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:

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.

思路：把每两个数拿出来，找出其所有的加减乘除组合，然后把每一个取出来，后剩余的两个数（总共也就是3个数），继续做同样的操作，直到只剩下一个数，看那个数是不是24.

class Solution {
    public boolean judgePoint24(int[] nums) {
        return helper(new double[] { nums[0], nums[1], nums[2], nums[3] });
    }

    private boolean helper(double[] nums) {
        if (nums.length == 1) return Math.abs(nums[0] - 24) < 0.01;
        for (int i = 0; i < nums.length; i++) {
            for (int j = i + 1; j < nums.length; j++) {
                double[] remainings = new double[nums.length - 1];
                int idx = 0;
                // add numbers in nums to remainings excluding nums[i] and nums[j]
                for (int k = 0; k < nums.length; k++) {
                    if (k != i && k != j) {
                        remainings[idx] = nums[k];
                        idx++;
                    }
                }
                for (double k : computeCombinations(nums[i], nums[j])) {
                    remainings[remainings.length - 1] = k;
                    if (helper(remainings)) {
                        return true;
                    }
                }
            }
        }
        return false;
    }

    private double[] computeCombinations(double a, double b) {
        return new double[] { a + b, a - b, b - a, a * b, a / b, b / a };
    }
}