longest_increasing_subsequence.py

"""
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?
"""
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        def binary_search(tails, target):
            left, right = 0, len(tails) - 1
            while left <= right:
                mid = (left + right) // 2
                if tails[mid] < target:
                    left = mid + 1
                else:
                    right = mid - 1
            return left

        tails = []

        for num in nums:
            if not tails or num > tails[-1]:
                tails.append(num)
            else:
                position = binary_search(tails, num)
                tails[position] = num
        return len(tails)