三個運算符，構造三種中綴表達式，遍歷，計算每一種可能
顯然可能的形式不止三種。但是，其它的形式要么得不到24點，要么在加、乘意義下可以轉化為這三種形式的表達式！
使用內置的eval函數計算中綴表達式，使得代碼變得非常簡潔！
完整代碼
# 作者：hhh5460
# 時間：2017年6月3日
import itertools
def twentyfour(cards):
'''史上最短計算24點代碼'''
for nums in itertools.permutations(cards): # 四個數
for ops in itertools.product('+-*/', repeat=3): # 三個運算符（可重復！）
# 構造三種中綴表達式 (bsd)
bds1 = '({0}{4}{1}){5}({2}{6}{3})'.format(*nums, *ops) # (a+b)*(c-d)
bds2 = '(({0}{4}{1}){5}{2}){6}{3}'.format(*nums, *ops) # (a+b)*c-d
bds3 = '{0}{4}({1}{5}({2}{6}{3}))'.format(*nums, *ops) # a/(b-(c/d))
for bds in [bds1, bds2, bds3]: # 遍歷
try:
if abs(eval(bds) - 24.0) < 1e-10: # eval函數
return bds
except ZeroDivisionError: # 零除錯誤！
continue
return 'Not found!'
# 測試
# 數據來源：http://www.cnblogs.com/grenet/archive/2013/02/28/2936965.html
cards =[[1,1,1,8],
[1,1,2,6],
[1,1,2,7],
[1,1,2,8],
[1,1,2,9],
[1,1,2,10],
[1,1,3,4],
[1,1,3,5],
[1,1,3,6],
[1,1,3,7],
[1,1,3,8],
[1,1,3,9],
[1,1,3,10],
[1,1,4,4],
[1,1,4,5],
[1,1,4,6],
[1,1,4,7],
[1,1,4,8],
[1,1,4,9],
[1,1,4,10],
[1,1,5,5],
[1,1,5,6],
[1,1,5,7],
[1,1,5,8],
[1,1,6,6],
[1,1,6,8],
[1,1,6,9],
[1,1,7,10],
[1,1,8,8],
[1,2,2,4],
[1,2,2,5],
[1,2,2,6],
[1,2,2,7],
[1,2,2,8],
[1,2,2,9],
[1,2,2,10],
[1,2,3,3],
[1,2,3,4],
[1,2,3,5],
[1,2,3,6],
[1,2,3,7],
[1,2,3,8],
[1,2,3,9],
[1,2,3,10],
[1,2,4,4],
[1,2,4,5],
[1,2,4,6],
[1,2,4,7],
[1,2,4,8],
[1,2,4,9],
[1,2,4,10],
[1,2,5,5],
[1,2,5,6],
[1,2,5,7],
[1,2,5,8],
[1,2,5,9],
[1,2,5,10],
[1,2,6,6],
[1,2,6,7],
[1,2,6,8],
[1,2,6,9],
[1,2,6,10],
[1,2,7,7],
[1,2,7,8],
[1,2,7,9],
[1,2,7,10],
[1,2,8,8],
[1,2,8,9],
[1,2,8,10],
[1,3,3,3],
[1,3,3,4],
[1,3,3,5],
[1,3,3,6],
[1,3,3,7],
[1,3,3,8],
[1,3,3,9],
[1,3,3,10],
[1,3,4,4],
[1,3,4,5],
[1,3,4,6],
[1,3,4,7],
[1,3,4,8],
[1,3,4,9],
[1,3,4,10],
[1,3,5,6],
[1,3,5,7],
[1,3,5,8],
[1,3,5,9],
[1,3,5,10],
[1,3,6,6],
[1,3,6,7],
[1,3,6,8],
[1,3,6,9],
[1,3,6,10],
[1,3,7,7],
[1,3,7,8],
[1,3,7,9],
[1,3,7,10],
[1,3,8,8],
[1,3,8,9],
[1,3,8,10],
[1,3,9,9],
[1,3,9,10],
[1,3,10,10],
[1,4,4,4],
[1,4,4,5],
[1,4,4,6],
[1,4,4,7],
[1,4,4,8],
[1,4,4,9],
[1,4,4,10],
[1,4,5,5],
[1,4,5,6],
[1,4,5,7],
[1,4,5,8],
[1,4,5,9],
[1,4,5,10],
[1,4,6,6],
[1,4,6,7],
[1,4,6,8],
[1,4,6,9],
[1,4,6,10],
[1,4,7,7],
[1,4,7,8],
[1,4,7,9],
[1,4,8,8],
[1,4,8,9],
[1,4,9,10],
[1,4,10,10],
[1,5,5,5],
[1,5,5,6],
[1,5,5,9],
[1,5,5,10],
[1,5,6,6],
[1,5,6,7],
[1,5,6,8],
[1,5,6,9],
[1,5,6,10],
[1,5,7,8],
[1,5,7,9],
[1,5,7,10],
[1,5,8,8],
[1,5,8,9],
[1,5,8,10],
[1,5,9,9],
[1,5,9,10],
[1,5,10,10],
[1,6,6,6],
[1,6,6,8],
[1,6,6,9],
[1,6,6,10],
[1,6,7,9],
[1,6,7,10],
[1,6,8,8],
[1,6,8,9],
[1,6,8,10],
[1,6,9,9],
[1,6,9,10],
[1,7,7,9],
[1,7,7,10],
[1,7,8,8],
[1,7,8,9],
[1,7,8,10],
[1,7,9,9],
[1,7,9,10],
[1,8,8,8],
[1,8,8,9],
[1,8,8,10],
[2,2,2,3],
[2,2,2,4],
[2,2,2,5],
[2,2,2,7],
[2,2,2,8],
[2,2,2,9],
[2,2,2,10],
[2,2,3,3],
[2,2,3,4],
[2,2,3,5],
[2,2,3,6],
[2,2,3,7],
[2,2,3,8],
[2,2,3,9],
[2,2,3,10],
[2,2,4,4],
[2,2,4,5],
[2,2,4,6],
[2,2,4,7],
[2,2,4,8],
[2,2,4,9],
[2,2,4,10],
[2,2,5,5],
[2,2,5,6],
[2,2,5,7],
[2,2,5,8],
[2,2,5,9],
[2,2,5,10],
[2,2,6,6],
[2,2,6,7],
[2,2,6,8],
[2,2,6,9],
[2,2,6,10],
[2,2,7,7],
[2,2,7,8],
[2,2,7,10],
[2,2,8,8],
[2,2,8,9],
[2,2,8,10],
[2,2,9,10],
[2,2,10,10],
[2,3,3,3],
[2,3,3,5],
[2,3,3,6],
[2,3,3,7],
[2,3,3,8],
[2,3,3,9],
[2,3,3,10],
[2,3,4,4],
[2,3,4,5],
[2,3,4,6],
[2,3,4,7],
[2,3,4,8],
[2,3,4,9],
[2,3,4,10],
[2,3,5,5],
[2,3,5,6],
[2,3,5,7],
[2,3,5,8],
[2,3,5,9],
[2,3,5,10],
[2,3,6,6],
[2,3,6,7],
[2,3,6,8],
[2,3,6,9],
[2,3,6,10],
[2,3,7,7],
[2,3,7,8],
[2,3,7,9],
[2,3,7,10],
[2,3,8,8],
[2,3,8,9],
[2,3,8,10],
[2,3,9,9],
[2,3,9,10],
[2,3,10,10],
[2,4,4,4],
[2,4,4,5],
[2,4,4,6],
[2,4,4,7],
[2,4,4,8],
[2,4,4,9],
[2,4,4,10],
[2,4,5,5],
[2,4,5,6],
[2,4,5,7],
[2,4,5,8],
[2,4,5,9],
[2,4,5,10],
[2,4,6,6],
[2,4,6,7],
[2,4,6,8],
[2,4,6,9],
[2,4,6,10],
[2,4,7,7],
[2,4,7,8],
[2,4,7,9],
[2,4,7,10],
[2,4,8,8],
[2,4,8,9],
[2,4,8,10],
[2,4,9,9],
[2,4,9,10],
[2,4,10,10],
[2,5,5,7],
[2,5,5,8],
[2,5,5,9],
[2,5,5,10],
[2,5,6,6],
[2,5,6,7],
[2,5,6,8],
[2,5,6,9],
[2,5,6,10],
[2,5,7,7],
[2,5,7,8],
[2,5,7,9],
[2,5,7,10],
[2,5,8,8],
[2,5,8,9],
[2,5,8,10],
[2,5,9,10],
[2,5,10,10],
[2,6,6,6],
[2,6,6,7],
[2,6,6,8],
[2,6,6,9],
[2,6,6,10],
[2,6,7,8],
[2,6,7,9],
[2,6,7,10],
[2,6,8,8],
[2,6,8,9],
[2,6,8,10],
[2,6,9,9],
[2,6,9,10],
[2,6,10,10],
[2,7,7,8],
[2,7,7,10],
[2,7,8,8],
[2,7,8,9],
[2,7,9,10],
[2,7,10,10],
[2,8,8,8],
[2,8,8,9],
[2,8,8,10],
[2,8,9,9],
[2,8,9,10],
[2,8,10,10],
[2,9,10,10],
[3,3,3,3],
[3,3,3,4],
[3,3,3,5],
[3,3,3,6],
[3,3,3,7],
[3,3,3,8],
[3,3,3,9],
[3,3,3,10],
[3,3,4,4],
[3,3,4,5],
[3,3,4,6],
[3,3,4,7],
[3,3,4,8],
[3,3,4,9],
[3,3,5,5],
[3,3,5,6],
[3,3,5,7],
[3,3,5,9],
[3,3,5,10],
[3,3,6,6],
[3,3,6,7],
[3,3,6,8],
[3,3,6,9],
[3,3,6,10],
[3,3,7,7],
[3,3,7,8],
[3,3,7,9],
[3,3,8,8],
[3,3,8,9],
[3,3,8,10],
[3,3,9,9],
[3,3,9,10],
[3,4,4,4],
[3,4,4,5],
[3,4,4,6],
[3,4,4,7],
[3,4,4,8],
[3,4,4,9],
[3,4,4,10],
[3,4,5,5],
[3,4,5,6],
[3,4,5,7],
[3,4,5,8],
[3,4,5,9],
[3,4,5,10],
[3,4,6,6],
[3,4,6,8],
[3,4,6,9],
[3,4,6,10],
[3,4,7,7],
[3,4,7,8],
[3,4,7,9],
[3,4,7,10],
[3,4,8,9],
[3,4,8,10],
[3,4,9,9],
[3,4,10,10],
[3,5,5,6],
[3,5,5,7],
[3,5,5,8],
[3,5,5,9],
[3,5,6,6],
[3,5,6,7],
[3,5,6,8],
[3,5,6,9],
[3,5,6,10],
[3,5,7,8],
[3,5,7,9],
[3,5,7,10],
[3,5,8,8],
[3,5,8,9],
[3,5,9,9],
[3,5,9,10],
[3,5,10,10],
[3,6,6,6],
[3,6,6,7],
[3,6,6,8],
[3,6,6,9],
[3,6,6,10],
[3,6,7,7],
[3,6,7,8],
[3,6,7,9],
[3,6,7,10],
[3,6,8,8],
[3,6,8,9],
[3,6,8,10],
[3,6,9,9],
[3,6,9,10],
[3,6,10,10],
[3,7,7,7],
[3,7,7,8],
[3,7,7,9],
[3,7,7,10],
[3,7,8,8],
[3,7,8,9],
[3,7,9,9],
[3,7,9,10],
[3,7,10,10],
[3,8,8,8],
[3,8,8,9],
[3,8,8,10],
[3,8,9,9],
[3,8,9,10],
[3,8,10,10],
[3,9,9,9],
[3,9,9,10],
[3,9,10,10],
[4,4,4,4],
[4,4,4,5],
[4,4,4,6],
[4,4,4,7],
[4,4,4,8],
[4,4,4,9],
[4,4,4,10],
[4,4,5,5],
[4,4,5,6],
[4,4,5,7],
[4,4,5,8],
[4,4,5,10],
[4,4,6,8],
[4,4,6,9],
[4,4,6,10],
[4,4,7,7],
[4,4,7,8],
[4,4,7,9],
[4,4,7,10],
[4,4,8,8],
[4,4,8,9],
[4,4,8,10],
[4,4,10,10],
[4,5,5,5],
[4,5,5,6],
[4,5,5,7],
[4,5,5,8],
[4,5,5,9],
[4,5,5,10],
[4,5,6,6],
[4,5,6,7],
[4,5,6,8],
[4,5,6,9],
[4,5,6,10],
[4,5,7,7],
[4,5,7,8],
[4,5,7,9],
[4,5,7,10],
[4,5,8,8],
[4,5,8,9],
[4,5,8,10],
[4,5,9,9],
[4,5,9,10],
[4,5,10,10],
[4,6,6,6],
[4,6,6,7],
[4,6,6,8],
[4,6,6,9],
[4,6,6,10],
[4,6,7,7],
[4,6,7,8],
[4,6,7,9],
[4,6,7,10],
[4,6,8,8],
[4,6,8,9],
[4,6,8,10],
[4,6,9,9],
[4,6,9,10],
[4,6,10,10],
[4,7,7,7],
[4,7,7,8],
[4,7,8,8],
[4,7,8,9],
[4,7,8,10],
[4,7,9,9],
[4,7,9,10],
[4,7,10,10],
[4,8,8,8],
[4,8,8,9],
[4,8,8,10],
[4,8,9,9],
[4,8,9,10],
[4,8,10,10],
[4,9,9,10],
[5,5,5,5],
[5,5,5,6],
[5,5,5,9],
[5,5,6,6],
[5,5,6,7],
[5,5,6,8],
[5,5,7,7],
[5,5,7,8],
[5,5,7,10],
[5,5,8,8],
[5,5,8,9],
[5,5,8,10],
[5,5,9,9],
[5,5,9,10],
[5,5,10,10],
[5,6,6,6],
[5,6,6,7],
[5,6,6,8],
[5,6,6,9],
[5,6,6,10],
[5,6,7,7],
[5,6,7,8],
[5,6,7,9],
[5,6,8,8],
[5,6,8,9],
[5,6,8,10],
[5,6,9,9],
[5,6,9,10],
[5,6,10,10],
[5,7,7,9],
[5,7,7,10],
[5,7,8,8],
[5,7,8,9],
[5,7,8,10],
[5,7,9,10],
[5,7,10,10],
[5,8,8,8],
[5,8,8,9],
[5,8,8,10],
[5,9,10,10],
[6,6,6,6],
[6,6,6,8],
[6,6,6,9],
[6,6,6,10],
[6,6,7,9],
[6,6,7,10],
[6,6,8,8],
[6,6,8,9],
[6,6,8,10],
[6,6,9,10],
[6,7,7,10],
[6,7,8,9],
[6,7,8,10],
[6,7,9,9],
[6,7,10,10],
[6,8,8,8],
[6,8,8,9],
[6,8,8,10],
[6,8,9,9],
[6,8,9,10],
[6,9,9,10],
[6,10,10,10],
[7,7,9,10],
[7,8,8,9],
[7,8,8,10],
[7,8,9,10],
[7,8,10,10],
[8,8,8,10]]
for card in cards:
print(twentyfour(card))