Target Sum

You are given a list of non-negative integers, a1, a2, …, an, and a target, S. Now you have 2 symbols + and -. For each integer, you should choose one from + and - as its new symbol.

Find out how many ways to assign symbols to make sum of integers equal to target S.

Example 1:
Input: nums is [1, 1, 1, 1, 1], S is 3.
Output: 5
Explanation:

-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3

There are 5 ways to assign symbols to make the sum of nums be target 3.
Note:
The length of the given array is positive and will not exceed 20.
The sum of elements in the given array will not exceed 1000.
Your output answer is guaranteed to be fitted in a 32-bit integer.

这题主要就是给一个算式，然后让我们填符号，要是最后的算式的结果等于一个特定的数，现在发现这种阶梯方法比较好就使用了动态规划，里面具体的东西就是递归求解了。

与此类似的体还有很多就是台阶问题等等，都可以使用类似的方法求解！

package LeetCode;

public class TargetSum {
    int count = 0;

    public int findTargetSumWays(int[] nums, int S) {
        calculate(nums, 0, 0, S);
        return count;
    }

    private void calculate(int[] nums,int i,int sum,int S){
        if (i == nums.length) {
            if (sum == S) {
                count++;
            }
        }else {
            calculate(nums, i + 1, sum + nums[i], S);
            calculate(nums, i + 1, sum - nums[i], S);
        }
    }
}