Introduction

In this blog post, we will explore how to solve the LeetCode problem "2542" 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 two 0-indexed integer arrays nums1 and nums2 of equal length n and a positive integer k. You must choose a subsequence of indices from nums1 of length k. For chosen indices i0, i1, ..., ik - 1, your score is defined as: The sum of the selected elements from nums1 multiplied with the minimum of the selected elements from nums2. It can defined simply as: (nums1[i0] + nums1[i1] +...+ nums1[ik - 1]) min(nums2[i0] , nums2[i1], ... ,nums2[ik - 1]). Return the maximum possible score. A subsequence of indices of an array is a set that can be derived from the set {0, 1, ..., n-1} by deleting some or no elements. Example 1: Input: nums1 = [1,3,3,2], nums2 = [2,1,3,4], k = 3 Output: 12 Explanation: The four possible subsequence scores are: - We choose the indices 0, 1, and 2 with score = (1+3+3) min(2,1,3) = 7. - We choose the indices 0, 1, and 3 with score = (1+3+2) min(2,1,4) = 6. - We choose the indices 0, 2, and 3 with score = (1+3+2) min(2,3,4) = 12. - We choose the indices 1, 2, and 3 with score = (3+3+2) min(1,3,4) = 8. Therefore, we return the max score, which is 12. Example 2: Input: nums1 = [4,2,3,1,1], nums2 = [7,5,10,9,6], k = 1 Output: 30 Explanation: Choosing index 2 is optimal: nums1[2] nums2[2] = 3 * 10 = 30 is the maximum possible score. Constraints: n == nums1.length == nums2.length 1 <= n <= 105 0 <= nums1[i], nums2[j] <= 105 1 <= k <= n

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• Key Approach:

  • Sort indices based on nums2 in descending order to consider potential minimum values.
  • Use a min-heap to maintain the k largest elements from nums1 encountered so far, allowing efficient calculation of the sum of top k elements.
  • Iterate through the sorted indices, updating the heap and calculating the score based on the current minimum (nums2 value) and the sum of the top k nums1 values.

• Complexity:

  • Runtime: O(n log n) due to sorting and heap operations.
  • Storage: O(n) to store the indices and the heap.

Code

    import heapq

def maxScore(nums1, nums2, k):
    """
    Calculates the maximum possible score based on the given conditions.

    Args:
        nums1: The first array of integers.
        nums2: The second array of integers.
        k: The number of elements to choose.

    Returns:
        The maximum possible score.
    """

    n = len(nums1)
    indices = sorted(range(n), key=lambda i: nums2[i], reverse=True)
    min_heap = []
    nums1_sum = 0
    max_score = 0

    for i in range(n):
        index = indices[i]
        num1 = nums1[index]
        num2 = nums2[index]

        heapq.heappush(min_heap, num1)
        nums1_sum += num1

        if len(min_heap) > k:
            smallest = heapq.heappop(min_heap)
            nums1_sum -= smallest

        if len(min_heap) == k:
            max_score = max(max_score, nums1_sum * num2)

    return max_score