What is the optimal time complexity of solving Target Sum?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Target Sum?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Target Sum?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Target Sum?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Target Sum

Learn how to solve the 'Target Sum' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

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.

Return the number of different expressions that you can build, which evaluates to target.

Write a function findTargetSumWays(nums: List[int], target: int) -> int.

Constraints

•1 <= len(nums) <= 20
•0 <= nums[i] <= 1000
•0 <= sum(nums) <= 1000
•-1000 <= target <= 1000

Examples

Example 1

Input

nums = [1,1,1,1,1], target = 3

Output

Explanation

There are 5 ways: -1+1+1+1+1, +1-1+1+1+1, +1+1-1+1+1, +1+1+1-1+1, +1+1+1+1-1.

Example 2

Input

nums = [1], target = 1

Output

Explanation

+1 = 1

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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