# L-10 MCS 275 Web 3 Feb 2008 : fibonacci

def Fibonacci(n):
   """
   returns the n-th Fibonacci number
   """
   if n == 0:
      return 0
   elif n == 1:
      return 1
   else:
      return Fibonacci(n-1) + Fibonacci(n-2)

def Fibotrace(n,k,c):
   """
   returns (f,c) where f is the n-th
   Fibonacci number and c the number
   of function calls
   prints execution trace
   using control parameter k
   """
   s = k*' ' + 'F(%d) = ' % n
   if n == 0:
      print s + '0'
      return (0,c)
   elif n == 1:
      print s + '1'
      return (1,c)
   else:
      print s + 'F(%d) + F(%d)' % (n-1,n-2)
      (f1,c1) = Fibotrace(n-1,k+1,c+1)
      (f2,c2) = Fibotrace(n-2,k+1,c+1)
      return (f1+f2,c1+c2)

def F(n):
   """
   iterative algorithm for n-th Fibonacci number
   """
   if n == 0:
      return 0
   else:
      a = 0
      b = 1
      for k in range(2,n+1):
         c = a + b
         a = b
         b = c
      return b

def main():
   """
   prompts user for n
   and computes n-th Fibonacci number
   """
   n = input("Give n : ")
   (f,c) = Fibotrace(n,0,0)
   print 'F(%d) = %d' % (n,f)
   print 'number of calls : %d' % c
   n = input("Give n : ")
   print 'F(%d) = %d' % (n,F(n))

main()