Longest Increasing Subsequence.md

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?

My code:

class Solution(object):
    def lengthOfLIS(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        if len(nums)<=1:
            return len(nums)
        self.max_length=0
        self.record=[-1]*len(nums)
        self.check_longest(nums,len(nums)-1)
        return self.max_length
    def check_longest(self,nums,j):
        if j==0:
            return 1
        if self.record[j]!=-1:
            return self.record[j]
        local_max=1
        for k in range(j):
            if nums[j]>nums[k]:
                count=self.check_longest(nums,k)
                local_max=max(local_max,count+1)
            else:
                count=self.check_longest(nums,k)
                self.max_length=max(self.max_length,count)
        self.record[j]=local_max
        self.max_length=max(self.max_length,self.record[j])
        return self.record[j]

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