leetcode 300. Longest Increasing Subsequence

Posted 2022-09-12 qinduanyinghua

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

Example:

Input: [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. 

Note:

• 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?

 

分析：求解数组最长递增子序列（严格递增）.

思路一：动态规划，时间复杂度：O(n²)。dp[i]表示以下标为i的数字为结尾的最长递增子序列长度。

 1 class Solution 
 2 public:
 3     int lengthOfLIS(vector<int>& nums) 
 4         int len = nums.size();
 5         vector<int> dp(len, 0);
 6         int maxn = 0;
 7         for (int i = 0; i < len; i++) 
 8             dp[i] = 1;
 9             for (int j = 0; j < i; j++) 
10                 if (nums[i] > nums[j])
11                     dp[i] = max(dp[i], dp[j] + 1);
12             
13             maxn = max(maxn, dp[i]);
14         
15         return maxn;
16     
17 ;

思路二：动归+二分