結果
問題 | No.1962 Not Divide |
ユーザー |
👑 |
提出日時 | 2022-05-28 15:43:36 |
言語 | PyPy3 (7.3.15) |
結果 |
RE
|
実行時間 | - |
コード長 | 3,689 bytes |
コンパイル時間 | 222 ms |
コンパイル使用メモリ | 82,288 KB |
実行使用メモリ | 99,700 KB |
最終ジャッジ日時 | 2024-09-20 22:24:29 |
合計ジャッジ時間 | 6,814 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 19 RE * 2 |
ソースコード
from collections import dequeMOD = 998244353class FFT:inv_ = [1]def __init__(self, MOD=998244353):FFT.MOD = MODg = self.primitive_root_constexpr()ig = pow(g, FFT.MOD - 2, FFT.MOD)FFT.W = [pow(g, (FFT.MOD - 1) >> i, FFT.MOD) for i in range(30)]FFT.iW = [pow(ig, (FFT.MOD - 1) >> i, FFT.MOD) for i in range(30)]def primitive_root_constexpr(self):if FFT.MOD == 998244353:return 3elif FFT.MOD == 200003:return 2elif FFT.MOD == 167772161:return 3elif FFT.MOD == 469762049:return 3elif FFT.MOD == 754974721:return 11divs = [0] * 20divs[0] = 2cnt = 1x = (FFT.MOD - 1) // 2while x % 2 == 0:x //= 2i = 3while i * i <= x:if x % i == 0:divs[cnt] = icnt += 1while x % i == 0:x //= ii += 2if x > 1:divs[cnt] = xcnt += 1g = 2while 1:ok = Truefor i in range(cnt):if pow(g, (FFT.MOD - 1) // divs[i], FFT.MOD) == 1:ok = Falsebreakif ok:return gg += 1def fft(self, k, f):for l in range(k, 0, -1):d = 1 << l - 1U = [1]for i in range(d):U.append(U[-1] * FFT.W[l] % FFT.MOD)for i in range(1 << k - l):for j in range(d):s = i * 2 * d + jf[s], f[s + d] = (f[s] + f[s + d]) % FFT.MOD, U[j] * (f[s] - f[s + d]) % FFT.MODdef ifft(self, k, f):for l in range(1, k + 1):d = 1 << l - 1for i in range(1 << k - l):u = 1for j in range(i * 2 * d, (i * 2 + 1) * d):f[j+d] *= uf[j], f[j + d] = (f[j] + f[j + d]) % FFT.MOD, (f[j] - f[j + d]) % FFT.MODu = u * FFT.iW[l] % FFT.MODdef convolve(self, A, B):n0 = len(A) + len(B) - 1k = (n0).bit_length()n = 1 << kA += [0] * (n - len(A))B += [0] * (n - len(B))self.fft(k, A)self.fft(k, B)A = [a * b % FFT.MOD for a, b in zip(A, B)]self.ifft(k, A)inv = pow(n, FFT.MOD - 2, FFT.MOD)A = [a * inv % FFT.MOD for a in A]del A[n0:]return A# [x ^ n] P(x) / Q(x)def BostanMori(P, Q, n):fft = FFT()while n:R = [(x * (-1) ** (i % 2)) % MOD for i, x in enumerate(Q)]Q = fft.convolve(Q, R[:])[::2]P = fft.convolve(P, R[:])[n % 2::2]n >>= 1return P[0] * pow(Q[0], MOD - 2, MOD) % MODn, m = map(int, input().split())queue = deque()fft = FFT()for i in range(2, m + 1):q = [1] * (i + 1)q[i] = -1p = [1] * ip[0] = 0queue.append((p, q))while len(queue) >= 2:p1, q1 = queue.popleft()p2, q2 = queue.popleft()l1 = len(q1)l2 = len(q2)nq = fft.convolve(q1[:], q2[:])np1 = fft.convolve(p1, q2)np2 = fft.convolve(p2, q1)assert len(np1) == len(np2)np = [(p1 + p2) % MOD for p1, p2 in zip(np1, np2)]queue.append((np, nq))P, Q = queue.popleft()Q_P = Q[:] + [0] * (len(P) - len(Q))for i, p in enumerate(P):Q_P[i] -= pQ_P[i] %= MODans = BostanMori(Q, Q_P, n)print(ans)"""(1 + x - x^2) / (1 - x^2)(1 + x - x^2) / (2 + x - 2x^2)(1 + x + x^2 - x^3) / (1 - x^3)(1 + x + x^2 - x^3) / (2 + x + x^2 - 2x^2)"""