LeetCode 1027: Longest Arithmetic Subsequence Solution

Master LeetCode problem 1027 (Longest Arithmetic Subsequence), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1027. Longest Arithmetic Subsequence

Medium

Array Hash Table Binary Search Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We will create a 2D dp array where dp[i][diff] represents the length of the longest arithmetic subsequence ending at index i with a common difference of diff. We iterate through each pair of elements (nums[i] and nums[j], where j < i) and update the dp array accordingly. Finally, we return the maximum value in the dp array as the result.

Algorithm:

Initialize a 2D dp array of size nums.length x nums.length with all values set to 2 (since we have at least two elements in any subsequence).
Initialize a variable maxLength to store the result.
Iterate over each pair of elements (nums[i] and nums[j]) where j < i:
- Calculate the common difference diff = nums[i] - nums[j].
- Update dp[i][diff] = max(dp[i][diff], dp[j][diff] + 1).
- Update maxLength = max(maxLength, dp[i][diff]).
Return maxLength as the final result.

Time Complexity: O(n^2), where n is the length of the input array nums. Space Complexity: O(n^2), for the 2D dp array.

Solution Code

class Solution {
    public int longestArithSeqLength(int[] nums) {
        int n = nums.length;
        int[][] dp = new int[n][n];
        int maxLength = 2;
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
                int diff = nums[i] - nums[j];
                dp[i][diff] = Math.max(dp[i][diff], dp[j][diff] + 1);
                maxLength = Math.max(maxLength, dp[i][diff]);
            }
        }
        
        return maxLength;
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 1027 (Longest Arithmetic Subsequence)?

This page provides optimized solutions for LeetCode problem 1027 (Longest Arithmetic Subsequence) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 1027 (Longest Arithmetic Subsequence)?

The time complexity for LeetCode 1027 (Longest Arithmetic Subsequence) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 1027 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 1027 in Java, C++, or Python.

Back to LeetCode Solutions