Answered: A subsequence of a sequence is obtained…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

A subsequence of a sequence is obtained by deleting zero or more values in the sequence. For example, acdfh is a subsequence of abcdefghi. The order must be preserved.

The longest common subsequence problem takes two strings as input and outputs the length of the longest string that is a subsequence of both input strings.

Describe an efficient dynamic programming algorithm for the longest common subsequence problem. Start by writing recursive equations using the shop around principle. Concentrate on the last values in the input strings. If they are the same, keep them and look for a longest common subsequence of the two strings with their last characters removed. If the last two characters are different, you can only keep one of them. Try keeping one, and throwing the other one away. Then keep the other one. Take a maximum, since you are looking for a longest common subsequence. Then implement the equations using memoization.

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