Question

In C++, you’ll be generating a program that performs several different functions in two different manners, iterative, and recursive. For the recursive portion of the program, you must use a function to pass data along. The program must be capable of doing the following, and without using the pre-existing mathematical functions for factorial, power, and so on.

1. Given one number, calculate the factorial of that given number. i.e. 7! = 5,040
2. Given one number, and one power, calculate the number raised to that power: i.e. 5 ^ 2 =25.
3. Given two numbers, calculate the GCD. i.e. gcd (14, 21) = 7.

The program will have to calculate these using TWO methods, iterative, and recursive, so display the result as calculated using each method.

1. 9!
2. 14!
3. 6 ^ 12
4. 2 ^ 24
5. gcd (325, 481)
6. gcd (203, 2523)

you may find the Binary GCD and Euclidean algorithms to be useful in guiding your code for the GCD problem.

sample output:

Iterative Factorial 9 : 362880 Recursive Factorial 9 : 362880 Iterative Factorial 14 : 87178291200 Recursive Factorial 14 : 87178291200 Iterative Power 6 12 : 2176782336 Recursive Power 6 12 : 2176782336 Iterative Power 2 ^24 : 16777216 Recursive Power 2 ^24 : 16777216 Iterative GCD (325,481) : 13 Recursive GCD (325,481) : 13 Iterative GCD (203,2523) : 29 Recursive GCD (203,2523) : 29

Answer 1

CODE:

#include<iostream>
using namespace std;
int fact(int num){
   if(num==0)
       return 1;
   return num*fact(num-1);
}
int power(int num,int pow){
   if(pow==0)
       return 1;
   return num*power(num,pow-1);
}
int gcd(int num1,int num2){
   static int res=num2;
   if((num1%res==0)&&(num2%res==0))
       return res;
   res--;
   gcd(num1,num2);
}
int main(){
   int i,num1=12,num2=6,fact1=1,res;
   for(i=num1;i>0;i--)
       fact1*=i;
   cout<<"Iterative Factorial "<<num1<<" : "<<fact1<<endl;
   cout<<"Recursive Factorial "<<num1<<" : "<<fact1<<endl;
   res=num1;
   while((num1%res!=0)||(num2%res!=0))
       res--;
   cout<<"Iterative GCD ("<<num1<<","<<num2<<") : "<<res<<endl;
   cout<<"Recursive GCD ("<<num1<<","<<num2<<") : "<<gcd(num1,num2)<<endl;
   res=1;
   for(i=1;i<=num2;i++)
       res*=num1;
   cout<<"Iterative Power "<<num1<<"^"<<num2<<" : "<<res<<endl;
   cout<<"Recursive Power "<<num1<<"^"<<num2<<" : "<<power(num1,num2)<<endl;
   return 0;
}

OUTPUT:

C:\Program Files (x86)\Dev-Cpp ConsolePauser.exe Iterative Factorial 12 : 479001600 Recursive Factorial 12 : 479001600 Iterative GCD (12,6) : 6 Recursive GCD (12,6) : 6 Iterative Power 12^6 : 2985984 Recursive Power 1246 : 2985984 Process exited normally. Press any key to continue ...