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continued_fraction.py

from decimal import Decimal, getcontext
from fractions import Fraction
from typing import Iterable, List
getcontext().prec = 4 * 8


def continued_fraction(n) -> Fraction:
    if len(n) == 1:
        return Fraction(n[0])
    else:
        return Fraction(n[0]) + 1 / continued_fraction(n[1:])


def fraction_to_dec(f: Fraction) -> Decimal:
    return Decimal(f.numerator) / Decimal(f.denominator)


def ans_to_dec(n: List[int]) -> Decimal:
    frac = ''.join(map(str, n))
    fs = f'0.{frac}'
    return Decimal(fs)


def continued_fraction_number(n, max_n: int) -> Iterable[int]:
    # 連分数表現を得る
    yield 0
    for _ in range(max_n):
        i = 1/n  # 逆数
        a = int(i)  # 整数部
        yield a
        n = i - a  # 小数部


def resolve(ans: List[int]) -> Decimal:

    # 答えを小数にする
    n = ans_to_dec(ans)

    # 連分数表現を得る
    con_frac_n = list(continued_fraction_number(n, 5))
    print(con_frac_n)

    con_frac_n += [1] * 100   # 末尾は1が続く

    # 再計算
    f = continued_fraction(con_frac_n)
    return fraction_to_dec(f)


def print4(n: Decimal):
    # 小数点以下
    fr = f'{n}'[2:]
    ans = [fr[x:x+4] for x in range(0, len(fr), 4)]
    for n, a in enumerate(ans):
        print(n, a)


def main():
    ans = [9005, 6439, 6704, 8685]
    print4(resolve(ans))


if __name__ == "__main__":
    main()