"""
 projecteuler.net problem 31 :

 In England the currency is made up of pound and pence
 with 1 pound = 100 pence.
 There are eight coins in general circulation:

    1p, 2p, 5p, 10p, 20p, 50p, 1 pound (100p) and 2 pound (200p).

 One way to make 2 pounds with these coins is 

    1 100p + 1 50p + 2 20p + 1 5p + 1 2p + 3 1p

 How many different ways can 2 pounds be made using any number of coins?

 Jim M | GPL | Nov 2010
"""

# index:   0    1   2   3   4  5  6  7
coins = [200, 100, 50, 20, 10, 5, 2, 1]
last_index = len(coins) - 1

def count_ways(amount_left, index):
  """Recursively calculate number of ways to make change.
     >>> count_ways(4, 7)   # 4p with [1p] coins: (4) 
     1
     >>> count_ways(4, 6)   # 4p with [2p, 1p] coins: (2,0),(1,2),(0,4)
     3
     >>> count_ways(200, 0) # answer to problem 31
     73682
  """
  if index == last_index:
    return 1              # 1 way : use amount_left of 1p coins
  else:
    coin_value = coins[index]
    ways = 0
    for n in range(1 + amount_left/coin_value):
      result = count_ways(amount_left - n*coin_value, index + 1)
      ways += result
    return ways

def main():
  print "Number of ways to get 200 pound = %i" % count_ways(200, 0)

if __name__ == "__main__":
  import doctest
  doctest.testmod()
  main()