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1027. Longest Arithmetic Subsequence

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


Given an array nums of integers, return the length of the longest arithmetic subsequence in nums.

Recall that a subsequence of an array nums is a list nums[i1], nums[i2], ..., nums[ik] with 0 <= i1 < i2 < ... < ik <= nums.length - 1, and that a sequence seq is arithmetic if seq[i+1] - seq[i] are all the same value (for 0 <= i < seq.length - 1).

 

Example 1:

Input: nums = [3,6,9,12]
Output: 4
Explanation: 
The whole array is an arithmetic sequence with steps of length = 3.

Example 2:

Input: nums = [9,4,7,2,10]
Output: 3
Explanation: 
The longest arithmetic subsequence is [4,7,10].

Example 3:

Input: nums = [20,1,15,3,10,5,8]
Output: 4
Explanation: 
The longest arithmetic subsequence is [20,15,10,5].

 

Constraints:

  • 2 <= nums.length <= 1000
  • 0 <= nums[i] <= 500


 

관련자료

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class Solution {
    public int longestArithSeqLength(int[] nums) {
        
        
        int[][] dp = new int[1001][1001];
        
        int n = nums.length;
        int maxLength = 1;
        // 3 6 9 12
        for(int i=1; i<n; i++){
            for(int j=0; j<i; j++){
                int diff = nums[i] - nums[j] + 500; // 500 is a complement from input
                dp[i][diff] = Math.max(dp[i][diff], dp[j][diff] + 1);
                maxLength = Math.max(maxLength, dp[i][diff]);
            }
        }
        
        return maxLength + 1;
    }
}
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