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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:4Explanation: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`

`-10`

^{4}<= nums[i] <= 10^{4}

**Follow up:**

- Could you come up with the
`O(n`

solution?^{2}) - Could you improve it to
`O(n log(n))`

time complexity?