A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k s an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 23? For each integer n ≥ 1, let s-1 be the number of operations the algorithm executes when it is run with an input of size n. Then so = 7 Therefore, S0, S₁, S₂,... is a geometric sequence ✔✔, which is 2 which equals 29360128 size 23, the number of operations executed by the algorithm is S 22 ✔✔with constant multiplier ✓ and Sk = ✔. So, for every integer n ≥ 0, Sn= 2sk-1 ✓ for each integer k ≥ 1. X. It follows that for an input of
A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k s an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 23? For each integer n ≥ 1, let s-1 be the number of operations the algorithm executes when it is run with an input of size n. Then so = 7 Therefore, S0, S₁, S₂,... is a geometric sequence ✔✔, which is 2 which equals 29360128 size 23, the number of operations executed by the algorithm is S 22 ✔✔with constant multiplier ✓ and Sk = ✔. So, for every integer n ≥ 0, Sn= 2sk-1 ✓ for each integer k ≥ 1. X. It follows that for an input of
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k is an integer that is greater than 1). When the algorithm is
run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 23?
For each integer n ≥ 1, let s - 1 be the number of operations the algorithm executes when it is run with an input of size n. Then so = 7
Therefore, So, S1, S2 ... is a geometric sequence
size 23, the number of operations executed by the algorithm is
with constant multiplier
22
+
, which is 2
which equals 29360128
and Sk
. So, for every integer n ≥ 0, Sn=
=
2S-1
for each integer k ≥ 1.
X. It follows that for an input of
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