/*

Module: twoton.c

Author: Yana

What:

-----

This program computes 2^n in four recursive ways.

Input: an integer n.

Output: 2^n.

How:

----

Algorithm: Four recursive algorithms - See functions.

notice the different complexity of the 4 versions.

*/

#include<stdio.h>

int Version1(int n);

int Version2(int n);

int Version3(int n);

int Version4(int n);

int main(){

int n; /* input number. */
printf( "Enter a number: ") ;
scanf("%d", &n);
printf("Version 1 = %d, Version 2 = %d, Version 3 = %d, Version 4 = %d\n", Version1(n), Version2(n), Version3(n), Version4(n));

return 0;

}

/* Algorithm: 2^n = 2^(n-1) + 2^(n-1) */

int Version1(int n){

if (n == 0)
return 1;
else
return (Version1(n-1) + Version1(n-1));

}

/* Algorithm: 2^n = 2 * 2^(n-1). */

int Version2(int n){

if (n == 0)
return 1;
else
return 2*Version2(n-1);

}

/* Algorithm: 2^n = 2^(n/2) * 2^(n/2) if n is even.

2^n = 2 * 2^(n/2) * 2^(n/2) if n is odd. */

int Version3(int n){

int result; /* result up to a factor of two. */

if (n == 0)
return 1;
result = Version3(n/2) * Version3(n/2);
if (n % 2 == 0)
return result;
else
return 2*result;

}

/* Algorithm: 2^n = (2^(n/2))^2 if n is even.

2^n = 2*(2^(n/2))^2 if n is odd. */

int Version4(int n){

int temp; /* almost sqrt of result. */

if (n == 0)
return 1;
temp = Version4(n/2);
if (n % 2 == 0)
return temp * temp;
else
return 2 * temp * temp;

}