Leetcode 300 Longest Increasing Subsequence

Posted 2020-06-30 Fourth Dimension

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

基本DP, dp数组代表当前位置最长序列长度，状态转移方程为 

dp[i] = max(dp[i],dp[j]+1)

class Solution(object):
    def lengthOfLIS(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        if len(nums) == 0:
            return 0
        dp = [1 for x in range(len(nums))]
        ans = 1
        for i in range(1,len(nums)):
            for j in range(i):
                if nums[j] < nums[i]:
                    dp[i] = max(dp[i],dp[j]+1)
            ans = max(ans,dp[i])
        return ans