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300. Longest Increasing Subsequence

Array Binary Search Dynamic Programming

Problem - Longest Increasing Subsequence

Medium

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

 

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?

Solutions

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class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        n = len(nums)
        dp = []
        dp.append(nums[0])

        lis = 1
        for i in range(1, n):
            if dp[-1] < nums[i]:
                dp.append(nums[i])
                lis += 1
                continue

            index = bisect_left(dp, nums[i])
            dp[index] = nums[i]

        return lis

Submission Stats:

  • Runtime: 4 ms (88.87%)
  • Memory: 17.9 MB (81.28%)