2542. Maximum Subsequence Score
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 fromnums2
. - 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.
Constraints:
n == nums1.length == nums2.length
1 <= n <= 105
0 <= nums1[i], nums2[j] <= 105
1 <= k <= n
Solutions
Solution 1: Sorting + Priority Queue (Min Heap)
Sort nums2 and nums1 in descending order according to nums2, then traverse from front to back, maintaining a min heap. The heap stores elements from nums1, and the number of elements in the heap does not exceed $k$. At the same time, maintain a variable $s$ representing the sum of the elements in the heap, and continuously update the answer during the traversal process.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array nums1.
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