結果

問題 No.187 中華風 (Hard)
コンテスト
ユーザー い
提出日時 2023-09-21 14:31:14
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 770 ms / 3,000 ms
コード長 3,132 bytes
コンパイル時間 135 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 12,288 KB
最終ジャッジ日時 2024-07-07 08:08:33
合計ジャッジ時間 12,456 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 25
権限があれば一括ダウンロードができます

ソースコード

diff # 

import sys

V = sys.version_info
_39 = False
_310 = False
_311 = False
if V.major == 3:
    _39 = V.minor >= 9
    _310 = V.minor >= 10
    _311 = V.minor >= 11

if _39:
    li = list
    tup = tuple
    dic = dict
    st = set
    ty = type
else:
    from typing import (
        List,
        Tuple,
        Type,
        Dict,
        Set,
    )

    li = List
    tup = Tuple
    dic = Dict
    st = Set
    ty = Type

from sys import stdin

read = stdin.buffer.read
rl = stdin.buffer.readline
rb = lambda: rl().split()
rls = stdin.buffer.readlines


from typing import (
    TypeVar,
    Sequence as Seq,
    Iterable as Iter,
    Protocol as Proto,
    Generic as Gen,
)
from typing import Callable as Fn


from typing import Iterable


def prints(
    a: Iterable[object],
    sep: str = "\n",
) -> None:
    print(sep.join(map(str, a)))


# import numpy as np


def egcd(
    a: int,
    b: int,
) -> tup[int, int, int]:
    if not b:
        if a < 0:
            return -a, -1, 0
        return a, 1, 0
    q, r = divmod(a, b)
    g, s, t = egcd(b, r)
    return g, t, s - q * t


def crt_mod(
    m: Seq[int],
    r: Seq[int],
    mod: int,
) -> int:
    l = len(m)
    assert len(r) == l
    m = list(m) + [mod]
    p = [1] * (l + 1)
    x = [0] * (l + 1)
    for i, (n, b) in enumerate(zip(m, r)):
        assert n > 0
        g, ip, _ = egcd(p[i], n)
        assert g == 1
        t = (b - x[i]) % n * ip % n
        for j in range(i + 1, l + 1):
            x[j] += t * p[j]
            x[j] %= m[j]
            p[j] = p[j] * n % m[j]
    return x[-1]


def factorize(n: int) -> li[tup[int, int]]:
    f = []
    for i in range(2, n):
        if i * i > n:
            break
        if n % i:
            continue
        c = 0
        while n % i == 0:
            n //= i
            c += 1
        f.append((i, c))
    if n > 1:
        f.append((n, 1))
    return f


from math import gcd


def to_coprime(
    m: int,
    a: int,
    n: int,
    b: int,
) -> tup[int, int, int, int]:
    g = gcd(m, n)
    if (a - b) % g:
        return (-1, -1, -1, -1)
    m //= g
    n //= g
    u = gcd(m, g)
    v = g // u
    while g > 1:
        g = gcd(u, v)
        u *= g
        v //= g
    m *= u
    n *= v
    a %= m
    b %= n
    return m, a, n, b


def to_pairwise_coprime(
    m: li[int],
    r: li[int],
) -> bool:
    n = len(m)
    assert len(r) == n
    for i in range(n):
        for j in range(i):
            (
                m[i],
                r[i],
                m[j],
                r[j],
            ) = to_coprime(
                m[i], r[i], m[j], r[j]
            )
            if m[i] == -1:
                return False
    return True


def solve() -> None:
    n = int(rl())
    rm = [map(int, rb()) for _ in range(n)]
    r, m = map(list, zip(*rm))
    if not to_pairwise_coprime(m, r):
        print(-1)
        return
    mod = 10**9 + 7
    if max(r) > 0:
        x = crt_mod(m, r, mod)
        print(x)
        return
    l = 1
    for x in m:
        l = l * x % mod
    print(l)


def main() -> None:
    t = 1
    # t = int(rl())
    for _ in range(t):
        solve()


main()
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