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3509. Maximum Product of Subsequences With an Alternating Sum Equal to K
Description
You are given an integer array nums and two integers, k and limit. Your task is to find a non-empty subsequence of nums that:
- Has an alternating sum equal to
k. - Maximizes the product of all its numbers without the product exceeding
limit.
Return the product of the numbers in such a subsequence. If no subsequence satisfies the requirements, return -1.
The alternating sum of a 0-indexed array is defined as the sum of the elements at even indices minus the sum of the elements at odd indices.
Example 1:
Input: nums = [1,2,3], k = 2, limit = 10
Output: 6
Explanation:
The subsequences with an alternating sum of 2 are:
[1, 2, 3]- Alternating Sum:
1 - 2 + 3 = 2 - Product:
1 * 2 * 3 = 6
- Alternating Sum:
[2]- Alternating Sum: 2
- Product: 2
The maximum product within the limit is 6.
Example 2:
Input: nums = [0,2,3], k = -5, limit = 12
Output: -1
Explanation:
A subsequence with an alternating sum of exactly -5 does not exist.
Example 3:
Input: nums = [2,2,3,3], k = 0, limit = 9
Output: 9
Explanation:
The subsequences with an alternating sum of 0 are:
[2, 2]- Alternating Sum:
2 - 2 = 0 - Product:
2 * 2 = 4
- Alternating Sum:
[3, 3]- Alternating Sum:
3 - 3 = 0 - Product:
3 * 3 = 9
- Alternating Sum:
[2, 2, 3, 3]- Alternating Sum:
2 - 2 + 3 - 3 = 0 - Product:
2 * 2 * 3 * 3 = 36
- Alternating Sum:
The subsequence [2, 2, 3, 3] has the greatest product with an alternating sum equal to k, but 36 > 9. The next greatest product is 9, which is within the limit.
Constraints:
1 <= nums.length <= 1500 <= nums[i] <= 12-105 <= k <= 1051 <= limit <= 5000