結果
| 問題 | No.931 Multiplicative Convolution |
| ユーザー |
 mkawa2
|
| 提出日時 | 2023-03-17 18:40:58 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 267 ms / 2,000 ms |
| コード長 | 5,988 bytes |
| コンパイル時間 | 689 ms |
| コンパイル使用メモリ | 81,652 KB |
| 実行使用メモリ | 134,500 KB |
| 最終ジャッジ日時 | 2023-10-18 13:48:06 |
| 合計ジャッジ時間 | 5,679 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge14 |
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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 | 40 ms
53,136 KB |
| testcase_01 | AC | 41 ms
53,176 KB |
| testcase_02 | AC | 40 ms
53,128 KB |
| testcase_03 | AC | 40 ms
53,160 KB |
| testcase_04 | AC | 40 ms
53,164 KB |
| testcase_05 | AC | 43 ms
54,176 KB |
| testcase_06 | AC | 89 ms
74,544 KB |
| testcase_07 | AC | 102 ms
78,100 KB |
| testcase_08 | AC | 218 ms
108,280 KB |
| testcase_09 | AC | 194 ms
111,892 KB |
| testcase_10 | AC | 216 ms
110,324 KB |
| testcase_11 | AC | 198 ms
110,940 KB |
| testcase_12 | AC | 185 ms
94,928 KB |
| testcase_13 | AC | 267 ms
134,500 KB |
| testcase_14 | AC | 230 ms
112,296 KB |
| testcase_15 | AC | 219 ms
107,556 KB |
| testcase_16 | AC | 215 ms
107,968 KB |
ソースコード
import sys
# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
# md = 10**9+7
md = 998244353
IMAG = 911660635
IIMAG = 86583718
rate2 = (
0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456,
131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443,
56250497,
867605899, 0)
irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882,
927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183,
824071951, 103369235, 0)
rate3 = (
0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
183021267,
402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365,
530924681, 0)
def butterfly(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)%md
a[i+offset+p] = (l-r)%md
rot *= rate2[(~s & -~s).bit_length()]
rot %= md
le += 1
else:
p = 1 << (h-le-2)
rot = 1
for s in range(1 << le):
rot2 = rot*rot%md
rot3 = rot2*rot%md
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)%md*IMAG
a[i+offset] = (a0+a2+a1+a3)%md
a[i+offset+p] = (a0+a2-a1-a3)%md
a[i+offset+p*2] = (a0-a2+a1na3imag)%md
a[i+offset+p*3] = (a0-a2-a1na3imag)%md
rot *= rate3[(~s & -~s).bit_length()]
rot %= md
le += 2
def butterfly_inv(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)%md
a[i+offset+p] = (l-r)*irot%md
irot *= irate2[(~s & -~s).bit_length()]
irot %= md
le -= 1
else:
p = 1 << (h-le)
irot = 1
for s in range(1 << (le-2)):
irot2 = irot*irot%md
irot3 = irot2*irot%md
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)*IIMAG%md
a[i+offset] = (a0+a1+a2+a3)%md
a[i+offset+p] = (a0-a1+a2na3iimag)*irot%md
a[i+offset+p*2] = (a0+a1-a2-a3)*irot2%md
a[i+offset+p*3] = (a0-a1-a2na3iimag)*irot3%md
irot *= irate3[(~s & -~s).bit_length()]
irot %= md
le -= 2
def multiply(s, t):
n = len(s)
m = len(t)
if min(n, m) <= 60:
a = [0]*(n+m-1)
for i in range(n):
if i%8 == 0:
for j in range(m):
a[i+j] += s[i]*t[j]
a[i+j] %= md
else:
for j in range(m):
a[i+j] += s[i]*t[j]
return [x%md for x in a]
a = s.copy()
b = t.copy()
z = 1 << (n+m-2).bit_length()
a += [0]*(z-n)
b += [0]*(z-m)
butterfly(a)
butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= md
butterfly_inv(a)
a = a[:n+m-1]
iz = pow(z, md-2, md)
return [v*iz%md for v in a]
def find_primitive_root(p):
def is_primitive_root(r):
atoe = [-1]*p
a = 1
for e in range(p-1):
if atoe[a] != -1: return None
atoe[a] = e
a = a*r%p
return atoe
for r in range(2, p):
atoe = is_primitive_root(r)
if atoe: return atoe
return None
p = II()
aa = LI()
bb = LI()
if p == 2:
print(aa[0]*bb[0]%md)
exit()
itoe = find_primitive_root(p)
etoi = [-1]*p
for i, e in enumerate(itoe[1:], 1): etoi[e] = i
def toxx(aa):
xx = [0]*p
for i, a in enumerate(aa, 1):
e = itoe[i]
xx[e] += a
return xx
xx = toxx(aa)
yy = toxx(bb)
cc = multiply(xx, yy)
# print(cc)
ans = [0]*p
for e, c in enumerate(cc):
i = etoi[e%(p-1)]
ans[i] += c
ans[i] %= md
print(*ans[1:])