# LeetCode 300. Longest Increasing Subsequence

## Description

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

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

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`

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 =  * 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)