Introduction

In this blog post, we will explore how to solve the LeetCode problem "1090" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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. Example 1: Input: values = [5,4,3,2,1], labels = [1,1,2,2,3], numWanted = 3, useLimit = 1 Output: 9 Explanation: The subset chosen is the first, third, and fifth items with the sum of values 5 + 3 + 1. Example 2: Input: values = [5,4,3,2,1], labels = [1,3,3,3,2], numWanted = 3, useLimit = 2 Output: 12 Explanation: The subset chosen is the first, second, and third items with the sum of values 5 + 4 + 3. Example 3: Input: values = [9,8,8,7,6], labels = [0,0,0,1,1], numWanted = 3, useLimit = 1 Output: 16 Explanation: The subset chosen is the first and fourth items with the sum of values 9 + 7. Constraints: n == values.length == labels.length 1 <= n <= 2 104 0 <= values[i], labels[i] <= 2 104 1 <= numWanted, useLimit <= n

Explanation

Here's the solution to the problem, broken down into high-level approach, complexity analysis, and the Python code.

• Sort by Value: The core idea is to prioritize items with higher values. We sort the items based on their values in descending order.
• Greedy Selection with Label Limit: We iterate through the sorted items and greedily pick them for our subset, but we need to respect the useLimit constraint for each label.

• Label Count Tracking: Use a dictionary (hash map) to keep track of the number of items selected for each label, ensuring that we don't exceed useLimit for any label.

• Time Complexity: O(n log n) due to sorting.

• Space Complexity: O(n) to store the sorted items and label counts.

Code

    def max_value_subset(values, labels, numWanted, useLimit):
    """
    Finds a subset of items with the maximum sum of their values subject to the given constraints.

    Args:
        values: A list of integers representing the values of the items.
        labels: A list of integers representing the labels of the items.
        numWanted: The maximum number of items allowed in the subset.
        useLimit: The maximum number of items allowed for each label.

    Returns:
        The maximum sum of the values of the items in the subset.
    """

    n = len(values)
    items = sorted(zip(values, labels), key=lambda x: x[0], reverse=True)  # Sort items by value in descending order

    total_sum = 0
    count = 0
    label_counts = {}

    for value, label in items:
        if count >= numWanted:
            break

        if label not in label_counts:
            label_counts[label] = 0

        if label_counts[label] < useLimit:
            total_sum += value
            count += 1
            label_counts[label] += 1

    return total_sum