3) Compare the number of operations and time taken to compute Fibona

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3) Compare the number of operations and time taken to

compute Fibonacci numbers recursively versus that

needed to compute them iteratively.

4) Use the above functions to write a C++ program for

solving each of the following computational problems.

* Find the exact value of f100, f500, and f1000, where fn is

the nth Fibonacci number. What are times taken to find out

the exact values?

* Find the smallest Fibonacci number greater than

1,000,000 and greater than 1,000,000,000.

* Find as many prime Fibonacci numbers as you can. It is

unknown whether there are infinitely many of these. Find

out the times taken to find first 10, 20, 30, 40…up to 200

and draw a graph and see the pattern.

Solution

Desired Program is given, here we can see that time taken

is less then a second and its very fast.

#include<stdio.h>

#include<conio.h>

#include<time.h>

int calSumOfFib(int n)

{

int a,b,c = 0, i,sum =0;

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a=0;

b=1;

sum=1;

for(i=1;i<=n-2;i++)

{

c=a+b;

sum=sum+c;

a=b;

b=c;

}

return sum;

}

int main ()

{

long int fibSum = 0;

double totalTimeTaken;

clock_t t;

t = clock();

fibSum = calSumOfFib(10);

t = clock() - t;

totalTimeTaken = ((double)t)/CLOCKS_PER_SEC;

printf(\"The value of f(10) is %d \ \", fibSum );

printf(\"f(10) takes %f seconds to execute \ \",

totalTimeTaken);

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3) Compare the number of operations and time taken to compute Fibonacci numbers recursively versus that needed to compute them iteratively. 4) Use the above functions to write a C++ program for solving each of the following computational problems. * Find the exact value of f100, f500, and f1000, where fn is the nth Fibonacci number. What are times taken to find out the exact values? * Find the smallest Fibonacci number greater than 1,000,000 and greater than 1,000,000,000. * Find as many prime Fibonacci numbers as you can. It is unknown whether there are infinitely many of these. Find out the times taken to find first 10, 20, 30, 40…up to 200 and draw a graph and see the pattern. Solution Desired Program is given, here we can see that time taken is less then a second and its very fast. #include #include #include int calSumOfFib(int n) { int a,b,c = 0, i,sum ...
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