This week in lab they will be writing a few short recursive programs.

Write a recursive function that returns the number of digits in a
nonnegative integer.  For example, it should return 4 if passes the
integer 1126 and should return 1 if passed the integer 0.  It should
take the form: 
		int num_digits(int num);

Write a recursive function that computes x raised to the power n.  You
only need to deal with nonnegative exponents.  Thus you can just print
out an error message if a negative exponent is passed.  Remember that
anything raised to the power of 0 is 1.  The function should be of the
form:  
		double power(double x, int n);

Write a recursive function that prints the digits in an integer in
reverse order.  For example, if passed the integer 1234, it should
print "4321".  (Hint: use the / and % operations)  This function
should take the form: 
		void print_rev(int num);

Write a recursive function that prints the equivalent number using a
different base.  It should be passed an decimal integer (base 10) and
should be passed the new base.  This is calculated by the following
approach:

        0   Remainder 1
        _
      2|1   Remainder 1
        _
      2|3   Remainder 0   
        _
      2|6   Remainder 1
       __
     2|13   Remainder 0
       __
     2|26

Thus, 26 = 11010(base 2).  The function should take the form:
		void convert_base(int num, int base);





Check off the first two in lab and have them turn the other 2 in next
week.  The following is a sample solution
------------------------------------------------------
#include <iostream.h>

int num_digits(int num)
{
  if(num > 10)
    return num_digits(num/10) + 1;
  else
    return 1;
}

double power(double x, int n)
{
  if (n == 0)
    return 1.0;
  else if (n > 0)
    return power(x, n-1) * x;
  else
  {
    cerr <<  "power has received a negative exponent." << endl;
    return -1.0;
  }
}

void print_reverse(int num)
{
  cout << num%10;
  int numrest = num/10;
  if (numrest > 0)
    print_reverse(numrest);
  else
    cout << endl;
}

void convert_base(int num, int base)
{
  if (num / base == 0)
    cout << num%base;
  else
  {
    convert_base(num/base, base);
    cout << num%base;
  }
}

void main()
{
  cout << power(2.0, 6) << endl;
  cout << power(2.3, 4) << endl;
  
  cout << num_digits(1) << endl;
  cout << num_digits(123) << endl;
  cout << num_digits(12345) << endl;
  
  int num = 26;
  int base = 2;
  cout << num << " = ";
  convert_base(num, base);
  cout << "(base " << base << ")" << endl;

  num = 32;
  base = 8;
  cout << num << " = ";
  convert_base(num, base);
  cout << "(base " << base << ")" << endl;

  print_reverse(12345);
  print_reverse(9876);
}