Target Sum

arraydynamic programmingbacktracking

Problem Statement

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 .

Examples

Example 1

Input: nums = [1,1,1,1,1], target = 3
Output: 5
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

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming