Consider the following algorithm segment.For each positive integer n, let bn be the number of iterations of the following while loop.while (n > 0)n := n div(3)end whileFind a recurrence relation for bⒸTo answer this question, observe that for each integer k ≥ 3, n div(3) = Lk/3]Thus, when the algorithm segment is run for a particular k and the while loop has iterated one time, the input to the next iteration is [k/3]It follows that the number of iterations of the loop for k is 1✔✔ more than the number of iterations for [k/3]In other words, for every integer k ≥ 1, we have which of the following?bk = 1 + bklo b₁ = 1 + bk/3Lk/3]bk = 1 + b[k/31bk = 3 + bk/3b₁ = 3 + blk/31bk = 3 + bDIK/31In addition, the initial values for the sequence b₁,b₂, bz₁are b₁ = 1and b₂ = 1©

Recurrence relation is used to define a function by means of expression which includes one or more…

Consider the following algorithm segment. For each positive integer n, let b be the number of iterations of the following while loop. while (n > 0) n := n div(3) end while Find a recurrence relation for b

Consider the following algorithm segment. For each positive integer n, let b be the number of iterations of the following while loop. while (n > 0) n := n div(3) end while Find a recurrence relation for b

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

Consider the following algorithm segment.
For each positive integer n, let bn be the number of iterations of the following while loop.
while (n > 0)
n := n div(3)
end while
Find a recurrence relation for b
Ⓒ
To answer this question, observe that for each integer k ≥ 3, n div(3) = Lk/3]
Thus, when the algorithm segment is run for a particular k and the while loop has iterated one time, the input to the next iteration is [k/3]
It follows that the number of iterations of the loop for k is 1✔✔ more than the number of iterations for [k/3]
In other words, for every integer k ≥ 1
, we have which of the following?
bk = 1 + bkl
o b₁ = 1 + b
k/3
Lk/3]
bk = 1 + b[k/31
bk = 3 + bk/3
b₁ = 3 + blk/31
bk = 3 + b
DIK/31
In addition, the initial values for the sequence b₁,b₂, bz₁
are b₁ = 1
and b₂ = 1
©

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