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# 300. Longest Increasing Subsequence

## Description

Given an integer array nums, return the length of the longest strictly increasing subsequence.

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, [3,6,2,7] is a subsequence of the array [0,3,1,6,2,2,7].

Example 1:

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.


Example 2:

Input: nums = [0,1,0,3,2,3]
Output: 4


Example 3:

Input: nums = [7,7,7,7,7,7,7]
Output: 1


Constraints:

• 1 <= nums.length <= 2500
• -104 <= nums[i] <= 104

• Could you come up with the O(n2) solution?
• Could you improve it to O(n log(n)) time complexity?