300-longest-increasing-subsequence¶

Description¶

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

Solution(Python)¶

class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        LIS = []
        for num in nums:
            if not LIS or LIS[-1] < num:
                LIS.append(num)
            else:
                pos = bisect_left(LIS,num)
                LIS[pos] = num

        return len(LIS)