COMP 271: Design and Analysis of Algorithms
Fall 2007
Assignment 10
Assigned: 29/11/07
Due Date: 6pm, 7/12/09
Question 1
:
Let
m
and
n
be two positive integers. Consider the following bruteforce
algorithm for Fnding the greatest common divider of
m
and
n
:
GCD(
m, n
)
•
let
r
= 1.
•
for (
k
= 1;
k < min
(
m, n
);
k
++
)
–
if
k
divides both
m
and
n
,
r
=
k
.
•
return
r
.
Give a measure for the size of the input to GCD and argue why it is
reasonable. And analyze the complexity of GCD in terms of the input
size. (You can assume that
m
≤
n
≤
am
b
for some positive constants
a
and
b
.)
Question 2
Show that the Subset Sum (
SS
) problem is NPcomplete. You
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This note was uploaded on 10/18/2009 for the course COMP 271 taught by Professor Arya during the Spring '07 term at HKUST.
 Spring '07
 ARYA
 Algorithms

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