LeetCode 3409: Longest Subsequence With Decreasing Adjacent Difference Solution

Master LeetCode problem 3409 (Longest Subsequence With Decreasing Adjacent Difference), 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.

3409. Longest Subsequence With Decreasing Adjacent Difference

Medium

Array Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We will create a dp array where dp[i] represents the length of the longest subsequence ending at index i. For each index i, we iterate over all previous indices j (0 <= j < i) and update dp[i] to be the maximum of dp[i] and dp[j] + 1 if the absolute difference between nums[i] and nums[j] is less than or equal to the absolute difference between nums[j] and the last element in the subsequence ending at index j.

Finally, we return the maximum value in the dp array as the length of the longest subsequence with decreasing adjacent difference.

Time complexity: O(n^2) where n is the number of elements in the input array nums.
Space complexity: O(n) for the dp array.

Solution Code

class Solution {
    public int longestSubsequence(int[] nums) {
        int n = nums.length;
        int[] dp = new int[n];
        Arrays.fill(dp, 1);
        
        int maxLen = 1;
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < i; j++) {
                if (Math.abs(nums[i] - nums[j]) <= Math.abs(nums[j] - nums[i - 1])) {
                    dp[i] = Math.max(dp[i], dp[j] + 1);
                }
            }
            maxLen = Math.max(maxLen, dp[i]);
        }
        
        return maxLen;
    }
}

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