You are given an integer array nums and an integer target.
You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.
For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".
Return the number of different expressions that you can build, which evaluates to target.
Example 1:
Input: nums = [1,1,1,1,1], target = 3
Output: 5
Explanation: There are 5 ways to assign symbols to make the sum of nums be target 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
+1 + 1 + 1 + 1 - 1 = 3
Example 2:
Input: nums = [1], target = 1
Output: 1
Constraints:
1 <= nums.length <= 20
0 <= nums[i] <= 1000
0 <= sum(nums[i]) <= 1000
-1000 <= target <= 1000
Tags
Dynamic Programming, Depth-first Search
Solution
We denote sum as the sum of nums, and neg as the sum of all elements whose sign is -. Then we can obtain (sum−neg)−neg=sum−2⋅neg=target , then we obtain neg=(sum−target)/2 . Now our goal is to find a subset of nums whose sum is neg.
We use Dynamic Programming strategy and build a 2D-array dp, and dp[i][j] represents the number of combination of some of elements in nums[:i] whose sum is j.
If num[i]>j, we will not pick it, and dp[i][j]=dp[i-1][j];
Otherwise, if we pick it, we will have extra dp[i-1][j-num[i]] choices, meaning that dp[i][j]=dp[i-1][j]+dp[i-1][j-num[i]].
func findTargetSumWays(nums []int, target int) int {
var sum int
for _, num := range nums {
sum += num
}
diff := sum - target
if diff < 0 || diff%2 == 1 {
return 0
}
neg := diff / 2
dp := make([]int, neg+1)
dp[0] = 1
for _, num := range nums {
for j := neg; j >= num; j-- {
dp[j] += dp[j-num]
}
}
return dp[neg]
}