Problem Statement

You are given a set of positive numbers and a target sum ‘S’. Each number should be assigned either a ‘+’ or ‘-’ sign. We need to find the total ways to assign symbols to make the sum of the numbers equal to the target ‘S’.

Example 1:

Input: {1, 1, 2, 3}, S=1
Output: 3
Explanation: The given set has '3' ways to make a sum of '1': {+1-1-2+3} & {-1+1-2+3} & {+1+1+2-3}

Example 2:

Input: {1, 2, 7, 1}, S=9
Output: 2
Explanation: The given set has '2' ways to make a sum of '9': {+1+2+7-1} & {-1+2+7+1}

Constraints:

• 1 <= num.length <= 20
• 0 <= num[i] <= 1000
• 0 <= sum(num[i]) <= 1000
• -1000 <= S <= 1000

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