Leetcode 300. Longest Increasing Subsequence. Python (DP Approach)

300. 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

 

Solution :

class Solution:

    def lengthOfLIS(self, n: List[int]) -> int:

        lis = [1] * len(n)

        for i in range(len(n)-1, -1, -1):

            for j in range(i+1, len(n)):

                if n[i] < n[j]:

                    lis[i] = max(lis[i], lis[j] + 1)

        return max(lis)

Explaination :