Largest Values From Labels

Problem Description

You are given n item's value and label as two integer arrays values and labels. You are also given two integers numWanted and useLimit. Your task is to find a subset of items with the maximum sum of their values such that:

• The number of items is at most numWanted.
• The number of items with the same label is at most useLimit.

Return the maximum sum.

Key Insights

• We need to maximize the sum of selected values while respecting the constraints on the number of items (numWanted) and the limit on the same labels (useLimit).
• Sorting the items by their values in descending order allows us to always consider the highest available values first.
• A dictionary or hash map can be used to keep track of how many items from each label have been selected.

Space and Time Complexity

Time Complexity: O(n log n) due to sorting the values. Space Complexity: O(n) for storing the counts of labels and the necessary data structures.

Solution

To solve this problem, we can use the following approach:

1. Pair each value with its corresponding label.
2. Sort these pairs in descending order based on the value.
3. Use a hash map to keep track of how many items from each label are included in the selection.
4. Iterate through the sorted list, adding values to the total sum while respecting the constraints of numWanted and useLimit.

This greedy approach ensures that we always select the highest possible values first while adhering to the label restrictions.

Code Solutions