Need help with Question #2.Question #1 has been provided to you for sample reference along with the work. 1. Suppose a recursive algorithm performs 2 recursive calls. Assume the first recursive call isof size at most 70% the original input size, and the second call is of size at most 25% of theoriginal input size. In addition, the algorithm performs O(n) additional work after makingthese recursive calls. What is the big-Oh run time of this algorithm?SoltSuppose total recursive call is l00% ie 'n' timesSo, maximum height of Hhe tree is:firet Call recursive sige atmost toy. (-e 3n'1Second recursive call size atmost ie 'n':(총)"So, re cuTrcnce relation i'!take 'log'both sidy,we getonT(n) = 3T(2) +T(4)log nK%3DAddlitionaltimeusing tree methed t→ o(n)S, Maximum number of level isandeach leveltake time of oln)6o, to tal time Compleuty isocn)3n→ o(n)K' stepsals. 2. Suppose the above algorithm performs a recursive call of size 75% for the first recursive call,with everything else remaining the same. What is the big-Oh run time for this algorithmnow?

Answered: 2. Suppose the above algorithm performs…

2. Suppose the above algorithm performs a recursive call of size 75% for the first recursive call, with everything else remaining the same. What is the big-Oh run time for this algorithm now?

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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Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

Question

Need help with Question #2.

Question #1 has been provided to you for sample reference along with the work.

1. Suppose a recursive algorithm performs 2 recursive calls. Assume the first recursive call is
of size at most 70% the original input size, and the second call is of size at most 25% of the
original input size. In addition, the algorithm performs O(n) additional work after making
these recursive calls. What is the big-Oh run time of this algorithm?
Solt
Suppose total recursive call is l00% ie 'n' times
So, maximum height of Hhe tree is:
firet Call recursive sige atmost toy. (-e 3n'
1
Second recursive call size atmost ie 'n'
:(총)"
So, re cuTrcnce relation i'!
take 'log'
both sidy,we get
on
T(n) = 3T
(2) +
T(4)
log n
K
%3D
Addlitional
time
using tree methed t
→ o(n)
S, Maximum number of level is
and
each level
take time of oln)
6o, to tal time Compleuty is
ocn)
3n
→ o(n)
K' steps
als.

2. Suppose the above algorithm performs a recursive call of size 75% for the first recursive call,
with everything else remaining the same. What is the big-Oh run time for this algorithm
now?

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