Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Matlab Help Problem W1.4 (Bzout's identity and certifying Euclidean algorithm). An algorithm is called certifying when it can check whether the output is correct or

image text in transcribedMatlab Help

Problem W1.4 (Bzout's identity and certifying Euclidean algorithm). An algorithm is called certifying when it can check whether the output is correct or not. For ex- ample, the highest common factor h of two integers n and m, not simultaneously 0, is characterised by being a divisor of both and writable in the form h=sm+tn for some stez. (W1.4.1) The latter is called Bzout's identity. The extended Euclidean algorithm provides a construction of such coefficients set as follows Require: m,n two integers with n=0 Ensure: r,s,t integers such that r=hcf{m, n} and sm+tn=r (Bzout) 1: procedure EXTENDED-EUCLID(m,n) r-1 m, ron , k- 1 while re #0 do answer is reached when rk = 0 (9k, rk) - div{rk-2, Pk-1) (sk, tk) - (Sk-1, tk-1)-9(Sk-2, tk-2) krk+1 7: end while 8: return Ik-1 phcf is the last non-zero remainder 9: end procedure Write a code that inputs two integers m, n, not simultaneously zero, and outputs three integers r, s, t such that r=hcf{m, n} and h=sm+tn. [40 marks] i Problem W1.4 (Bzout's identity and certifying Euclidean algorithm). An algorithm is called certifying when it can check whether the output is correct or not. For ex- ample, the highest common factor h of two integers n and m, not simultaneously 0, is characterised by being a divisor of both and writable in the form h=sm+tn for some stez. (W1.4.1) The latter is called Bzout's identity. The extended Euclidean algorithm provides a construction of such coefficients set as follows Require: m,n two integers with n=0 Ensure: r,s,t integers such that r=hcf{m, n} and sm+tn=r (Bzout) 1: procedure EXTENDED-EUCLID(m,n) r-1 m, ron , k- 1 while re #0 do answer is reached when rk = 0 (9k, rk) - div{rk-2, Pk-1) (sk, tk) - (Sk-1, tk-1)-9(Sk-2, tk-2) krk+1 7: end while 8: return Ik-1 phcf is the last non-zero remainder 9: end procedure Write a code that inputs two integers m, n, not simultaneously zero, and outputs three integers r, s, t such that r=hcf{m, n} and h=sm+tn. [40 marks]

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Professional SQL Server 2012 Internals And Troubleshooting

Authors: Christian Bolton, Justin Langford

1st Edition

1118177657, 9781118177655

More Books

Students also viewed these Databases questions

Question

Explain the focus of safety programs.

Answered: 1 week ago