Software Engineer

You are given an array “nums” of size N. Your task is to find the length of the longest subsequence of array “nums” such that the absolute difference between every adjacent element in the subsequence is one.

For Example:

If “nums” = {2, 1, 3}.

The valid non-empty subsequences of the array are {2}, {1}, {3}, {2, 1}, {1, 3}, {2, 3} and {2, 1, 3}. So, the longest subsequence satisfying the given conditions are {2, 1} and {2, 3}. The length of the longest subsequence is 2. So, the answer is 2.

The subsequence of an array is a sequence of numbers that can be formed by deleting some or no elements without changing the order of the remaining elements. For example, if the given array “nums” = {1, 2, 5, 4, 8}, then {1, 2, 5, 4, 8}, {1, 5, 8}, {2} are some of the valid subsequences whereas the sequence {4, 2} is not a valid subsequence as the order of the elements differ from the original array.

Note:

Any subsequence of length = 1 is also a valid subsequence.

Ayush is given a number ‘X’. He has been told that he has to find the first ‘X’ terms of the series 3 * ‘N’ + 2, which are not multiples of 4. Help Ayush to find it as he has not been able to answer.

Example: Given an ‘X’ = 4. The output array/list which must be passed to Ayush will be [ 5, 11, 14, 17 ].

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