// Fig. 3.14: fig03_14.cpp
// Recursive factorial function
#include <iostream.h>
#include <iomanip.h>
#include <stdlib.h>

long factorial( short );

int main( int argc, char* argv[] ) {
   int tableSize = 1;
   if (argc > 1) tableSize = atoi(argv[1]);

   for ( short i = 0; i <= tableSize; i++ )
      cout << setw( 2 ) << i << "! = " << factorial( i ) << endl;

   return 0;
}

/* definition of factorial:  
for a positive integer n, n! is 1*2*...*n, and 0! is 1.
Thus 4! = 1*2*3*4 = 24.
*/

///// Recursive definition of function factorial

long factorial( short number ) {
   if ( number <= 1 )  // base case
      return 1;
   else                // recursive case
      return number * factorial( number - 1 );
}


///// Another recursive definition of function factorial
long fact2( short n ) {
  return (n <= 1) ? 1 : n*fact2( n - 1 );
}


///// An iterative definition of factorial

long fact3( short n ) {
  long result;

  result = 1;
  for ( short k = n; k > 1; k-- ) {
    result *= k;
  }
  
  return result;
}