Entity-Relationship diagram: Entity-Relationship (ER) diagram is the method to represent the relational database using graphical form. This graphical representation shows only primary elements such as records, types, attributes, relationships between entities, and so on. The graphical representation of the ER diagram clearly describes the relationship among entities. In the diagram, every connector is labeled. On one side it is represented by the value 1, and on the other side it is labeled with the value “M”. This labeling is referred to as “cardinality constraint” of the relationship.

Question

Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)

Answer 1

Question

Chapter 6, Problem 3PE

Program Plan Intro

Entity-Relationship diagram:

Entity-Relationship (ER) diagram is the method to represent the relational database using graphical form.

This graphical representation shows only primary elements such as records, types, attributes, relationships between entities, and so on.

The graphical representation of the ER diagram clearly describes the relationship among entities.

In the diagram, every connector is labeled.

On one side it is represented by the value 1, and on the other side it is labeled with the value “M”. This labeling is referred to as “cardinality constraint” of the relationship.

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Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)

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