300. 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: 4 
Explanation: 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(n2) complexity.

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

class Solution(object):
    def lengthOfLIS(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        if nums == []:
            return 0
        
        n = len(nums)
        dp = [1] * n
        
        for i in range(1,n):
            for j in range(0,i):
                if(nums[j] < nums[i]):
                    dp[i] = max(dp[i],dp[j]+1)
        
        res = 0
        for i in dp:
            res = max(res,i)
        
        return res