The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b) Require: a, b > 0 Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end while return a We want to prove the correctness of this algorithm using the loop invariant technique. Answer the following questions: a. Show the property is maintained during the execuation of the While loop (i.e., maintenance property). b. Prove the termination property and conclude. c. What would happen if a > 0 and b = 0 and thus the pre-condition is not satisfied?
The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b) Require: a, b > 0 Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end while return a We want to prove the correctness of this algorithm using the loop invariant technique. Answer the following questions: a. Show the property is maintained during the execuation of the While loop (i.e., maintenance property). b. Prove the termination property and conclude. c. What would happen if a > 0 and b = 0 and thus the pre-condition is not satisfied?
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The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm.
Algorithm 1 Euclid1(a,b)
Require: a, b > 0
Ensure: a = GCD(a, b)
while a ̸= b do
if a > b then
a ← a − b
else
b ← b − a
end if
end while
return a
We want to prove the correctness of this algorithm using the loop invariant technique. Answer the following questions:
a. Show the property is maintained during the execuation of the While loop (i.e., maintenance property).
b. Prove the termination property and conclude.
c. What would happen if a > 0 and b = 0 and thus the pre-condition is not satisfied?
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