What do these algorithms compute?
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Question # 2
Consider the following three different algorithms that solve the same problem:
a) What do these algorithms compute?
b) What are their pre-condition and post condition?
c) Clearly define your loop invariant for the given algorithms.
d) Prove correctness of above algorithms by showing initialization, maintenance and termination. For
Algorithm-3, c>2
ALGORITHM-1 secret1(y, z)
// Input:,
// Output:
ALGORITHM-2 secret2(y, z)
// Input:
// Output:
while z> 0 do
while z> 0 do
if z% 2 = 1 then
x+x+y*( z% 2)
ye 2*y
ze [:/2]
x+x+y
end if
ye 2*y
ze L:/2]
end while
return
end while
return x
ALGORITHM-3 secret3(y, z)
// Input:
// Output:
x+0
while z> 0 do
x+x+y*( z% c)
ye c*y
end while
return x
Ouestion # 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18a82450-8f76-42cc-b3fe-5a98b65d7393%2F73a9bb6a-cc75-4aa0-860c-33f263e1c59d%2Fbhqaynk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question # 2
Consider the following three different algorithms that solve the same problem:
a) What do these algorithms compute?
b) What are their pre-condition and post condition?
c) Clearly define your loop invariant for the given algorithms.
d) Prove correctness of above algorithms by showing initialization, maintenance and termination. For
Algorithm-3, c>2
ALGORITHM-1 secret1(y, z)
// Input:,
// Output:
ALGORITHM-2 secret2(y, z)
// Input:
// Output:
while z> 0 do
while z> 0 do
if z% 2 = 1 then
x+x+y*( z% 2)
ye 2*y
ze [:/2]
x+x+y
end if
ye 2*y
ze L:/2]
end while
return
end while
return x
ALGORITHM-3 secret3(y, z)
// Input:
// Output:
x+0
while z> 0 do
x+x+y*( z% c)
ye c*y
end while
return x
Ouestion # 3
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