Maximum Subsequence Score

arraygreedysorting

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 i _0 , i _1 , ..., i _k - 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[i _0 ] + nums1[i _1 ] +...+ nums1[i _k - 1 ]) * min(nums2[i _0 ] , nums2[i _1 ], ... ,nums2[i _k - 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.

Examples

Example 1

Input: nums1 = [1,3,3,2], nums2 = [2,1,3,4], k = 3
Output: 12
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
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 <= 10 ^5

0 <= nums1[i], nums2[j] <= 10 ^5

1 <= k <= n

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy