Longest Increasing Subsequence II

arraydivide and conquerdynamic programming

Problem Statement

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.

Examples

Example 1

Input: nums = [4,2,1,4,3,4,5,8,15], k = 3
Output: 5
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
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
The longest subsequence that meets the requirements is [1].
The subsequence has a length of 1, so we return 1.

Constraints

1 <= nums.length <= 10 ^5

1 <= nums[i], k <= 10 ^5

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDivide and Conquer