23-TargetSum.py

"""
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



SOLUTIONS - https://leetcode.com/problems/target-sum/solution/
"""

class Solution:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        total = sum(nums)
        dp = [0]*(2*total+ 1)
        dp[nums[0] + total] = 1
        dp[-nums[0] + total] += 1
        
        for i in range(1, len(nums)):
            nextarr = [0]*(2*total+1)
            currsum = -total
            while currsum <= total:
                if dp[currsum + total] > 0:
                    nextarr[currsum + nums[i] + total] += dp[currsum + total]
                    nextarr[currsum - nums[i] + total] += dp[currsum + total]
                currsum += 1
            dp = nextarr
        return 0 if abs(target) > total else dp[target + total]