## Description

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

Given an unsorted array of integers, find the length of longest increasing subsequence.

**Example:**

Input:`[10,9,2,5,3,7,101,18]`

Output:4Explanation:The longest increasing subsequence is`[2,3,7,101]`

, therefore the length is`4`

.

**Note:**

- There may be more than one LIS combination, it is only necessary for you to return the length.
- Your algorithm should run in O(
*n*) complexity.^{2}

**Follow up:** Could you improve it to O(*n* log *n*) time complexity?

## Explanation

one 5 one zero

## Python Solution

```
class Solution:
def lengthOfLIS(self, nums: List[int]) -> int:
if nums is None or not nums:
return 0
dp = [1] * len(nums)
for i in range(0, len(nums)):
for j in range(0, i):
if nums[j] < nums[i]:
dp[i] = max(dp[i], dp[j] + 1)
return max(dp)
```

- Time complexity: ~N^2
- Space complexity: ~N

## One Thought to “LeetCode 300. Longest Increasing Subsequence”