算24程序设计题

使用加、减、乘、除4种运算以及括号把给出的4 个小于10的正整数连接起来得到一个表达式，并且使得所得的这个表达式的结果等于24

这里加、减、乘、除4种运算以及括号的运算结果与运算优先级跟平常定义一致

第一种方法：

number = [0] * 4
result = [''] * 4
def PointsGame(n):
    if n == 1:
        return abs(number[0] - 24) < 1e-6
    
    for i in range(n):
        for j in range(i+1,n):
            a, b = number[i], number[j]
            number[j] = number[n-1]
            
            charA, charB = result[i],result[j]
            result[j] = result[n-1]
            
            result[i] = '(' + charA + '+' + charB + ')'
            number[i] = a + b
            if PointsGame(n-1):
                return True
            
            result[i] = '(' + charA + '-' + charB + ')'
            number[i] = a - b
            if PointsGame(n-1):
                return True
            
            result[i] = '(' + charA + '*' + charB + ')'
            number[i] = a * b
            if PointsGame(n-1):
                return True
            
            if b != 0:
                result[i] = '(' + charA + '/' + charB + ')'
                number[i] = a / b
                if PointsGame(n-1):
                    return True
                
            if a != 0:
                result[i] = '(' + charB + '/' + charA + ')'
                number[i] = b / a
                if PointsGame(n-1):
                    return True
            
            number[i], number[j] = a, b
            result[i], result[j] = charA ,charB
    return False

if __name__ == '__main__':
    for i in range(4):
        x = input()
        number[i] = int(x)
        result[i] = x
    if PointsGame(4):
        print('YES')
        print(result[0])
    else:
        print('NO')

第二种方法：

from itertools import permutations
n1 = input("")
n2 = input("")
n3 = input("")
n4 = input("")
n = n1+n2+n3+n4
sum = 1
for i in n:
    sum *= eval(i)
if sum < 24:
    print("NO")
    exit()
notation = ['+', '-', '*', "/"]
st = set()
num = 0
number = set(permutations(n))
for i in notation:
    s = i
    t1 = notation.copy()
    t1.remove(i)
    for j in t1:
        s += j
        t2 = t1.copy()
        t2.remove(j)
        for p in t2:
            s += p
            st.add(s)
            s = i+j
        s = i
newst = set()
for i in number:
    for j in st:
        newst.add(i[0]+j[0]+i[1]+j[1]+i[2]+j[2]+i[3])
# print(newst)
all = set()
for i in newst:
    i1 = '('+i[0:3]+')'+i[3:]
    i2 = i[0:2]+'('+i[2:5]+')'+i[5:]
    i3 = i[0:4] + '(' + i[4:] + ')'
    i4 = '(('+i[0:3]+')'+i[3:5]+")"+i[5:]
    i5 = i[0:2]+'(('+i[2:5]+')'+i[5:]+")"
    i6 = '(' + i[0:2] + '(' + i[2:5] + '))' + i[5:]
    i7 = i[0:2]+'('+i[2:4]+'('+i[4:]+"))"
    all.add(i1)
    all.add(i2)
    all.add(i3)
    all.add(i4)
    all.add(i5)
    all.add(i6)
    all.add(i7)
result = []
for i in all:
    try:
        if eval(i) == 24:
          result.append(i)
    except:
        pass
print("YES")
print("("+sorted(result)[0]+")")