300\. Longest Increasing Subsequence

Medium

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`
*   <code>-10<sup>4</sup> <= nums[i] <= 10<sup>4</sup></code>

**Follow up:** Can you come up with an algorithm that runs in `O(n log(n))` time complexity?