24 Game

Description

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:

1. The division operator / represents real division, not integer division. For example, 4 / (1 - 2/3) = 12.
2. 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.
3. You cannot concatenate numbers together. For example, if the input is [1, 2, 1, 2], we cannot write this as 12 + 12.

Solution(javascript)

/*
 * @lc app=leetcode id=679 lang=javascript
 *
 * [679] 24 Game
 */

// @lc code=start
/** 括号怎么处理
 * @param {number[]} nums
 * @return {boolean}
 */
const judgePoint24 = function (nums) {
  const isValid = x => Math.abs(x - 24) < 0.0000001
  const aux = (arr = []) => {
    if (arr.length === 1) {
      return isValid(arr[0])
    }
    let valid = false
    for (let i = 0; i < arr.length; i++) {
      for (let j = i + 1; j < arr.length; j++) {
        const nextArr = arr.filter((x, index) => index !== i && index !== j)
        valid = valid || aux([...nextArr, arr[i] + arr[j]])
          || aux([...nextArr, arr[i] - arr[j]])
          || aux([...nextArr, arr[j] - arr[i]])
          || aux([...nextArr, arr[i] * arr[j]])
          || aux([...nextArr, arr[i] / arr[j]])
          || aux([...nextArr, arr[j] / arr[i]])
      }
    }
    return valid
  }

  return aux(nums)
}