You are given a list of integers nums and a positive integer k. Your task is to implement a function find_subsequence(nums, k) that returns the length of the longest increasing subsequence of nums such that the difference between the maximum and minimum element in the subsequence is at most k. For example, given the list [1, 3, 2, 4] and k = 2, the longest increasing subsequence satisfying the condition has length 2 and is [1, 2]. You may assume that the list nums has at least one element and that k is at least 1. Constraints: The list nums has at most length $10^6$. Examples:  find_subsequence([1, 3, 2, 4], 2) => 2 find_subsequence([1, 2, 3, 4, 5], 1) => 5 find_subsequence([5, 4, 3, 2, 1], 3) => 1 find_subsequence([1, 2, 3, 2, 3, 4, 5, 4, 5, 6], 2) => 4

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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You are given a list of integers nums and a positive integer k. Your task is to implement a function find_subsequence(nums, k) that returns the length of the longest increasing subsequence of nums such that the difference between the maximum and minimum element in the subsequence is at most k.

For example, given the list [1, 3, 2, 4] and k = 2, the longest increasing subsequence satisfying the condition has length 2 and is [1, 2].

You may assume that the list nums has at least one element and that k is at least 1.

Constraints:

The list nums has at most length $10^6$.

Examples:

 find_subsequence([1, 3, 2, 4], 2) => 2

find_subsequence([1, 2, 3, 4, 5], 1) => 5

find_subsequence([5, 4, 3, 2, 1], 3) => 1

find_subsequence([1, 2, 3, 2, 3, 4, 5, 4, 5, 6], 2) => 4

 

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