Consider the algorithm below for checking whether a string represented in an array A of ncharacters is a palindrome. A palindrome is defined as a word that is spelled the same forward and backward(e.g. rotor, kayak).CHECK-PALINDROME (A[1: n]):1. If n = 0 or n 1, return True.2. Otherwise, if A[1] = A[n] and CHECK-PALINDROME(A[2: n-1]) returns True, return True.3. Return False.We analyze CHECK-PALINDROME in this question.(a) Use induction to prove the correctness of this algorithm. Write a recurrence for this algorithm and solve it to obtain a tight upper bound on the worst caseruntime of this algorithm. You can use any method you like for solving this recurrence.

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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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Consider the algorithm below for checking whether a string represented in an array A of n
characters is a palindrome. A palindrome is defined as a word that is spelled the same forward and backward
(e.g. rotor, kayak).
CHECK-PALINDROME (A[1: n]):
1. If n = 0 or n 1, return True.
2. Otherwise, if A[1] = A[n] and CHECK-PALINDROME(A[2: n-1]) returns True, return True.
3. Return False.
We analyze CHECK-PALINDROME in this question.
(a) Use induction to prove the correctness of this algorithm.

Write a recurrence for this algorithm and solve it to obtain a tight upper bound on the worst case
runtime of this algorithm. You can use any method you like for solving this recurrence.

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Step 1

Introduction

Palindrome:

A word, phrase, statistic, or string of characters that reads the same backward as it does forwards is called a palindrome. In other words, it's a string that is true whether it is read left or right. Palindromes can be applied with numbers or any string of characters and are not just restricted to words or phrases. Palindromic words include some well-known instances such as "level," "deified," "racecar," and "rotor." Palindromes have long piqued people's interest and have been included in writing, poetry, and brain teasers. They act as a benchmark for measuring performance and algorithm optimization in computer science.

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