300 Longest Increasing Subsequence

https://leetcode.com/problems/longest-increasing-subsequence/

solution

• dp

class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        if not nums:
            return 
        
        dp = [1] * len(nums)  # dp[i]: 以nums[i]结尾的最长子序列
        for i in range(1, len(nums)):
            for j in range(i):
                if nums[i] > nums[j]:
                    dp[i] = max(dp[i], dp[j]+1)
        return max(dp)

时间复杂度：O(n^2) 空间复杂度：O(n)

• binary search

class Solution:
    def lengthOfLIS(self, nums: list[int]) -> int:
        tails = []
        for num in nums:
            if not tails or num > tails[-1]:
                tails.append(num)
            else:
                tails[bisect.bisect_left(tails, num)] = num
        return len(tails)

时间复杂度：O(nlog(n)) 空间复杂度：O(n)

follow up

674 Longest Continuous Increasing Subsequence

• 最长连续递增序列，由于要求必须连续，因此只需要dp(i)与dp(i-1)比较即可

646. Maximum Length of Pair Chain