Problem 2. 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. 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.

Answered: Write a recurrence for this algorithm…

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

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Problem 2. 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.

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.

Expert Solution

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Worst case: The worst case runtime of an algorithm refers to the maximum amount of time the algorithm can take to solve a problem of size n. It is usually expressed as a function of n, denoted by T(n).

For example, if we have an algorithm for sorting an array of n elements, the worst-case runtime would be the maximum amount of time the algorithm can take to sort an array of size n. This would depend on the specific algorithm and the properties of the input array.

Analyzing the worst-case runtime of an algorithm is important for understanding its performance and scalability. It allows us to predict how the algorithm will perform on larger input and to compare different algorithms for the same problem.

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