494-target-sum

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Description

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

Solution(Python)

class Solution:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        self.nums = nums
        self.target = target
        return self.topdown()

    # Time Complexity: O(2^n)
    # Space Complexity: O(n)
    def bruteforce(self, nums: List[int], target: int) -> int:
        cnt = 0
        n = len(nums)

        def calculate(i, sumsofar):
            nonlocal cnt
            if i == n:
                if sumsofar == target:
                    cnt += 1
            else:
                calculate(i + 1, sumsofar + nums[i])
                calculate(i + 1, sumsofar - nums[i])

        calculate(0, 0)
        return cnt

    # Time Complexity: O(n*sum)
    # Space Complexity: O(n*sum)
    @cache
    def topdown(self, index: int = 0, sumsofar: int = 0) -> int:
        if index == len(self.nums):
            return sumsofar == self.target
        else:
            add = self.topdown(index + 1, sumsofar + self.nums[index])
            sub = self.topdown(index + 1, sumsofar - self.nums[index])
            return add + sub