Maximum Score Of Spliced Array

arraydynamic programming

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 ).

Examples

Example 1

Input: nums1 = [60,60,60], nums2 = [10,90,10]
Output: 210
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
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
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 <= 10 ^5

1 <= nums1[i], nums2[i] <= 10 ^4

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming