Introduction

In this blog post, we will explore how to solve the LeetCode problem "2321" 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, both of length n. You can choose two integers left and right where 0 <= left <= right < n and swap the subarray nums1[left...right] with the subarray nums2[left...right]. For example, if nums1 = [1,2,3,4,5] and nums2 = [11,12,13,14,15] and you choose left = 1 and right = 2, nums1 becomes [1,12,13,4,5] and nums2 becomes [11,2,3,14,15]. You may choose to apply the mentioned operation once or not do anything. The score of the arrays is the maximum of sum(nums1) and sum(nums2), where sum(arr) is the sum of all the elements in the array arr. Return the maximum possible score. A subarray is a contiguous sequence of elements within an array. arr[left...right] denotes the subarray that contains the elements of nums between indices left and right (inclusive). Example 1: Input: nums1 = [60,60,60], nums2 = [10,90,10] Output: 210 Explanation: Choosing left = 1 and right = 1, we have nums1 = [60,90,60] and nums2 = [10,60,10]. The score is max(sum(nums1), sum(nums2)) = max(210, 80) = 210. Example 2: Input: nums1 = [20,40,20,70,30], nums2 = [50,20,50,40,20] Output: 220 Explanation: Choosing left = 3, right = 4, we have nums1 = [20,40,20,40,20] and nums2 = [50,20,50,70,30]. The score is max(sum(nums1), sum(nums2)) = max(140, 220) = 220. Example 3: Input: nums1 = [7,11,13], nums2 = [1,1,1] Output: 31 Explanation: We choose not to swap any subarray. The score is max(sum(nums1), sum(nums2)) = max(31, 3) = 31. Constraints: n == nums1.length == nums2.length 1 <= n <= 105 1 <= nums1[i], nums2[i] <= 104

Explanation

Here's the approach to solve this problem:

• Calculate Initial Sums: Compute the initial sums of nums1 and nums2 without any swaps.
• Kadane's Algorithm Variation: Iterate through the arrays and use a modified Kadane's algorithm to find the maximum difference that can be achieved by swapping a subarray. The difference array will be nums2[i] - nums1[i]. We will maintain a current_max and a global_max representing the maximum possible increase achievable through a swap.

• Determine Maximum Score: The maximum possible score is the maximum of the initial sum of nums1 plus the global_max difference we found, and the initial sum of nums2.

• Runtime Complexity: O(n)

• Storage Complexity: O(1)

Code

    def maximum_score(nums1, nums2):
    n = len(nums1)
    sum1 = sum(nums1)
    sum2 = sum(nums2)

    max_diff = 0
    current_diff = 0

    for i in range(n):
        diff = nums2[i] - nums1[i]
        current_diff = max(diff, current_diff + diff)
        max_diff = max(max_diff, current_diff)

    return max(sum1 + max_diff, sum2)