leetcode-300 - Longest Increasing Subsequence

動機

我們不要dp了，jojo

Problem

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: 4Explanation: 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?

Sol

讓可能的解在符合順序的情況下，數字越小越好 詳細看Longest Increasing Subsequence

class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        lis = [nums[0]]
        for n in nums[1:]:
            if lis[-1] < n:
                lis.append(n)
            else:
                lis[bisect_left(lis,n)] = n
        return len(lis)