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92 lines
2.7 KiB
Python
92 lines
2.7 KiB
Python
"""
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Problem 112: https://projecteuler.net/problem=112
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Working from left-to-right if no digit is exceeded by the digit to its left it is
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called an increasing number; for example, 134468.
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Similarly if no digit is exceeded by the digit to its right it is called a decreasing
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number; for example, 66420.
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We shall call a positive integer that is neither increasing nor decreasing a "bouncy"
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number, for example, 155349.
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Clearly there cannot be any bouncy numbers below one-hundred, but just over half of
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the numbers below one-thousand (525) are bouncy. In fact, the least number for which
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the proportion of bouncy numbers first reaches 50% is 538.
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Surprisingly, bouncy numbers become more and more common and by the time we reach
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21780 the proportion of bouncy numbers is equal to 90%.
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Find the least number for which the proportion of bouncy numbers is exactly 99%.
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"""
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def check_bouncy(n: int) -> bool:
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"""
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Returns True if number is bouncy, False otherwise
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>>> check_bouncy(6789)
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False
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>>> check_bouncy(-12345)
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False
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>>> check_bouncy(0)
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False
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>>> check_bouncy(6.74)
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Traceback (most recent call last):
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...
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ValueError: check_bouncy() accepts only integer arguments
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>>> check_bouncy(132475)
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True
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>>> check_bouncy(34)
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False
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>>> check_bouncy(341)
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True
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>>> check_bouncy(47)
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False
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>>> check_bouncy(-12.54)
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Traceback (most recent call last):
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...
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ValueError: check_bouncy() accepts only integer arguments
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>>> check_bouncy(-6548)
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True
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"""
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if not isinstance(n, int):
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raise ValueError("check_bouncy() accepts only integer arguments")
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str_n = str(n)
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sorted_str_n = "".join(sorted(str_n))
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return sorted_str_n != str_n and sorted_str_n[::-1] != str_n
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def solution(percent: float = 99) -> int:
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"""
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Returns the least number for which the proportion of bouncy numbers is
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exactly 'percent'
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>>> solution(50)
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538
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>>> solution(90)
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21780
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>>> solution(80)
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4770
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>>> solution(105)
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Traceback (most recent call last):
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...
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ValueError: solution() only accepts values from 0 to 100
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>>> solution(100.011)
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Traceback (most recent call last):
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...
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ValueError: solution() only accepts values from 0 to 100
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"""
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if not 0 < percent < 100:
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raise ValueError("solution() only accepts values from 0 to 100")
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bouncy_num = 0
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num = 1
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while True:
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if check_bouncy(num):
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bouncy_num += 1
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if (bouncy_num / num) * 100 >= percent:
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return num
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num += 1
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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print(f"{solution(99)}")
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