#2542

Maximum Subsequence Score

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array · greedy · sorting · heap (priority queue)

Description

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 i0, i1, ..., ik - 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[i0] + nums1[i1] +...+ nums1[ik - 1]) * min(nums2[i0] , nums2[i1], ... ,nums2[ik - 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.

Example 1:

Input: nums1 = [1,3,3,2], nums2 = [2,1,3,4], k = 3

Output: 12

Explanation:

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

Explanation:

Choosing index 2 is optimal: nums1[2] * nums2[2] = 3 * 10 = 30 is the maximum possible score.

Solution