sol1.py

"""
Coin sums
Problem 31: https://projecteuler.net/problem=31

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

1p, 2p, 5p, 10p, 20p, 50p, f1 (100p) and f2 (200p).
It is possible to make f2 in the following way:

1xf1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p
How many different ways can f2 be made using any number of coins?
"""


defone_pence() ->int:
return1


deftwo_pence(x: int) ->int:
return0ifx<0elsetwo_pence(x-2) +one_pence()


deffive_pence(x: int) ->int:
return0ifx<0elsefive_pence(x-5) +two_pence(x)


deften_pence(x: int) ->int:
return0ifx<0elseten_pence(x-10) +five_pence(x)


deftwenty_pence(x: int) ->int:
return0ifx<0elsetwenty_pence(x-20) +ten_pence(x)


deffifty_pence(x: int) ->int:
return0ifx<0elsefifty_pence(x-50) +twenty_pence(x)


defone_pound(x: int) ->int:
return0ifx<0elseone_pound(x-100) +fifty_pence(x)


deftwo_pound(x: int) ->int:
return0ifx<0elsetwo_pound(x-200) +one_pound(x)


defsolution(n: int=200) ->int:
"""Returns the number of different ways can n pence be made using any number of
 coins?

 >>> solution(500)
 6295434
 >>> solution(200)
 73682
 >>> solution(50)
 451
 >>> solution(10)
 11
 """
returntwo_pound(n)


if__name__=="__main__":
print(solution(int(input().strip())))