【679. 24 Game】

You have 4 cards each containing a number from 1 to 9. You need to judge whether they could operated through *, /, +, -, (, ) to get the value of 24.

Example 1:

Input: [4, 1, 8, 7]
Output: True

Explanation: (8-4) * (7-1) = 24
Example 2:

Input: [1, 2, 1, 2]
Output: False

Note:
The division operator / represents real division, not integer division. For example, 4 / (1 - 2/3) = 12.
Every operation done is between two numbers. In particular, we cannot use - as a unary operator. For example, with [1, 1, 1, 1] as input, the expression -1 - 1 - 1 - 1 is not allowed.
You cannot concatenate numbers together. For example, if the input is [1, 2, 1, 2], we cannot write this as 12 + 12.

【题目解析】

本题难度属于高难度题目，所采用的办法是递归，列举出全部结果。
递归办法是从列表中取出两个数字，进行±*/运算。得到的结果与剩余数字重新组成列表，此时数字列表中减少一个元素，采用递归，再取出两个数字，直至列表长度为1，判断是否为24，因涉及到除法操作，故判断时应当采用24±1e-6范围内即判断为24。

【python代码】

class Solution:
    
    def judgePoint24(self, nums: List[int]) -> bool:
        def Ju(nums):
            if len(nums)==0:
                return False
            if len(nums)==1:
                return abs(nums[0]-24)<0.000006
        
            for i in range(len(nums)):
                for j in range(len(nums)):
                    if i == j:
                        continue
                    else:
                        x = nums[i]
                        y = nums[j]
                        new_nums = [nums[k] for k in range(len(nums)) if k != i and k != j]

                        Status = False
                        Status = Status or Ju(new_nums+[x+y])
                        Status = Status or Ju(new_nums+[x*y])
                        Status = Status or Ju(new_nums+[x-y])
                        if abs(y)>0.000006:
                            Status = Status or Ju(new_nums+[x/y])
                        if Status:
                            return True
            return Status
        return Ju(nums)