How do you solve K Items With the Maximum Sum on LeetCode?

K Items With the Maximum Sum (LeetCode #2600) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: Always prioritize taking items with the highest value (1s) to maximize the sum.

What is the brute force solution for K Items With the Maximum Sum?

The brute force approach for K Items With the Maximum Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we consider all possible combinations of items we could pick from the bag. This method is straightforward but inefficient, as it explores all combinations to find the maximum sum. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve K Items With the Maximum Sum?

K Items With the Maximum Sum uses the following concepts: Math, Greedy. The recommended patterns to study are: Greedy, Array Manipulation.

What are the interview tips for K Items With the Maximum Sum?

Clearly explain your thought process and the reasoning behind your approach. Be prepared to discuss the trade-offs between brute-force and optimal solutions. Practice similar problems to recognize patterns and improve your problem-solving speed.

What are common mistakes when solving K Items With the Maximum Sum?

Forgetting to check how many items can be taken when k exceeds available items. Not considering the impact of negative items when calculating the sum.

#2600

K Items With the Maximum Sum

Easy

MathGreedyGreedyArray Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(1)
Space	O(1)	O(1)

💡

Intuition

Time O(1)Space O(1)

The optimal solution leverages the fact that we should always prioritize picking items with the highest value (1s) first, followed by 0s if needed. This approach is efficient and avoids unnecessary computations.

⚙️

Algorithm

3 steps

1Step 1: Take as many 1s as possible, up to k.
2Step 2: If k is greater than the number of 1s, take 0s to fill the remaining count.
3Step 3: If k is still greater than the total items taken, the remaining items must be -1s, which do not contribute positively to the sum.

solution.py5 lines

1def max_sum_optimal(numOnes, numZeros, numNegOnes, k):
2    takeOnes = min(numOnes, k)
3    remaining = k - takeOnes
4    takeZeros = min(numZeros, remaining)
5    return takeOnes + takeZeros

ℹ

Complexity note: This solution runs in constant time because it only involves a few arithmetic operations and comparisons, regardless of the input size.

1Always prioritize taking items with the highest value (1s) to maximize the sum.
2If k exceeds the number of available 1s, use 0s to fill the gap before considering negative items.

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