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[8/8] 300. Longest Increasing Subsequence

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Given an integer array nums, return the length of the longest strictly increasing subsequence.

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: Can you come up with an algorithm that runs in O(n log(n)) time complexity?

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class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        dp = [1]*len(nums)
        
        for i in range(len(nums)-1, -1, -1):
            max_lis = 0
            for j in range(i+1, len(nums)):
                if nums[i] < nums[j]:
                    max_lis = max(dp[j], max_lis)
            dp[i] = max_lis + 1
        
        return max(dp)
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