In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

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

It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

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



In [1]:

    
5//2









    Out[1]:





2



In [2]:

    
def foo(n, coins):
    total = 0
    coins = sorted(coins, reverse=True)
    if n == 0:
        return 1
    if len(coins) == 1:
        return 1
    for i in range(n//coins[0] + 1):
        # print i
        total += foo(n - i*coins[0], coins[1:])
    return total



In [3]:

    
%timeit foo(200, [1, 2, 5, 10, 20, 50, 100, 200])
foo(200, [1, 2, 5, 10, 20, 50, 100, 200])









    



1 loops, best of 3: 231 ms per loop






    Out[3]:





73682