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.

列出四个数的全排列，对每一个排列进行所有可能的运算（三个位置的运算符加减乘除有4*4*4=64种可能，插入括号有6种方式），检查运算结果是否为24。

#include
#include
#include 
#include 
using namespace std;
class Solution {
public:
	vector operands;
    	bool judgePoint24(vector& nums) {
    		for (int i = 0 ;i < 4; i++)
    			operands.push_back(nums[i]);
        	for (int i = 0; i < 24; i++) {
			for (int x = 1; x <= 4; x++)
			for (int y = 1; y <= 4; y++)
			for (int z = 1; z <= 4; z++) {
				double left,middle,right,result;
				left=compute(x, operands[0], operands[1]);
				middle=compute(y, operands[1],operands[2]);
				right=compute(z,operands[2], operands[3]);
				
				result=compute(y,left,operands[2]);
				result=compute(z,result,operands[3]);
				if (fabs(result-24)<0.001) return true;//a?b?c?d

				result=compute(y, left,right);
				if (fabs(result-24)<0.001) return true;//(a?b)?(c?d)

				result=compute(x, operands[0], middle);
				result=compute(z, result, operands[3]);//(a?(b?c))?d
				if (fabs(result-24)<0.001) return true;

				result=compute(z, middle,operands[3]);
                		result=compute(x, operands[0],result);//a?((b?c)?d)
                		if (fabs(result-24)<0.001) return true;

				result= compute(y,left,right);
				if (fabs(result-24)<0.001) return true;//a?b?(c?d)

				result=compute(y,operands[1],right);
				result=compute(x,operands[0],result);
				if (fabs(result-24)<0.001) return true;//a?(b?(c?d))
			}
			next_permutation(operands.begin(),operands.end());
		}
		return false;
    	}
	double compute(int oper, double & a, double& b) {
		if (oper==1) return a+b;
		if (oper==2) return a-b;
		if (oper==3) return a*b;
		if (oper==4) {
			if (b==0) return 0;		 
			return a/b;
		}
	}
};