LeetCode 300. Longest Increasing Subsequence

Description

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

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?

Explanation

one 5 one zero

Python Solution

class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:

        if nums is None or not nums:
            return 0

        dp = [1] * len(nums)
        
        for i in range(0, len(nums)):
            for j in range(0, i):
                if nums[j] < nums[i]:
                    dp[i] = max(dp[i], dp[j] + 1)
        
        return max(dp)
  • Time complexity: ~N^2
  • Space complexity: ~N

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