Help me solve computer science algorithm problems

I need someone who can provide me algorithm problem solution in the given format, it will be time bounded, for e.g. after asking the problem I need solution within 1 hour, I need you to do this 3 times on specific days and time, so this is at most 3 hours of work in total

A problem could look like below

A sequence S= [S1, S2, ...,Sn] is said to be nicely spaced if every two adjacent elements differ by at most 5. More precisely. S is nicely spaced if Isi - si+1| <= 5 for all 1 <=i<=n-1

Example: S [2,0,-1,0,0] is nicely spaced while S= [3510, 6515,3511] is not Design a Dynamic Programming to solve the following

problem: Input: a sequence S] of integers.

Output: the length of the longest nicely spaced subsequence of S.

Example: for input S (1,0, 10, 5, 10, 3) the answer is 4, since [1,0,-5,-3] is the longest nicely spaced subsequence.

Please answer the following parts:

1. Define the entries of your table in words. E.g. T() or T(i, j) is...

2. State a recurrence for the entries of your table in

terms of smaller subproblems. Don't forget your base

case(s).

3. Write pseudocode for your algorithm to solve this problem.

4. State and analyze the running time of your algorithm.