300. Longest Increasing Subsequence

难度: Medium

题目描述

Given an integer array nums, return the length of the longest strictly increasing subsequence.

 

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

 

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?

解题思路

代码实现

解决方案

java

class Solution {
    public int lengthOfLIS(int[] nums) {

        int n = nums.length;
        int[] dp = new int[n];
        dp[0] = 1;
        int maxLength = 1;
        for (int i = 1; i < n; i++) {
            int max = 0;
            for (int j = i - 1; j > -1; j--) {
                if (nums[j] < nums[i] && dp[j] > max) {
                    max = dp[j];
                }

            }
            dp[i] = max + 1;
            maxLength = Math.max(maxLength, dp[i]);
        }
        return maxLength;

    }
}