Maximum Score Of Spliced Array Solution in Python

Problem Description

So, you think you can just swap elements between two arrays and magically get a higher score? Welcome to the world of the Maximum Score Of Spliced Array! Imagine you have two arrays, nums1 and nums2, and you want to swap some elements to maximize the sum of one of the arrays. It’s like trying to convince your friend to trade their delicious pizza slice for your sad, cold broccoli. Spoiler alert: it’s not going to work out well for you unless you have a solid strategy!

In this problem, you need to find the maximum possible sum of one of the arrays after performing some swaps. The catch? You can only swap elements between the two arrays. So, if you’re ready to play the swap game, let’s dive into the code!

Code Solution

Copy Code

class Solution:
    def maximumsSplicedArray(self, nums1: list[int], nums2: list[int]) -> int:
        def kadane(nums1: list[int], nums2: list[int]) -> int:
            """
            Returns the maximum gain of swapping some numbers in `nums1` with some
            numbers in `nums2`.
            """
            gain = 0
            maxGain = 0

            for num1, num2 in zip(nums1, nums2):
                gain = max(0, gain + num2 - num1)
                maxGain = max(maxGain, gain)

            return maxGain + sum(nums1)

        return max(kadane(nums1, nums2), kadane(nums2, nums1))

Approach

The solution employs a clever technique known as Kadane’s algorithm, which is typically used to find the maximum subarray sum. Here, it’s repurposed to calculate the maximum gain from swapping elements between the two arrays. The algorithm iterates through both arrays simultaneously, calculating the potential gain from each swap and keeping track of the maximum gain found. Finally, it adds this gain to the sum of the original array to get the maximum possible score.

Time and Space Complexity

Time Complexity: O(n), where n is the length of the input arrays. The algorithm processes each element of the arrays exactly once.

Space Complexity: O(1), as it uses a constant amount of space for variables, regardless of the input size.

Real-World Example

Imagine you’re at a potluck dinner, and you have a plate of bland salad (nums1) while your friend has a plate of mouth-watering lasagna (nums2). You can swap some of your salad for their lasagna to make your meal more enjoyable. The goal is to maximize the deliciousness of your plate by strategically swapping items. This problem is all about finding the best swaps to maximize your score, just like you would at that potluck!