Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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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.
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Transcribed Image Text: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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Transcribed Image Text: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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