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7ef2e4d1d0
* adde solution to problem 092 * added solution to problem 092 * fixed the pre-comit shebang issue
94 lines
2.7 KiB
Python
94 lines
2.7 KiB
Python
"""
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Project Euler Problem 092: https://projecteuler.net/problem=92
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Square digit chains
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A number chain is created by continuously adding the square of the digits in
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a number to form a new number until it has been seen before.
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For example,
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44 → 32 → 13 → 10 → 1 → 1
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85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89
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Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop.
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What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
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How many starting numbers below ten million will arrive at 89?
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"""
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def next_number(number: int) -> int:
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"""
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Returns the next number of the chain by adding the square of each digit
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to form a neww number.
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For example if number = 12, next_number() will return 1^2 + 2^2 = 5.
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Therefore 5 is the next number of the chain.
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>>> next_number(44)
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32
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>>> next_number(10)
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1
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>>> next_number(32)
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13
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"""
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num = 0
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for i in range(len(str(number))):
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num += int(str(number)[i]) ** 2
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return num
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def chain(number: int) -> bool:
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"""
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Generates the chain of numbers until the nest number generated is 1 0r 89.
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for example, if starting number is 44, then the function generates the
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following chain of numbers.
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chain: 44 → 32 → 13 → 10 → 1 → 1
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once the next number generated is 1 or 89, the function
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Returns True if the next number generated by next_number() if 1.
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Returns False if the next number generated by next_number() is 89.
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>>> chain(10)
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True
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>>> chain(58)
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False
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>>> chain(1)
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True
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"""
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while number != 1 and number != 89:
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number = next_number(number)
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if number == 1:
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return True
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elif number == 89:
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return False
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def solution(number: int = 10000000) -> int:
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"""
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The function returns the total numbers that end up in 89 after the chain generation.
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The function accepts a range number and the function checks all the values
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under value number.
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if the chain generation leads to the end number as 1 or 89. If the chain()
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returns True, then total is incremented, implying that the number we
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started with ended up with 1 else total2 is incremented, implying that
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the number we started with ended up in 89 after chain generation.
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But the function returns total2 as the requirement of question is
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to find out how many ended up in 89.
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>>> solution(100)
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80
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>>> solution(10000000)
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8581146
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"""
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total = 0
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total2 = 0
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for i in range(1, number):
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val = chain(i)
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if val is True:
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total += 1
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elif val is False:
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total2 += 1
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return total2
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if __name__ == "__main__":
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print(f"{solution() = }")
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