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A sequence of integers A = { a _ 1 , a _ 2 , ldots , a _ n } is
A sequence of integers Aa aldots an is said to be bumpy when the signs of the differences between two consecutive terms in the sequence strictly alternate between and values. A difference of zero can never be part of a bumpy sequence. So the sequence either follows a a a aldots or it follows a a a aldots
An example of a bumpy sequence is On the other hand, the sequence is not bumpy because the differences between the three consecutive elements do not alternate. Two s also show up at the end of the sequence causing the consecutive difference to be zero.
You are given a sequence of integers Aa aldots an Your task is to find the length of the longest bumpy subsequence in A Design a dynamic programming algorithm to solve this problem.
Please answer the following parts in Fastest Possible Method.
Define the entries of your table in words. Do it in Ti or Ti j format
State a recurrence for the entries of your table in terms of smaller subproblems.
State the base cases
Write pseudocode for your algorithm to solve this problem.
State and analyze the running time of your algorithm in Big O Notation.
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