Leetcode** 300. Longest Increasing Subsequence

Description: 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].

Link: 300. Longest Increasing Subsequence

Examples:

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

思路: 这是一道动态规划题目。dp[i]表示到第i个元素，的最长递增子序列。dp[0] = 1; dp[i] = max{dp[j]+1} if nums[j] < nums[i] and j < i，否则dp[i] = 1.找到i前面以小于nums[i]结尾的最长子序列，它可以和nums[i]构成新的最长子序列，更新dp,如果i前面没有比它小的，那么dp[i] = 1。

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

日期: 2021-04-16 又周五了，我还没干啥呢，快快进步吧