Garner
(expansion/math/Garner.py)

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• Last update: 2023-07-06 23:24:06+09:00

概要

$R = [R_1, R_2, \ldots]$, $M = [M_1, M_2, \ldots]$

が与えられたときに， $x \% M_i = R_i$ を満たす x (なければ -1) と M の最小公倍数 を返します．

使い方

x, m = Garner(R, M)

Code

def ext_gcd(a, b):
    """
    return (x, y, gcd(a, b)) s.t. ax + by = gcd(a, b)
    """
    if b == 0:
        return 1, 0, a
    else:
        y, x, g = ext_gcd(b, a % b)
        return x, y - (a // b) * x, g


def Garner(R, M):
    r = 0
    m = 1
    for ri, mi in zip(R, M):
        if ri < 0 or mi <= ri:
            ri %= mi

        if m < mi:
            m, mi = mi, m
            r, ri = ri, r

        if m % mi == 0:
            if r % mi != ri:
                return -1, -1
            continue

        im, _, g = ext_gcd(m, mi)
        if im < 0:
            im += mi

        if (ri - r) % g != 0:
            return -1, -1

        ui = mi // g
        x = ((ri - r) // g % ui) * im % ui
        r += x * m
        m *= ui

    return r, m

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/documentation/build.py", line 81, in _render_source_code_stat
    bundled_code = language.bundle(
                   ^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/languages/python.py", line 108, in bundle
    raise NotImplementedError
NotImplementedError

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