Longest Increasing Subsequence

Problem Statement

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

Leetcode Link

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

Code

Python Code

class Solution:
    def lengthOfLIS(self, nums):
        tails = [0] * len(nums)
        size = 0
        for x in nums:
            i, j = 0, size
            while i != j:
                m = (i + j) / 2
                if tails[m] < x:
                    i = m + 1
                else:
                    j = m
            tails[i] = x
            size = max(i + 1, size)
        return size