4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj) such that A[x] = x; otherwise, returns false. You may assume A is a sorted integer array in which every element is unique. a. Write an efficient recursive algorithm for IndexEqual(A,i.j). b. What is the situation resulting in the best-case running time of your function, and give an expression for that running time? c. What is the situation resulting in the worst-case running time of your function, and give an expression for that running time in terms of n, where n=j-i+1?

4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj) such that A[x] = x; otherwise, returns false. You may assume A is a sorted integer array in which every element is unique. a. Write an efficient recursive algorithm for IndexEqual(A,i.j). b. What is the situation resulting in the best-case running time of your function, and give an expression for that running time? c. What is the situation resulting in the worst-case running time of your function, and give an expression for that running time in terms of n, where n=j-i+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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Concept explainers

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj)
such that A[x] = x; otherwise, retums false. You may assume A is a sorted integer array in
which every element is unique.
a. Write an efficient recursive algorithm for IndexEqual(A,i.j).
b. What is the situation resulting in the best-case running time of your function, and give
an expression for that running time?
c. What is the situation resulting in the worst-case running time of your function, and give
an expression for that running time in terms of n, where n=j-i+1?

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