python实现二十四点

给定n个数字,计算出一个满足24点的表达式:比如1,11,2,1:(11+1)*2/1

基本思路就是枚举计算顺序(在一开始进行一次全排列),括号,加减乘除。其实有很多是重复计算过了的。这个程序我为了高效找到一个解就算了,但是我们把程序稍微修改就可以找到所有的解(表达顺序可能会重复,比如1+2和2+1),同时也可以计算多个数字的组合。

def compute(x,y,op):
    if op=='+':return x+y
    elif op=='*':return x*y
    elif op=='-':return x-y
    else:return x/y if y else None

def exp(p,iter=0):
    from itertools import permutations
    if len(p)==1:return [(p[0],str(p[0]))]
    operation = ['+','-','*','/']
    ret = []
    p = permutations(p) if iter==0 else [p]
    for array_n in p:
        #print(array_n)
        for num in range(1,len(array_n)):
            ret1 = exp(array_n[:num],iter+1)
            ret2 = exp(array_n[num:],iter+1)
            for op in operation:
                for va1,expression in ret1:
                    if va1==None:continue
                    for va2,expression2 in ret2:
                        if va2==None:continue
                        combined_exp = '{}{}' if expression.isalnum() else '({}){}'
                        combined_exp += '{}' if expression2.isalnum() else '({})'
                        new_val = compute(va1,va2,op)
                        ret.append((new_val,combined_exp.format(expression,op,expression2)))
                        if iter==0 and new_val==24:
                            return ''.join(e+'\n' for x,e in ret if x==24)
    return ret
print(exp([2,3,4,11,1,3]))

做的一点优化:记忆式搜索

EXP = {}
def exp(array_n,target,iter=0):
    if len(array_n)==1:return [(array_n[0],str(array_n[0]))]
    operation = ['+','-','*','/']
    ret = []
    for num in range(1,len(array_n)):
        exp1 = array_n[:num]
        exp2 = array_n[num:]

        ret1 = EXP[exp1] if exp1 in EXP else exp(exp1,target,iter+1)
        ret2 = EXP[exp2] if exp2 in EXP else exp(exp2,target,iter+1)
        EXP[exp1] = ret1
        EXP[exp2] = ret2
        for op in operation:
            for va1,expression in ret1:
                if va1==None:continue
                for va2,expression2 in ret2:
                    if va2==None:continue
                    combined_exp = '{}{}' if expression.isalnum() else '({}){}'
                    combined_exp += '{}' if expression2.isalnum() else '({})'
                    new_val = compute(va1,va2,op)
                    ret.append((new_val,combined_exp.format(expression,op,expression2)))
                    if iter==0 and new_val==target:
                        #print('ans')
                        return ''.join(e for x,e in ret if x==target)
    return ret if iter else None
def search(array):
    record = set()
    from itertools import permutations
    for p in permutations(array):
        if p in record:continue
        record.add(p)
        ret = exp(tuple(p),100)
        if ret:print(ret);break