Program 5TH in C++

PROBLEM STATEMENT :

WAP TO FIND NTH FIBONACCI NUMBER

METHOD 1 : RECURSIVE METHOD

#include <iostream.h>

#include <cstdio>

#include <unistd.h>

#include <cstdlib>

using namespace std;

//funtion to generate nth fibonacci number

int findF(int n)

{

if (n-1 > 2)

{

return findF(n-1)+findF(n-2);

}

else if(n-1 > 0)

{

return 1;

}

else

{

return 0;

}

}

int main()

{

int position=0;

int val=0;

cout<<"\n\nWhich no in fibonacci series you want to generate : \n\n";

//loop for entering correct value with error checking.

while(true)

{

cout<<"Enter : ";

cin>>position;

if(cin.good() && position > 0)

{

break;

}

else

{

cout<<"\n\n Enter positive integer only\n\n";

cin.clear();

cin.ignore(numeric_limits<streamsize>::max(),'\n');

continue;

}

}

//finding required value;

val=val+findF(position);

cout<<"\n\nThe number at position "<<position<<" in the fibonacci series is : "<<val;

cout<<endl<<endl;

}

METHOD 2 : ITERATIVE METHOD

#include <iostream.h>

#include <cstdio>

#include <unistd.h>

#include <cstdlib>

using namespace std;

int main()

{

int i=1;

int first=0;

int second=1;

int third=1;

int position=1;

cout<<"\n\nEnter the position whose value you want to print in the fibonacci series : \n\n";

//loop to enter integer value with error checking

while(true)

{

cout<<"Enter : ";

cin>>position;

if(cin.good() && position>0)

{

break;

}

else

{

cout<<"\n\nEnter only positive integer \n\n";

cin.clear();

cin.ignore(numeric_limits<streamsize>::max(),'\n');

continue;

}

}

//loop to generate nth fibonacci number

while(i < position-1)

{

third=first+second; //next number is sum of previous two

first=second; //first is set to second

second=third;//second is set to third

i++;

}

cout<<"\n\nThe number at position "<<position << " in the fibonacci series is : " <<third <<endl << endl;

}

METHOD 3 : MATRIX METHOD

#include <iostream.h>

#include <cstdio>

#include <unistd.h>

using namespace std;

void power(int [][2], int);

void multiply(int [][2], int [][2]);

int fib(int n)

{

if(n == 1)

{

return 0;

}

int m[2][2]={{1,1},{1,0}};

power(m,n-2);

return m[0][0];

}

void power(int m[2][2],int n)

{

if( n==1 || n==0)

{

return;

}

int p[][2]={{1,1},{1,0}};

power(m,n/2);

multiply(m,m);

if( n%2 != 0)

{

multiply(m,p);

}

}

void multiply(int m[2][2], int n[2][2])

{

int w=m[0][0]*n[0][0]+m[0][1]*n[1][0];

int x=m[0][0]*n[0][1]+m[0][1]*n[1][1];

int y=m[1][0]*n[0][0]+m[1][1]*n[1][0];

int z=m[1][0]*n[0][1]+m[1][1]*n[1][1];

m[0][0]=w;

m[0][1]=x;

m[1][0]=y;

m[1][1]=z;

}

int main()

{

int position=0;

cout<<"\n\nEnter the position whose value you want to print in the fibonacci series : \n\n";

while(true)

{

cout<<"\n\nEnter : ";

cin>>position;

if(cin.good() && position > 0)

{

break;

}

else

{

cout<<"\n\nEnter only positive integers \n\n";

cin.clear();

cin.ignore(numeric_limits<streamsize>::max(),'\n');

cin.sync();

}

}

int value = fib(position);

cout < <"\n\n The number at position " < <position < <" in the fibonacci series is : " < <value < <endl < <endl;

}