How do you solve Target Sum on LeetCode?

Target Sum (LeetCode #494) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * sum(nums)) time complexity and O(sum(nums)) space complexity. Key insight: The problem can be transformed into a subset sum problem.

What is the brute force solution for Target Sum?

The brute force approach for Target Sum is Brute Force, with O(2^n) time complexity and O(n) space complexity. The brute force approach tries all possible combinations of adding '+' or '-' before each number in the array. This means we explore every possible way to assign signs to the numbers to see if they sum up to the target. The optimal Optimal Solution approach improves this to O(n * sum(nums)).

What algorithm or data structure is used to solve Target Sum?

Target Sum uses the following concepts: Array, Dynamic Programming, Backtracking. The recommended patterns to study are: Dynamic Programming, Backtracking.

What are the interview tips for Target Sum?

Clarify the problem statement and constraints before diving into solutions. Discuss the brute force approach first to show understanding before optimizing. Explain your thought process clearly while coding, as it helps interviewers understand your approach.

What are common mistakes when solving Target Sum?

Not considering edge cases like when total_sum < target. Confusing the signs and not properly tracking the counts.

#494

Target Sum

Medium

ArrayDynamic ProgrammingBacktrackingDynamic ProgrammingBacktracking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(2^n)	O(n * sum(nums))
Space	O(n)	O(sum(nums))

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Intuition

Time O(n * sum(nums))Space O(sum(nums))

The optimal approach uses dynamic programming to count the number of ways to achieve the target sum. Instead of exploring all combinations, we build a table that keeps track of the number of ways to reach each possible sum using the numbers provided.

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Algorithm

3 steps

1Step 1: Calculate the total sum of nums and determine the required positive sum needed to reach the target.
2Step 2: Use dynamic programming to find the number of ways to achieve this positive sum using the numbers in nums.
3Step 3: Return the count of ways to achieve the target.

solution.py11 lines

1def findTargetSumWays(nums, target):
2    total_sum = sum(nums)
3    if total_sum < target or (total_sum + target) % 2 != 0:
4        return 0
5    positive_sum = (total_sum + target) // 2
6    dp = [0] * (positive_sum + 1)
7    dp[0] = 1
8    for num in nums:
9        for j in range(positive_sum, num - 1, -1):
10            dp[j] += dp[j - num]
11    return dp[positive_sum]

ℹ

Complexity note: The time complexity is O(n * sum(nums)) because we iterate through each number and update our dp array for each possible sum. The space complexity is O(sum(nums)) due to the dp array storing counts for each possible sum.

1The problem can be transformed into a subset sum problem.
2Dynamic programming is effective for counting combinations rather than generating them.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.