## Description

https://leetcode.com/problems/longest-increasing-subsequence/

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

Use dynamic programming to solve this problem. Each position’s longest increasing subsequence is the from a previous position which is less than the position and has the largest longest increasing subsequence.

```
class Solution:
def lengthOfLIS(self, nums: List[int]) -> int:
if not nums:
return 0
dp = [1] * len(nums)
for i in range(len(nums)):
for j in range(i):
if nums[j] < nums[i]:
dp[i] = max(dp[i], dp[j] + 1)
return max(dp)
```

- Time complexity: O(N^2)
- Space complexity: O(N)

Here is a Solutionsof this problem in java https://thebest681.blogspot.com/2022/10/leetcode-300-longest-increasing.html