Maximum Score Of Spliced Array

Problem Description

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]. 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). Return the maximum possible score.

Key Insights

• The core of the problem is to identify which subarray swap (if any) maximizes the score.
• Calculate the initial sums of both arrays, sum1 and sum2.
• For each possible subarray defined by indices left and right, determine the effect of swapping on the total sums.
• Utilize prefix sums to efficiently calculate the sums of subarrays.
• The score is determined by comparing the original sums with the potential new sums after the swap.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a sliding window approach to find the maximum possible increase in score from swapping subarrays. We calculate the difference in sums for each possible subarray and track the best possible score.

Code Solutions