TheAlgorithms-Python

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"""
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Coin sums
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Problem 31: https://projecteuler.net/problem=31
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In England the currency is made up of pound, £, and pence, p, and there are
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eight coins in general circulation:
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1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
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It is possible to make £2 in the following way:
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1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
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How many different ways can £2 be made using any number of coins?
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"""
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def one_pence() -> int:
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    return 1
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def two_pence(x: int) -> int:
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    return 0 if x < 0 else two_pence(x - 2) + one_pence()
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def five_pence(x: int) -> int:
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    return 0 if x < 0 else five_pence(x - 5) + two_pence(x)
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def ten_pence(x: int) -> int:
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    return 0 if x < 0 else ten_pence(x - 10) + five_pence(x)
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def twenty_pence(x: int) -> int:
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    return 0 if x < 0 else twenty_pence(x - 20) + ten_pence(x)
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def fifty_pence(x: int) -> int:
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    return 0 if x < 0 else fifty_pence(x - 50) + twenty_pence(x)
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def one_pound(x: int) -> int:
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    return 0 if x < 0 else one_pound(x - 100) + fifty_pence(x)
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def two_pound(x: int) -> int:
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    return 0 if x < 0 else two_pound(x - 200) + one_pound(x)
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def solution(n: int = 200) -> int:
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    """Returns the number of different ways can n pence be made using any number of
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    coins?
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    >>> solution(500)
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    6295434
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    >>> solution(200)
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    73682
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    >>> solution(50)
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    451
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    >>> solution(10)
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    11
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    """
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    return two_pound(n)
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if __name__ == "__main__":
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    print(solution(int(input().strip())))
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