mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
92 lines
2.7 KiB
Python
92 lines
2.7 KiB
Python
"""
|
|
Problem 112: https://projecteuler.net/problem=112
|
|
|
|
Working from left-to-right if no digit is exceeded by the digit to its left it is
|
|
called an increasing number; for example, 134468.
|
|
Similarly if no digit is exceeded by the digit to its right it is called a decreasing
|
|
number; for example, 66420.
|
|
We shall call a positive integer that is neither increasing nor decreasing a "bouncy"
|
|
number, for example, 155349.
|
|
Clearly there cannot be any bouncy numbers below one-hundred, but just over half of
|
|
the numbers below one-thousand (525) are bouncy. In fact, the least number for which
|
|
the proportion of bouncy numbers first reaches 50% is 538.
|
|
Surprisingly, bouncy numbers become more and more common and by the time we reach
|
|
21780 the proportion of bouncy numbers is equal to 90%.
|
|
|
|
Find the least number for which the proportion of bouncy numbers is exactly 99%.
|
|
"""
|
|
|
|
|
|
def check_bouncy(n: int) -> bool:
|
|
"""
|
|
Returns True if number is bouncy, False otherwise
|
|
>>> check_bouncy(6789)
|
|
False
|
|
>>> check_bouncy(-12345)
|
|
False
|
|
>>> check_bouncy(0)
|
|
False
|
|
>>> check_bouncy(6.74)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: check_bouncy() accepts only integer arguments
|
|
>>> check_bouncy(132475)
|
|
True
|
|
>>> check_bouncy(34)
|
|
False
|
|
>>> check_bouncy(341)
|
|
True
|
|
>>> check_bouncy(47)
|
|
False
|
|
>>> check_bouncy(-12.54)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: check_bouncy() accepts only integer arguments
|
|
>>> check_bouncy(-6548)
|
|
True
|
|
"""
|
|
if not isinstance(n, int):
|
|
raise ValueError("check_bouncy() accepts only integer arguments")
|
|
str_n = str(n)
|
|
sorted_str_n = "".join(sorted(str_n))
|
|
return sorted_str_n != str_n and sorted_str_n[::-1] != str_n
|
|
|
|
|
|
def solution(percent: float = 99) -> int:
|
|
"""
|
|
Returns the least number for which the proportion of bouncy numbers is
|
|
exactly 'percent'
|
|
>>> solution(50)
|
|
538
|
|
>>> solution(90)
|
|
21780
|
|
>>> solution(80)
|
|
4770
|
|
>>> solution(105)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: solution() only accepts values from 0 to 100
|
|
>>> solution(100.011)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: solution() only accepts values from 0 to 100
|
|
"""
|
|
if not 0 < percent < 100:
|
|
raise ValueError("solution() only accepts values from 0 to 100")
|
|
bouncy_num = 0
|
|
num = 1
|
|
|
|
while True:
|
|
if check_bouncy(num):
|
|
bouncy_num += 1
|
|
if (bouncy_num / num) * 100 >= percent:
|
|
return num
|
|
num += 1
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|
|
print(f"{solution(99)}")
|