JAVA SOLUTION BEATS 100%
IntuitionApproachThe recursive approach involves:Recursively generating all possible subsequences of the given array.For each subsequence, we check if the absol
# Intuition
<!-- Describe your first thoughts on how to solve this problem. --> The initial thought is to consider finding subsequences with non-increasing absolute differences between consecutive elements. We can do this by exploring all possible subsequences and validating each one to see if it satisfies the condition.

# Approach
<!-- Describe your approach to solving the problem. -->
The recursive approach involves:

Recursively generating all possible subsequences of the given array.

For each subsequence, we check if the absolute differences between consecutive elements form a non-increasing sequence.

Track the maximum length of such valid subsequences.

However, this approach can lead to time limit exceeded (TLE) errors due to its exponential time complexity.

The dynamic programming approach involves:

Using a 2D array dp where dp[num][diff] keeps track of the longest subsequence ending with num and having absolute difference diff with the previous element.

Iterating from the end of the array to the start, updating dp based on current and next elements.

Finally, finding the maximum value in the dp array representing the length of the longest valid subsequence.

# Code
```java []
// class Solution {
//     int ans = 0;
//     public int longestSubsequence(int[] nums) {
//         rec(nums, 0, new ArrayList<>());
//         return ans;
//     }

//     void rec(int[] arr, int idx, List<Integer> ls){
//         if(idx==arr.length){
//             int current = Integer.MAX_VALUE;
//             for(int i=1; i<ls.size(); i++){
//                 if(current<Math.abs(ls.get(i)-ls.get(i-1))) return;
//                 else current = Math.abs(ls.get(i)-ls.get(i-1));
//             }
//             ans = Math.max(ans, ls.size());
//             return;
//         }

//         ls.add(arr[idx]);
//         rec(arr, idx+1, ls);
//         ls.remove(ls.size()-1);
//         rec(arr, idx+1, ls);
//     }
// }

class Solution {
    public int longestSubsequence(int[] nums) {
         // Create a 2D array for dynamic programming
        int[][] dp = new int[302][302];
        
        // Iterate through the array from right to left
        for (int i = nums.length - 1; i >= 0; --i) {
            int num = nums[i];
            
            // For each possible next number
            for (int next = 1; next <= 300; ++next) {
                int diff = Math.abs(next - num);
                dp[num][diff] = Math.max(dp[num][diff], dp[next][diff] + 1);
            }
            
            // Update dp values for current number
            for (int j = 1; j <= 300; ++j) {
                dp[num][j] = Math.max(dp[num][j], dp[num][j - 1]);
            }
        }
        
        // Find the maximum value in dp array
        int ans = Integer.MIN_VALUE;
        for (int i = 0; i <= 301; ++i) {
            for (int j = 0; j <= 301; ++j) {
                ans = Math.max(ans, dp[i][j]);
            }
        }
        
        return ans;
    }
}
```
['Dynamic Programming', 'Recursion', 'Java']