sol1.py

"""
Project Euler Problem 092: https://projecteuler.net/problem=92
Square digit chains
A number chain is created by continuously adding the square of the digits in
a number to form a new number until it has been seen before.
For example,
44 → 32 → 13 → 10 → 1 → 1
85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop.
What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
How many starting numbers below ten million will arrive at 89?
"""

DIGITS_SQUARED = [sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(100000)]


def next_number(number: int) -> int:

    """
    Returns the next number of the chain by adding the square of each digit
    to form a new number.
    For example, if number = 12, next_number() will return 1^2 + 2^2 = 5.
    Therefore, 5 is the next number of the chain.
    >>> next_number(44)
    32
    >>> next_number(10)
    1
    >>> next_number(32)
    13
    """

    sum_of_digits_squared = 0
    while number:

        # Increased Speed Slightly by checking every 5 digits together.
        sum_of_digits_squared += DIGITS_SQUARED[number % 100000]
        number //= 100000

    return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
CHAINS: list[bool | None] = [None] * 10000000
CHAINS[0] = True
CHAINS[57] = False


def chain(number: int) -> bool:
    """
    The function generates the chain of numbers until the next number is 1 or 89.
    For example, if starting number is 44, then the function generates the
    following chain of numbers:
    44 → 32 → 13 → 10 → 1 → 1.
    Once the next number generated is 1 or 89, the function returns whether
    or not the next number generated by next_number() is 1.
    >>> chain(10)
    True
    >>> chain(58)
    False
    >>> chain(1)
    True
    """

    if CHAINS[number - 1] is not None:
        return CHAINS[number - 1]  # type: ignore

    number_chain = chain(next_number(number))
    CHAINS[number - 1] = number_chain

    while number < 10000000:
        CHAINS[number - 1] = number_chain
        number *= 10

    return number_chain


def solution(number: int = 10000000) -> int:
    """
    The function returns the number of integers that end up being 89 in each chain.
    The function accepts a range number and the function checks all the values
    under value number.

    >>> solution(100)
    80
    >>> solution(10000000)
    8581146
    """
    for i in range(1, number):
        if CHAINS[i] is None:
            chain(i + 1)

    return CHAINS[:number].count(False)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    print(f"{solution() = }")