function NaiveGCD(a, b)
Input: a, b (two positive integers)
Output: gcd(a, b) (the greatest common divisor of a and b)
while a ≠ b do
if a > b then
a ( a – b
else
b ( b – a
endif
endwhile
return(a)
end NaïveGCD
function EuclidGCD(a, b)
Input: a, b (two nonnegative integers)
Output: gcd(a, b) (the greatest common divisor of a and b)
while b ≠ 0 do
Remainder ( a mod b
a ( b
b ( Remainder
endwhile
|
~
¤
¦
А
В
2
X
ђ
¬
Ш
т
urn(a)
end EuclidGCD
function BabylonianSQRT(a, error)
Input: a (a positive number), error (a positive real number)
accurate to within error
x ( a
while |x - a/x| > error do
x ( (x + a/x)/2
endwhile
return(x)
end BabylonianSQRT
Computer Science Homework Solutions
#137258
Algorithms
Trace the action of the algorithm NaiveGCD for the following input pairs.
a. (24,108)
b. (23,108)
c. (89,144)
d. (1953,1937)
Exercise 1.8:
Repeat Exercise 1.7 for the algorithm EuclidGCD.
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