mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
44254cf112
* 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
66 lines
1.4 KiB
Python
66 lines
1.4 KiB
Python
"""
|
||
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())))
|