# Leetcode: Target Sum

Target Sum Similar Problems:

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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

```// Blog link: https://code.dennyzhang.com/target-sum
// Basic Ideas: BFS + hashmap
// Complexity: Time O(pow(2, n)), Space O(1)
//   The value would be in between -1000 and 1000
//   Thus Space is O(1)
func findTargetSumWays(nums []int, S int) int {
m := make(map[int]int)
m = 1
for _, num := range nums {
m2 := make(map[int]int)
for v := range m {
m2[v+num] += m[v]
m2[v-num] += m[v]
}
m = m2
}
return m[S]
}
```

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