'''
   20211004
   
   Robin Dawes
'''


def multiply_rec(x,y):
   '''multiply by repeated addition, using recursion
      x must be a positive integer
   '''
   if x == 1:                                      # base case
      return y
   else:                                              # recursive part
      return y + multiply_rec(x-1, y)
            
n1 = 23
n2 = 17
print("product of", n1, "and", n2, "is", multiply_rec(n1, n2))



def egyptian_multiply_rec(x,y):
   '''"Ancient Egyptian" mutiplication, revised to use recursion instead of a loop
      x must be a positive integer
   '''
   if x == 1:                    # base case
      return y
   else:                            # recursive part
      if x % 2 == 1:
         return y + egyptian_multiply_rec(x // 2, y*2)
      else:
         return egyptian_multiply_rec(x // 2, y*2)
        
print("product of", n1, "and", n2, "is", egyptian_multiply_rec(n1, n2))