結果

問題 No.2272 多項式乗算 mod 258280327
ユーザー とりゐとりゐ
提出日時 2023-04-14 22:09:31
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 9,718 bytes
コンパイル時間 374 ms
コンパイル使用メモリ 82,688 KB
実行使用メモリ 194,988 KB
最終ジャッジ日時 2024-10-10 12:56:26
合計ジャッジ時間 10,596 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 71 ms
68,992 KB
testcase_01 AC 66 ms
69,248 KB
testcase_02 AC 66 ms
68,864 KB
testcase_03 AC 67 ms
69,376 KB
testcase_04 AC 65 ms
68,992 KB
testcase_05 AC 71 ms
69,376 KB
testcase_06 AC 65 ms
68,992 KB
testcase_07 AC 65 ms
69,376 KB
testcase_08 AC 65 ms
69,376 KB
testcase_09 AC 68 ms
68,992 KB
testcase_10 RE -
testcase_11 RE -
testcase_12 RE -
testcase_13 RE -
testcase_14 RE -
testcase_15 WA -
testcase_16 RE -
testcase_17 RE -
testcase_18 AC 84 ms
69,120 KB
testcase_19 AC 67 ms
69,504 KB
testcase_20 AC 65 ms
69,120 KB
testcase_21 AC 95 ms
77,696 KB
testcase_22 AC 92 ms
78,004 KB
testcase_23 AC 92 ms
77,848 KB
testcase_24 AC 177 ms
80,480 KB
testcase_25 AC 215 ms
84,188 KB
testcase_26 AC 211 ms
83,936 KB
testcase_27 AC 307 ms
89,700 KB
testcase_28 AC 287 ms
89,868 KB
testcase_29 AC 757 ms
124,904 KB
testcase_30 AC 1,412 ms
172,720 KB
testcase_31 AC 1,386 ms
168,920 KB
testcase_32 AC 1,470 ms
194,988 KB
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 # 

from typing import List


MOD1 = 167772161
MOD2 = 469762049
MOD3 = 754974721

sum_e1 = [
    65249968,
    137365239,
    35921276,
    103665800,
    89728614,
    164955302,
    108901219,
    163950188,
    113252399,
    166581688,
    59783366,
    95476790,
    130818126,
    39440948,
    65800545,
    14559656,
    3285286,
    36462062,
    164082627,
    9320421,
    66343657,
    69024390,
    38289678,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
]
sum_ie1 = [
    102522193,
    71493608,
    26998229,
    133555027,
    128975965,
    16363816,
    145463520,
    130828795,
    26375299,
    18078794,
    87407453,
    28151929,
    49401241,
    112914531,
    118959329,
    68815302,
    71865958,
    21459372,
    44393528,
    43709352,
    30681399,
    153195333,
    141748999,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
]
sum_e2 = [
    450151958,
    26623616,
    25192837,
    305390008,
    399060560,
    78724413,
    312251397,
    151088193,
    437503217,
    339869829,
    197503427,
    460844482,
    64795813,
    392699793,
    323591778,
    435162849,
    324666788,
    397071166,
    191521520,
    39442863,
    102932772,
    52822010,
    231589706,
    155147527,
    0,
    0,
    0,
    0,
    0,
    0,
]
sum_ie2 = [
    19610091,
    129701348,
    104677229,
    445839763,
    375500824,
    451642859,
    145445927,
    77724141,
    367250623,
    54456563,
    257713867,
    444918711,
    335270416,
    371371281,
    307213086,
    452878044,
    243328637,
    152011944,
    315423951,
    456185089,
    218081060,
    136058803,
    203260256,
    412215962,
    0,
    0,
    0,
    0,
    0,
    0,
]
sum_e3 = [
    323860177,
    709730407,
    436702940,
    377572811,
    498550177,
    265767825,
    100966039,
    179671739,
    669698534,
    133401683,
    473130419,
    31725267,
    490947959,
    457689220,
    238049902,
    49087920,
    531104465,
    448493484,
    262339740,
    717535334,
    230862726,
    416349974,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
]
sum_ie3 = [
    431114544,
    205430076,
    560644912,
    287842920,
    662221072,
    3742006,
    250769401,
    512611432,
    114808946,
    480642746,
    472385404,
    152834416,
    131937947,
    932118,
    246823069,
    305783701,
    453008707,
    746618366,
    510123862,
    69538303,
    659667489,
    259138136,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
]


def butterfly1(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p] * now
                arr[i + offset] = (l + r) % MOD1
                arr[i + offset + p] = (l - r) % MOD1
            now *= sum_e1[(~s & -~s).bit_length() - 1]
            now %= MOD1


def butterfly_inv1(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1)[::-1]:
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p]
                arr[i + offset] = (l + r) % MOD1
                arr[i + offset + p] = (MOD1 + l - r) * inow % MOD1
            inow *= sum_ie1[(~s & -~s).bit_length() - 1]
            inow %= MOD1


def convolution1(a, b):
    n = len(a)
    m = len(b)
    if not n or not m:
        return []
    if min(n, m) <= 100:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD1
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly1(a)
    butterfly1(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD1
    butterfly_inv1(a)
    a = a[: n + m - 1]
    iz = pow(z, MOD1 - 2, MOD1)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD1
    return a


def butterfly2(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p] * now
                arr[i + offset] = (l + r) % MOD2
                arr[i + offset + p] = (l - r) % MOD2
            now *= sum_e2[(~s & -~s).bit_length() - 1]
            now %= MOD2


def butterfly_inv2(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1)[::-1]:
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p]
                arr[i + offset] = (l + r) % MOD2
                arr[i + offset + p] = (MOD2 + l - r) * inow % MOD2
            inow *= sum_ie2[(~s & -~s).bit_length() - 1]
            inow %= MOD2


def convolution2(a, b):
    n = len(a)
    m = len(b)
    if not n or not m:
        return []
    if min(n, m) <= 100:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD2
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly2(a)
    butterfly2(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD2
    butterfly_inv2(a)
    a = a[: n + m - 1]
    iz = pow(z, MOD2 - 2, MOD2)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD2
    return a


def butterfly3(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p] * now
                arr[i + offset] = (l + r) % MOD3
                arr[i + offset + p] = (l - r) % MOD3
            now *= sum_e3[(~s & -~s).bit_length() - 1]
            now %= MOD3


def butterfly_inv3(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1)[::-1]:
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p]
                arr[i + offset] = (l + r) % MOD3
                arr[i + offset + p] = (MOD3 + l - r) * inow % MOD3
            inow *= sum_ie3[(~s & -~s).bit_length() - 1]
            inow %= MOD3


def convolution3(a, b):
    n = len(a)
    m = len(b)
    if not n or not m:
        return []
    if min(n, m) <= 100:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD3
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly3(a)
    butterfly3(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD3
    butterfly_inv3(a)
    a = a[: n + m - 1]
    iz = pow(z, MOD3 - 2, MOD3)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD3
    return a


def inv_gcd(a, b):
    a %= b
    if a == 0:
        return b, 0
    s = b
    t = a
    m0 = 0
    m1 = 1
    while t:
        u = s // t
        s -= t * u
        m0 -= m1 * u
        s, t = t, s
        m0, m1 = m1, m0
    if m0 < 0:
        m0 += b // s
    return s, m0


def crt(r, m):
    n = len(r)
    r0 = 0
    m0 = 1
    for i in range(n):
        r1 = r[i] % m[i]
        m1 = m[i]
        if m0 < m1:
            r0, r1 = r1, r0
            m0, m1 = m1, m0
        if m0 % m1 == 0:
            if r0 % m1 != r1:
                return 0, 0
            continue
        g, im = inv_gcd(m0, m1)

        u1 = m1 // g
        if (r1 - r0) % g:
            return 0, 0

        x = (r1 - r0) // g * im % u1
        r0 += x * m0
        m0 *= u1
        if r0 < 0:
            r0 += m0
    return r0, m0


def convolution(a: List[int], b: List[int], mod: int) -> List[int]:
    n = len(a)
    m = len(b)
    c1 = convolution1(a[:], b[:])[: n + m - 1]
    c2 = convolution2(a[:], b[:])[: n + m - 1]
    c3 = convolution3(a[:], b[:])[: n + m - 1]
    res = [0] * (n + m - 1)
    for i, v in enumerate(zip(c1, c2, c3)):
        cr, _ = crt(v, (MOD1, MOD2, MOD3))
        res[i] = (res[i] + cr) % mod
    return res


def multiConvolution(arrs: List[List[int]], mod: int) -> List[int]:
    if not arrs:
        return []
    if len(arrs) == 1:
        return arrs[0]
    if len(arrs) == 2:
        return convolution(arrs[0], arrs[1], mod)
    m = len(arrs) >> 1
    return convolution(multiConvolution(arrs[:m], mod), multiConvolution(arrs[m:], mod), mod)


n=int(input())
a=list(map(int,input().split()))
m=int(input())
b=list(map(int,input().split()))
mod=258280327
ans=convolution([i%mod for i in a],[i%mod for i in b],mod)
while ans and ans[-1]==0:
  ans.pop()
if len(ans)==0:
  raise Exception
else:
  print(len(ans)-1)
  print(*ans)
0