Longest Increasing Subsequence

Statement

The Longest Increasing Subsequence (LIS) is the longest subsequence from a given array in which the subsequence elements are sorted in strictly increasing order. Given an integer array, nums, find the length of the LIS in this array.

Let’s say we have an integer array [6, 9, 8, 2, 3, 5, 1, 4, 7], and we want to get the longest increasing subsequence in this array. There are multiple increasing subsequences of different lengths, such as [6, 9], [6, 8], [2, 3, 5], [2, 3, 5, 7], and so on. The longest increasing subsequences, in this case, are [2, 3, 4, 7] and [2, 3, 5, 7], both of length 4.

Constraints:

• $1 \leq$ nums.length $\leq 5500$
• $-10^5 \leq$ nums[i] $\leq 10^5$

Examples