## Question

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

time complexity?

## Python Solution

class Solution: def lengthOfLIS(self, nums: List[int]) -> int: dp = [1]*len(nums) for i in range(1,len(nums)): for j in range(i): if nums[j]<nums[i]: dp[i] = max(dp[i],dp[j]+1) return max(dp)