public class Solution
extends Object
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:**
* 1 <= nums.length <= 105
* 1 <= nums[i], k <= 105