結果

問題 No.931 Multiplicative Convolution
ユーザー ayaoniayaoni
提出日時 2020-12-19 12:05:32
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 251 ms / 2,000 ms
コード長 2,753 bytes
コンパイル時間 205 ms
コンパイル使用メモリ 81,976 KB
実行使用メモリ 121,856 KB
最終ジャッジ日時 2024-09-21 10:11:21
合計ジャッジ時間 5,141 ms
ジャッジサーバーID
(参考情報)
judge4 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 14
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ソースコード

diff #
プレゼンテーションモードにする

import sys
sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def LS2(): return list(sys.stdin.readline().rstrip())
def min_primitive_root(p): # p
if p == 2:
return 1
n = p-1
prime_list = [] # n
for i in range(2,int(n**.5)+1):
if n % i == 0:
prime_list.append(i)
while n % i == 0:
n //= i
if n != 1:
prime_list.append(n)
a = 2 #
n = p-1
while True:
for prime in prime_list:
if pow(a,n//prime,p) == 1:
a += 1
break
else:
return a
# 998244353 = 119*2**23+1
mod = 998244353
primitive_root = 3 # mod
roots = [pow(primitive_root,(mod-1) >> i,mod) for i in range(24)]
inv_roots = [pow(r,mod-2,mod) for r in roots]
# roots[i] = 1 2**i inv_roots[i] = 1 2**i
#
def ntt(A,n):
for i in range(n):
m = 1 << (n-i-1)
for start in range(1 << i):
w = 1
start *= m*2
for j in range(m):
A[start+j],A[start+j+m] = (A[start+j]+A[start+j+m]) % mod,(A[start+j]-A[start+j+m])*w % mod
w *= roots[n-i]
w %= mod
return A
def inv_ntt(A,n):
for i in range(n):
m = 1 << i
for start in range(1 << (n-i-1)):
w = 1
start *= m*2
for j in range(m):
A[start+j],A[start+j+m] = (A[start+j]+A[start+j+m]*w) % mod,(A[start+j]-A[start+j+m]*w) % mod
w *= inv_roots[i+1]
w %= mod
a = pow(2,n*(mod-2),mod)
for i in range(1 << n):
A[i] *= a
A[i] %= mod
return A
def convolution(A,B):
a,b = len(A),len(B)
deg = a+b-2
n = deg.bit_length()
N = 1 << n
A += [0]*(N-a) # A 2-1
B += [0]*(N-b) # B 2-1
A = ntt(A,n)
B = ntt(B,n)
C = [(A[i]*B[i]) % mod for i in range(N)]
C = inv_ntt(C,n)
return C[:deg+1]
P = I()
A,B = [0]+LI(),[0]+LI()
r = min_primitive_root(P)
AA = []
BB = []
x = 1
for i in range(P-1):
AA.append(A[x])
BB.append(B[x])
x *= r
x %= P
CC = convolution(AA,BB)
ANS = [0]*P
x = 1
for i in range(len(CC)):
ANS[x % P] += CC[i]
ANS[x % P] %= mod
x *= r
x %= P
print(*ANS[1:])
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