### Understanding Palindromes and Nearly-PalindromesA **palindrome** is a sequence that reads the same forwards and backwards. For example, the word **"RACECAR"** is a palindrome.For this problem, we introduce the concept of an **almost palindrome**. An almost palindrome is a sequence that can be transformed into its reverse with 2 or fewer character additions, deletions, replacements, or swaps. A character swap involves swapping two adjacent characters.#### Examples:- **"MARJORAM"** can be reversed by swapping the 'J' and the 'O'.- **"FOOLPROOF"** can be reversed by replacing 'R' with 'L' and vice versa.- The word **"BONOBO"** can be reversed by deleting the final 'O' and reinserting it at the beginning.---### Dynamic Programming AlgorithmThe goal is to devise a dynamic programming algorithm to determine the number of edits necessary to transform a sequence into its reverse. Here are the steps:1. **State the Problem with Formal Input and Output Conditions.**2. **State a Self-Reduction for This Problem.**3. **Develop a Dynamic Programming Algorithm Based on the Self-Reduction.**4. **Determine the Minimum Number of Edits for Given Sequences Using the Algorithm.**#### a) Problem Statement**Input:** A string `S` of length `n`.**Output:** The minimum number of edits (additions, deletions, replacements, swaps) required to transform `S` into its reverse, and whether it qualifies as an almost palindrome.#### b) Self-Reduction- **Base Case:** If the length of `S` is 0 or 1, `S` is already a palindrome, so the required edits are 0.- **Recursive Case:** - If the first and last characters of `S` are the same, the problem reduces to the same problem on the substring `S[1:-1]`. - Otherwise, consider the following possible edits: - Replace the first character with the last character, or vice versa. - Delete the first character or the last character. - Swap the first two characters, then solve the subproblem for `S[2:]`.#### c) Dynamic Programming AlgorithmLet `dp[i][j]` represent the minimum number of edits required to transform the substring `S[i:j+1

dp[i, j] — minimum number of operations to convert substring s[i..j] into palindrome. Below are the…

A palindrome is a sequence that is the same as its reverse. For example, the word "RACECAR" is a palindrome. For this problem we will define an almost palindrome to be a sequence that can be transformed into its reverse with 2 or fewer character additions, deletions, replacements, or swaps. A character swap swaps two adjacent characters. For instance "MARJORAM" can be reversed by swapping the 'J' and the 'O'. In addition, "FOOLPROOF" can be reversed by replacing the 'R' with and 'L' and vice versa. Finally, the word "BONOBO" can be reversed by deleting the final 'O' and reinserting it at the beginning. Devise a dynamic programming algorithm that will determine the number of edits necessary to to transform a sequence into its reverse. a) State this problem with formal input and output conditions. b) State a self-reduction for this problem. c) State a dynamic programming algorithm based off of your self-reduction that computes the minimum number of edits to transform a sequence into its reverse. d) Use your algorithm to determine the minimum number of edits to transform "MARJORAM", "FOOLPROOF" and "BONOBO" into their reverses. Show your work.

A palindrome is a sequence that is the same as its reverse. For example, the word "RACECAR" is a palindrome. For this problem we will define an almost palindrome to be a sequence that can be transformed into its reverse with 2 or fewer character additions, deletions, replacements, or swaps. A character swap swaps two adjacent characters. For instance "MARJORAM" can be reversed by swapping the 'J' and the 'O'. In addition, "FOOLPROOF" can be reversed by replacing the 'R' with and 'L' and vice versa. Finally, the word "BONOBO" can be reversed by deleting the final 'O' and reinserting it at the beginning. Devise a dynamic programming algorithm that will determine the number of edits necessary to to transform a sequence into its reverse. a) State this problem with formal input and output conditions. b) State a self-reduction for this problem. c) State a dynamic programming algorithm based off of your self-reduction that computes the minimum number of edits to transform a sequence into its reverse. d) Use your algorithm to determine the minimum number of edits to transform "MARJORAM", "FOOLPROOF" and "BONOBO" into their reverses. Show your work.

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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