algoadvance

You are given three integers numOnes, numZeros, and numNegOnes. You are also given an integer k. We want to choose a total of k items from numOnes, numZeros, and numNegOnes such that we maximize their sum.

Return the maximum possible sum of k items.

Clarifying Questions

  1. Can k be greater than the sum of numOnes, numZeros, and numNegOnes?
    • No, k will be a valid integer such that k ≤ numOnes + numZeros + numNegOnes.
  2. Are the values of numOnes, numZeros, and numNegOnes guaranteed to be non-negative integers?
    • Yes, all given values will be non-negative integers.

Strategy

To maximize the sum of k items:

  1. Prioritize taking all 1s first since they have the highest value.
  2. If more items are needed and we run out of 1s, take 0s next as they do not affect the sum.
  3. If we still need more items and run out of 0s, take -1s as they decrease the sum.

Steps:

  1. Take the minimum of k and numOnes number of 1s.
  2. Subtract the number of 1s taken from k.
  3. Use the remaining k to take as many 0s as possible.
  4. Use the remaining k to take -1s and reduce the sum accordingly.

Code

def kItemsWithMaximumSum(numOnes, numZeros, numNegOnes, k):
    # Initialize the sum
    max_sum = 0
    
    # Take as many 1s as possible
    ones_taken = min(numOnes, k)
    max_sum += ones_taken
    k -= ones_taken
    
    # If k is still greater than 0, take 0s
    zeros_taken = min(numZeros, k)
    k -= zeros_taken
    
    # If k is still greater than 0, take -1s (which subtract from the sum)
    neg_ones_taken = min(numNegOnes, k)
    max_sum -= neg_ones_taken
    
    return max_sum

Time Complexity

The time complexity of this solution is O(1) because the number of operations we perform does not depend on the size of the input but on a series of constant-time comparisons and arithmetic operations.

By using this strategy, we ensure that we are maximizing the sum efficiently within the constraints provided.

Try our interview co-pilot at AlgoAdvance.com