300-longest-increasing-subsequence.py

"""
Problem Link: https://leetcode.com/problems/longest-increasing-subsequence/

Given an integer array nums, return the length of the longest strictly increasing subsequence.
A 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:
Could you come up with the O(n2) solution?
Could you improve it to O(n log(n)) time complexity?
"""
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        dp = [1] * len(nums)
        
        max_length = 1
        for i in range(1, len(nums)):
            for j in range(i+1):
                if nums[j] < nums[i]:
                    dp[i] = max(dp[i], dp[j] + 1)
                    max_length = max(max_length, dp[i])
        
        return max_length