1. Tracing an algorithm means reading it as if you were a computer running the instructions keeping track of values in variables at each iteration of a loop. Trace the following Extended Euclidean Algorithm starting with the initial values of n = 1234 and m = 357. NOTE: The div operator is integer division that gives you a whole number i.e. round down. For example: 25 div 10 = 2. i 0 1 2 3 4 5 6 7 8 9 procedure Extended Euclidean(n, m: positive integers) i:=0 rn 9 0 s_prev = 1 S: 0 t_prev:= 0 t: 1 print i, r, q, s_prev, t_prev r_prev=r r:=m while r>0 i=i+1 q=r_prev div r print i, r, q, s, t temp_r:=r temp_s:=s temp_t:= t r=r_prev-r.q s:=s_prev-s.q t: t_prev-t.q r_prev:= temp_r s_prev:= temp_s t_prev:= temp_t return r, s, t r 9 S t

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
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1. Tracing an algorithm means reading it as if you were a computer running the instructions keeping track of values
in variables at each iteration of a loop. Trace the following Extended Euclidean Algorithm starting with the initial
values of n = 1234 and m = 357. NOTE: The div operator is integer division that gives you a whole number i.e.
round down. For example: 25 div 10 = 2.
i
0
1
2
3
4
5
6
7
8
9
procedure ExtendedEuclidean(n, m: positive integers)
i: 0
r := n
q=0
s_prev = 1
S: 0
t_prev=0
t :=1
print i, r, q, s prev, t_prev
r_prev :=r
r: m
while r> 0
i=i+1
q=r_prev div r
print i, r, q, s, t
temp_r:=r
temp_s:=s
temp_t:= t
r=r_prev-r.q
s=s_prev-s.q
t:= t_prev-t.q
r_prev= temp_r
s_prev := temp_s
t_prev:= temp_t
return r, s, t
9
S
Transcribed Image Text:1. Tracing an algorithm means reading it as if you were a computer running the instructions keeping track of values in variables at each iteration of a loop. Trace the following Extended Euclidean Algorithm starting with the initial values of n = 1234 and m = 357. NOTE: The div operator is integer division that gives you a whole number i.e. round down. For example: 25 div 10 = 2. i 0 1 2 3 4 5 6 7 8 9 procedure ExtendedEuclidean(n, m: positive integers) i: 0 r := n q=0 s_prev = 1 S: 0 t_prev=0 t :=1 print i, r, q, s prev, t_prev r_prev :=r r: m while r> 0 i=i+1 q=r_prev div r print i, r, q, s, t temp_r:=r temp_s:=s temp_t:= t r=r_prev-r.q s=s_prev-s.q t:= t_prev-t.q r_prev= temp_r s_prev := temp_s t_prev:= temp_t return r, s, t 9 S
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