leetcode 300 Title: increased longest sequence

Subject description:

A disorder of a given integer array, the length of the longest found rising sequence.
Example:

Input: [10,9,2,5,3,7,101,18]
Output: 4
explained: the longest sequence is increased [2,3,7,101], its length is 4.

Description:

Various combinations may be increased up sequence, you only need to output a corresponding length.
The time complexity of your algorithm should be O (n2).
Advanced: You can reduce the time complexity of the algorithm to O (n log n) do?

python code

class Solution:
    # 动态规划的思路：将 dp 数组定义为：以 nums[i] 结尾的最长上升子序列的长度
    # 那么题目要求的，就是这个 dp 数组中的最大者
    # 以数组  [10, 9, 2, 5, 3, 7, 101, 18] 为例：
    # dp 的值： 1  1  1  2  2  3  4    4
    def lengthOfLIS(self, nums: List[int]) -> int:
        size = len(nums)
        if size <= 1:
            return size
        dp = [1] * size
        for i in range(1, size):
            for j in range(i):
                if nums[i] > nums[j]:
                    dp[i] = max(dp[i], dp[j] + 1)
        return max(dp)