# 494. Target Sum (Medium)

https://leetcode.com/problems/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:

1. The length of the given array is positive and will not exceed 20.
2. The sum of elements in the given array will not exceed 1000.
3. Your output answer is guaranteed to be fitted in a 32-bit integer.

## Solutions

``````class Solution {

int ans = 0;

Map<Integer, Integer> maxMap = new HashMap<>();
Map<Integer, Integer> minMap = new HashMap<>();

public int findTargetSumWays(int[] nums, int S) {
if (nums == null || nums.length == 0) {
return 0;
}

int len = nums.length;

maxMap.put(len, 0);
minMap.put(len, 0);

for (int i = len - 1; i >= 0; i--) {

// max sum after i (inclusive)
maxMap.put(i, maxMap.get(i + 1) + nums[i]);

// min sum after i (inclusive)
minMap.put(i, minMap.get(i + 1) - nums[i]);
}

recurse(nums, S, 0, 0);

return ans;
}

private void recurse(int[] nums, int target, int idx, int sum) {
if (idx == nums.length) {
if (target == sum) {
ans++;
}

return;
}

// sum + maxMap.get(idx) < target means even all the rest numbers
// keep positive, still less than target.
if (sum + maxMap.get(idx) >= target) {
// ith number remains positive
recurse(nums, target, idx + 1, sum + nums[idx]);
}

// sum + minMap.get(idx) > target means even all the rest numbers
// turn to be negative, still larger than target.
if (sum + minMap.get(idx) <= target) {
// ith number turns to be negative
recurse(nums, target, idx + 1, sum - nums[idx]);
}
}
}
``````