Given two strings S of length n and T of length m, we want to reconstruct T from S with a minimum number of the following operations: i) delete a character from S, ii) insert a character into S, or iii) swap two consecutive characters in S. For example, when S = yorkun and T = ayokru, one can insert an 'a' at index 1 of S, swap 'r' and 'k' in S, and remove 'n' from the end of S. Therefore, we can reconstruct T from S with 3 operations. Devise a DP solution to report the minimum number of operations to reconfigure S to T. The actual operations in a minimum-cost reconfiguration are not needed. It suffices to show Steps 1 and 2 in the DP paradigm in your solution. In Step 1, you must specify the subproblems, and how the value of the optimal solutions for smaller subproblems can be used to describe those of large subproblems. In Step 2, you must write down a recursive formula for the minimum number of operations to reconfigure. Assume indices start at 1.

Given two strings S of length n and T of length m, we want to reconstruct T from S with a minimum number of the following operations: i) delete a character from S, ii) insert a character into S, or iii) swap two consecutive characters in S. For example, when S = yorkun and T = ayokru, one can insert an 'a' at index 1 of S, swap 'r' and 'k' in S, and remove 'n' from the end of S. Therefore, we can reconstruct T from S with 3 operations. Devise a DP solution to report the minimum number of operations to reconfigure S to T. The actual operations in a minimum-cost reconfiguration are not needed. It suffices to show Steps 1 and 2 in the DP paradigm in your solution. In Step 1, you must specify the subproblems, and how the value of the optimal solutions for smaller subproblems can be used to describe those of large subproblems. In Step 2, you must write down a recursive formula for the minimum number of operations to reconfigure. Assume indices start at 1.

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

Given two strings S of length n and T of length m, we want to reconstruct T from S with
a minimum number of the following operations: i) delete a character from S, ii) insert a
character into S, or iii) swap two consecutive characters in S. For example, when S = yorkun
and T = ayokru, one can insert an 'a' at index 1 of S, swap 'r' and 'k' in S, and remove 'n'
from the end of S. Therefore, we can reconstruct T from S with 3 operations.
Devise a DP solution to report the minimum number of operations to reconfigure S to
T. The actual operations in a minimum-cost reconfiguration are not needed. It suffices to
show Steps 1 and 2 in the DP paradigm in your solution. In Step 1, you must specify the
subproblems, and how the value of the optimal solutions for smaller subproblems can be
used to describe those of large subproblems. In Step 2, you must write down a recursive
formula for the minimum number of operations to reconfigure. Assume indices start at 1.

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