1027. Longest Arithmetic Subsequence

Problem

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

Solution (Java)

class Solution {
    public int longestArithSeqLength(int[] nums) {
        int max = maxElement(nums);
        int min = minElement(nums);
        int diff = max - min;
        int n = nums.length;
        int[][] dp = new int[n][2 * diff + 2];
        for (int[] d : dp) {
            Arrays.fill(d, 1);
        }
        int ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i - 1; j >= 0; j--) {
                int difference = nums[i] - nums[j] + diff;
                int temp = dp[j][difference];
                dp[i][difference] = Math.max(dp[i][difference], temp + 1);
                if (ans < dp[i][difference]) {
                    ans = dp[i][difference];
                }
            }
        }
        return ans;
    }

    private int maxElement(int[] arr) {
        int max = Integer.MIN_VALUE;
        for (Integer e : arr) {
            if (max < e) {
                max = e;
            }
        }
        return max;
    }

    private int minElement(int[] arr) {
        int min = Integer.MAX_VALUE;
        for (Integer e : arr) {
            if (min > e) {
                min = e;
            }
        }
        return min;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).