結果

問題 No.931 Multiplicative Convolution
ユーザー ygd.
提出日時 2022-03-05 17:33:29
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 668 ms / 2,000 ms
コード長 3,483 bytes
コンパイル時間 200 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 171,084 KB
最終ジャッジ日時 2024-07-19 23:18:53
合計ジャッジ時間 7,867 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 14
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 #
プレゼンテーションモードにする

import sys
#input = sys.stdin.readline
input = sys.stdin.buffer.readline #
#sys.setrecursionlimit(1000000)
#import bisect
#import itertools
#import random
#from heapq import heapify, heappop, heappush
#from collections import defaultdict
#from collections import deque
#import copy
#import math
#from functools import lru_cache
#@lru_cache(maxsize=None)
#MOD = pow(10,9) + 7
MOD = 998244353
#dx = [1,0,-1,0]
#dy = [0,1,0,-1]
import random
def prime_factorize(n):
ret = []
#if n == 1:
# ret.append((1,1))
# return ret
cnt = 0
while n % 2 == 0:
cnt += 1
n //= 2
if cnt > 0:
ret.append((2,cnt))
i = 3
while i * i <= n:
cnt = 0
while n % i == 0:
cnt += 1
n //= i
else:
if cnt != 0: #cnt==0
ret.append((i,cnt))
i += 2
if n != 1:
ret.append((n,1))
return ret #()
def get_root(p):
#p-1
L = prime_factorize(p-1)
#p-1pia^((p-1)/pi) != 1
while True:
a = random.randint(2,p-1) #2 <= a <= p-1
for pi, dummy in L:
x = (p-1)//pi
if pow(a,x,p) == 1:
break
else:
return a
rt = 3
#rtn.rt^MOD-1 = 1n
def pr(n):
return pow(rt, (MOD-1)//n, MOD)
def convolution(a,b):
#3998244353. 3^998244352 = 1
#998244352 = 2^23 * 7 * 17
d = len(a) + len(b) - 1 #
#2^ndn
n = 1
while (1<<n) < d:
n += 1
N = 1 << n
w = pr(N)
#a,b2
a += [0] * (N - len(a))
b += [0] * (N - len(b))
A = FFT(a,w)
B = FFT(b,w)
#
C = [A[i] * B[i] % MOD for i in range(N)]
#print(w)
winv = pow(w, MOD-2,MOD)
c = FFT(C, winv) #wwinv
Ninv = pow(N, MOD-2,MOD) #1/N
for i in range(N):
c[i] *= Ninv
c[i] %= MOD
return c
def FFT(a,w): #Σ(ai * w^(ik))
#O(N)O(logN)
N = len(a)
if N == 1: return a
even = a[::2]
odd = a[1::2] #12(1)
ww = w * w % MOD
EVEN = FFT(even, ww%MOD)
ODD = FFT(odd, ww%MOD)
A = [0] * N
wk = 1 #w^k
for k in range(N):
A[k] = (EVEN[k%(N//2)] + wk * ODD[k%(N//2)] %MOD) %MOD
wk = wk * w %MOD
return A
def main():
P = int(input())
A = [0] + list(map(int,input().split()))
B = [0] + list(map(int,input().split()))
if P == 2:
ans = A[1]*B[1]%MOD
print(ans);exit()
#g
AN = [0]*P
BN = [0]*P
g = get_root(P)
#print(g)
v = 1
for i in range(P-1): #g^i = v
AN[i] = A[v]
BN[i] = B[v]
v *= g
v %= P
#print(AN,BN)
CN = convolution(AN,BN)
#print(CN)
C = [0]*P
v = 1
for i in range(len(CN)):
C[v] += CN[i]
C[v] %= MOD
v *= g
v %= P
print(*C[1:])
if __name__ == '__main__':
main()
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