program in python 3 Euclid's Algorithm is an efficient method for getting the greatestcommon divisor (GCD) of two numbers. Given two positiveintegers, a and b, where a > b, the algorithm works as follows:a=qob+rob=qıro+r1ro=q2ri+r2ri=q3r2+r3...... Ik=qk+2rk+1+0The gcd of a and b is rk+1Write a program that computes the GCD of two positivenumbers a and b. The program should handle nonpositive inputby printing "invalid input".

The python code has the following steps: First two numbers a and b are inputted and then both are…

Answered: Write a program that computes the GCD…

Write a program that computes the GCD of two positive numbers a and b. The program should handle nonpositive input by printing "invalid input".

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

Problem 1PE

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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 > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn 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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