2407 - Longest Increasing Subsequence II\.

Hard

You are given an integer array nums and an integer k.

Find the longest subsequence of nums that meets the following requirements:

• The subsequence is strictly increasing and

• The difference between adjacent elements in the subsequence is at most k.

Return the length of the longest subsequence that meets the requirements.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: nums = 4,2,1,4,3,4,5,8,15, k = 3

Output: 5

Explanation:

The longest subsequence that meets the requirements is 1,3,4,5,8.

The subsequence has a length of 5, so we return 5.

Note that the subsequence 1,3,4,5,8,15 does not meet the requirements because 15 - 8 = 7 is larger than 3.

Example 2:

Input: nums = 7,4,5,1,8,12,4,7, k = 5

Output: 4

Explanation:

The longest subsequence that meets the requirements is 4,5,8,12.

The subsequence has a length of 4, so we return 4.

Example 3:

Input: nums = 1,5, k = 1

Output: 1

Explanation: The longest subsequence that meets the requirements is 1. The subsequence has a length of 1, so we return 1.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= numsi, k <= 10⁵</code>