Python/project_euler/problem_031/sol1.py
Dhruv 44254cf112
Rename Project Euler directories and other dependent changes (#3300)
* Rename all Project Euler directories:

Reason:
The change was done to maintain consistency throughout the directory
and to keep all directories in sorted order.

Due to the above change, some config files had to be modified:
'problem_22` -> `problem_022`

* Update scripts to pad zeroes in PE directories
2020-10-15 12:43:28 +05:30

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"""
Coin sums
Problem 31: https://projecteuler.net/problem=31
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?
"""
def one_pence() -> int:
return 1
def two_pence(x: int) -> int:
return 0 if x < 0 else two_pence(x - 2) + one_pence()
def five_pence(x: int) -> int:
return 0 if x < 0 else five_pence(x - 5) + two_pence(x)
def ten_pence(x: int) -> int:
return 0 if x < 0 else ten_pence(x - 10) + five_pence(x)
def twenty_pence(x: int) -> int:
return 0 if x < 0 else twenty_pence(x - 20) + ten_pence(x)
def fifty_pence(x: int) -> int:
return 0 if x < 0 else fifty_pence(x - 50) + twenty_pence(x)
def one_pound(x: int) -> int:
return 0 if x < 0 else one_pound(x - 100) + fifty_pence(x)
def two_pound(x: int) -> int:
return 0 if x < 0 else two_pound(x - 200) + one_pound(x)
def solution(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
"""
return two_pound(n)
if __name__ == "__main__":
print(solution(int(input().strip())))