Question

Question 32 (Programming)

The Fibonacci sequence of number is defined as: In this question we examine a property of this sequence.

a) Write a C function definition with header int fib(int [ ] a, int n) which generates an array, a of the first n Fibonacci numbers.

(Hint: You do not have to write this recursively. You just have to generate each array entry from the previous two entries.)

b) Two numbers are said to be coprime if they have no divisors in common. (For example 16 and 81 are coprime numbers). Write a C function definition with header int coprime(int a, int b) which returns 1 (true) if a and b are coprime and 0 (false) otherwise.

c) A property of Fibonacci numbers is that any two consecutive numbers in the sequence are coprime. Write a C program to verify this property. Your program should read an input value N, generate an array of the first N Fibonacci numbers, and then test them to verify that each pair of consecutive numbers is coprime. It should return a message indicating “Success” if that is the case or “Fail” if there is a pair of consecutive numbers which is not coprime.

Question 33 (Programming)

Write a Matlab function definition that takes a parameter n and returns an vector consisting of the first n Fibonacci numbers. (See the previous question for the definition of Fibonacci numbers.

Answer 1

C Program for fibnocci series and coprimes

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#include<stdio.h>

#include<conio.h>

int coprime(int a,int b);

int main()

{

int a=0,b=1,n,i,first=0,second=0,c=0,flag=0;

int fib[100];

printff("Enter number of elements");

scanf("%d",&n);

fib[0]=0;

fib[1]=1;

for(i=2;i<n;i++)

{

c=a+b;

fib[i]=c;

a=b;

b=c;

}

for(i=0;i<(n-1);i++)

{

first=fib[i];

second=fib[i+1]

flag=coprime(first,second);

if(flag==1)

printf("Success");

else

printf("Fail");

}

}

int coprime(int a,int b)

{

int temp;

while(1)

{

temp=a%b;

if(temp==0)

return b;

a=b;

b=temp;

}

}

Matlab program for fibonacci series

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create a function named as fibonacci:

function[result]=fibonacci(i);

if n==0||n==1
    result = n;

else
    result = fibonacci(n-2)+fibonacci(n-1);
end
end

Write the code to your command window:

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for n = 0:10
   fprintf('Fibonacci(%d)= %d\n', n, fibonacci(n));
end