結果
| 問題 |
No.1307 Rotate and Accumulate
|
| コンテスト | |
| ユーザー |
 rin204
|
| 提出日時 | 2022-11-08 17:58:12 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 210 ms / 5,000 ms |
| コード長 | 6,901 bytes |
| コンパイル時間 | 271 ms |
| コンパイル使用メモリ | 82,164 KB |
| 実行使用メモリ | 116,764 KB |
| 最終ジャッジ日時 | 2024-07-22 02:08:09 |
| 合計ジャッジ時間 | 4,908 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 19 |
ソースコード
class FFT:
def __init__(self, MOD=998244353):
FFT.MOD = MOD
self.make_info(MOD)
def make_info(self, MOD):
g = self.primitive_root_constexpr()
m = MOD - 1
rank2 = (m & -m).bit_length() - 1
root = [0] * (rank2 + 1)
iroot = [0] * (rank2 + 1)
rate2 = [0] * (rank2 + 1)
irate2 = [0] * (rank2 + 1)
rate3 = [0] * (rank2)
irate3 = [0] * (rank2)
root[rank2] = pow(g, (MOD - 1) >> rank2, MOD)
iroot[rank2] = pow(root[rank2], MOD - 2, MOD)
for i in range(rank2 - 1, -1, -1):
root[i] = root[i + 1] * root[i + 1] % MOD
iroot[i] = iroot[i + 1] * iroot[i + 1] % MOD
prod = 1
iprod = 1
for i in range(1, rank2):
rate2[i] = root[i + 1] * prod % MOD
irate2[i] = iroot[i + 1] * iprod % MOD
prod = prod * iroot[i + 1] % MOD
iprod = iprod * root[i + 1] % MOD
prod = 1
iprod = 1
for i in range(1, rank2 - 1):
rate3[i] = root[i + 2] * prod % MOD
irate3[i] = iroot[i + 2] * iprod % MOD
prod = prod * iroot[i + 2] % MOD
iprod = iprod * root[i + 2] % MOD
self.IMAG = rate2[1]
self.IIMAG = irate2[1]
self.rate2 = rate2
self.irate2 = irate2
self.rate3 = rate3
self.irate3 = irate3
def primitive_root_constexpr(self):
if FFT.MOD == 998244353:
return 3
elif FFT.MOD == 200003:
return 2
elif FFT.MOD == 167772161:
return 3
elif FFT.MOD == 469762049:
return 3
elif FFT.MOD == 754974721:
return 11
divs = [0] * 20
divs[0] = 2
cnt = 1
x = (FFT.MOD - 1) // 2
while x % 2 == 0:
x //= 2
i = 3
while i * i <= x:
if x % i == 0:
divs[cnt] = i
cnt += 1
while x % i == 0:
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while 1:
ok = True
for i in range(cnt):
if pow(g, (FFT.MOD - 1) // divs[i], FFT.MOD) == 1:
ok = False
break
if ok:
return g
g += 1
def butterfly(self, A):
n = len(A)
h = (n - 1).bit_length()
le = 0
while le < h:
if h - le == 1:
p = 1 << (h - le - 1)
rot = 1
for s in range(1 << le):
offset = s << (h - le)
for i in range(p):
l = A[i + offset]
r = A[i + offset + p] * rot
A[i + offset] = (l + r) % FFT.MOD
A[i + offset + p] = (l - r) % FFT.MOD
rot *= self.rate2[(~s & -~s).bit_length()]
rot %= FFT.MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % FFT.MOD
rot3 = rot2 * rot % FFT.MOD
offset = s << (h - le)
for i in range(p):
a0 = A[i + offset]
a1 = A[i + offset + p] * rot
a2 = A[i + offset + p * 2] * rot2
a3 = A[i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % FFT.MOD * self.IMAG
A[i + offset] = (a0 + a2 + a1 + a3) % FFT.MOD
A[i + offset + p] = (a0 + a2 - a1 - a3) % FFT.MOD
A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % FFT.MOD
A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % FFT.MOD
rot *= self.rate3[(~s & -~s).bit_length()]
rot %= FFT.MOD
le += 2
def butterfly_inv(self, A):
n = len(A)
h = (n - 1).bit_length()
le = h
while le:
if le == 1:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 1)):
offset = s << (h - le + 1)
for i in range(p):
l = A[i + offset]
r = A[i + offset + p]
A[i + offset] = (l + r) % FFT.MOD
A[i + offset + p] = (l - r) * irot % FFT.MOD
irot *= self.irate2[(~s & -~s).bit_length()]
irot %= FFT.MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % FFT.MOD
irot3 = irot2 * irot % FFT.MOD
offset = s << (h - le + 2)
for i in range(p):
a0 = A[i + offset]
a1 = A[i + offset + p]
a2 = A[i + offset + p * 2]
a3 = A[i + offset + p * 3]
a2na3iimag = (a2 - a3) * self.IIMAG % FFT.MOD
A[i + offset] = (a0 + a1 + a2 + a3) % FFT.MOD
A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % FFT.MOD
A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % FFT.MOD
A[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % FFT.MOD
irot *= self.irate3[(~s & -~s).bit_length()]
irot %= FFT.MOD
le -= 2
def convolve(self, A, B):
n = len(A)
m = len(B)
if min(n, m) <= 60:
C = [0] * (n + m - 1)
for i in range(n):
if i % 8 == 0:
for j in range(m):
C[i + j] += A[i] * B[j]
C[i + j] %= FFT.MOD
else:
for j in range(m):
C[i + j] += A[i] * B[j]
return [c % FFT.MOD for c in C]
A = A[:]
B = B[:]
z = 1 << (n + m - 2).bit_length()
A += [0] * (z - n)
B += [0] * (z - m)
self.butterfly(A)
self.butterfly(B)
for i in range(z):
A[i] *= B[i]
A[i] %= FFT.MOD
self.butterfly_inv(A)
A = A[:n + m - 1]
iz = pow(z, FFT.MOD - 2, FFT.MOD)
return [a * iz % FFT.MOD for a in A]
n, Q = map(int, input().split())
A = list(map(int, input().split()))
R = list(map(int, input().split()))
B = [0] * n
for r in R:
B[-r] += 1
fft = FFT()
A = fft.convolve(A, B)
for i in range(n, len(A)):
A[i - n] += A[i]
print(*A[:n])