結果
| 問題 | No.2506 Sum of Weighted Powers |
| ユーザー |
 suisen
|
| 提出日時 | 2023-03-31 21:29:27 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 474 ms / 2,000 ms |
| コード長 | 6,641 bytes |
| コンパイル時間 | 306 ms |
| コンパイル使用メモリ | 82,048 KB |
| 実行使用メモリ | 149,864 KB |
| 最終ジャッジ日時 | 2024-09-15 14:12:11 |
| 合計ジャッジ時間 | 9,142 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
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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 | 74 ms
67,968 KB |
| testcase_01 | AC | 72 ms
67,968 KB |
| testcase_02 | AC | 73 ms
68,096 KB |
| testcase_03 | AC | 118 ms
79,104 KB |
| testcase_04 | AC | 79 ms
70,400 KB |
| testcase_05 | AC | 76 ms
68,992 KB |
| testcase_06 | AC | 128 ms
79,360 KB |
| testcase_07 | AC | 120 ms
79,104 KB |
| testcase_08 | AC | 129 ms
79,616 KB |
| testcase_09 | AC | 119 ms
79,104 KB |
| testcase_10 | AC | 129 ms
79,488 KB |
| testcase_11 | AC | 128 ms
79,744 KB |
| testcase_12 | AC | 76 ms
68,736 KB |
| testcase_13 | AC | 104 ms
78,976 KB |
| testcase_14 | AC | 79 ms
70,144 KB |
| testcase_15 | AC | 80 ms
70,400 KB |
| testcase_16 | AC | 105 ms
78,720 KB |
| testcase_17 | AC | 121 ms
79,488 KB |
| testcase_18 | AC | 124 ms
79,616 KB |
| testcase_19 | AC | 106 ms
78,336 KB |
| testcase_20 | AC | 121 ms
79,104 KB |
| testcase_21 | AC | 131 ms
79,232 KB |
| testcase_22 | AC | 122 ms
79,104 KB |
| testcase_23 | AC | 291 ms
126,152 KB |
| testcase_24 | AC | 421 ms
134,408 KB |
| testcase_25 | AC | 223 ms
103,276 KB |
| testcase_26 | AC | 432 ms
140,592 KB |
| testcase_27 | AC | 158 ms
83,072 KB |
| testcase_28 | AC | 470 ms
149,480 KB |
| testcase_29 | AC | 474 ms
149,704 KB |
| testcase_30 | AC | 467 ms
148,800 KB |
| testcase_31 | AC | 469 ms
149,864 KB |
| testcase_32 | AC | 468 ms
149,604 KB |
| testcase_33 | AC | 73 ms
67,968 KB |
| testcase_34 | AC | 74 ms
67,968 KB |
| testcase_35 | AC | 179 ms
124,628 KB |
| testcase_36 | AC | 183 ms
133,508 KB |
| testcase_37 | AC | 73 ms
68,224 KB |
| testcase_38 | AC | 80 ms
67,840 KB |
| testcase_39 | AC | 74 ms
67,968 KB |
| testcase_40 | AC | 74 ms
68,096 KB |
| testcase_41 | AC | 74 ms
67,968 KB |
ソースコード
from typing import List
def bsf(x):
res = 0
while not (x & 1):
res += 1
x >>= 1
return res
P = 943718401
G = 7
rank2 = bsf(P - 1)
class NTT:
class __RootInitializer:
@staticmethod
def root():
return [pow(G, (P - 1) >> i, P) for i in range(0, rank2 + 1)]
@staticmethod
def iroot():
return [pow(pow(G, P - 2, P), (P - 1) >> i, P) for i in range(0, rank2 + 1)]
root = __RootInitializer.root()
iroot = __RootInitializer.iroot()
class __RateInitializer:
@staticmethod
def rates(root: List[int], iroot: List[int]):
rate2 = [0] * max(0, rank2 - 1)
irate2 = [0] * max(0, rank2 - 1)
prod = iprod = 1
for i in range(rank2 - 1):
rate2[i] = root[i + 2] * prod % P
irate2[i] = iroot[i + 2] * iprod % P
prod = prod * iroot[i + 2] % P
iprod = iprod * root[i + 2] % P
rate3 = [0] * max(0, rank2 - 2)
irate3 = [0] * max(0, rank2 - 2)
prod = iprod = 1
for i in range(rank2 - 2):
rate3[i] = root[i + 3] * prod % P
irate3[i] = iroot[i + 3] * iprod % P
prod = prod * iroot[i + 3] % P
iprod = iprod * root[i + 3] % P
return rate2, irate2, rate3, irate3
rate2, irate2, rate3, irate3 = __RateInitializer.rates(__RootInitializer.root(), __RootInitializer.iroot())
@staticmethod
def butterfly(a: List[int]) -> None:
n = len(a)
h = bsf(n)
l = 0
while l < h:
if h - l == 1:
p = 1 << (h - l - 1)
rot = 1
for s in range(1 << l):
offset = s << (h - l)
for i in range(p):
u = a[i + offset]
v = a[i + offset + p] * rot
a[i + offset] = (u + v) % P
a[i + offset + p] = (u - v) % P
if s + 1 != 1 << l:
rot = rot * NTT.rate2[bsf(~s)] % P
l += 1
else:
p = 1 << (h - l - 2)
rot, imag = 1, NTT.root[2]
for s in range(1 << l):
rot2 = rot * rot % P
rot3 = rot2 * rot % P
offset = s << (h - l)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + 2 * p] * rot2
a3 = a[i + offset + 3 * p] * rot3
a1na3imag = (a1 - a3) % P * imag
a[i + offset] = (a0 + a2 + a1 + a3) % P
a[i + offset + 1 * p] = (a0 + a2 - a1 - a3) % P
a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % P
a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % P
if s + 1 != (1 << l):
rot = rot * NTT.rate3[bsf(~s)] % P
l += 2
@staticmethod
def butterfly_inv(a : List[int]) -> None:
n = len(a)
h = bsf(n)
l = h
while l:
if l == 1:
p = 1 << (h - l)
irot = 1
for s in range(1 << (l - 1)):
offset = s << (h - l + 1)
for i in range(p):
u = a[i + offset]
v = a[i + offset + p]
a[i + offset] = (u + v) % P
a[i + offset + p] = ((u - v) * irot) % P
if s + 1 != 1 << (l - 1):
irot = irot * NTT.irate2[bsf(~s)] % P
l -= 1
else:
p = 1 << (h - l)
irot = 1
iimag = NTT.iroot[2]
for s in range(1 << (l - 2)):
irot2 = irot * irot % P
irot3 = irot2 * irot % P
offset = s << (h - l + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + 2 * p]
a3 = a[i + offset + 3 * p]
a2na3iimag = (a2 - a3) * iimag % P
a[i + offset] = (a0 + a1 + a2 + a3) % P
a[i + offset + p] = ((a0 - a1 + a2na3iimag) * irot) % P
a[i + offset + 2 * p] = ((a0 + a1 - a2 - a3) * irot2) % P
a[i + offset + 3 * p] = ((a0 - a1 - a2na3iimag) * irot3) % P
if s + 1 != 1 << (l - 2):
irot = irot * NTT.irate3[bsf(~s)] % P
l -= 2
@staticmethod
def convolution(a, b):
n = len(a)
m = len(b)
if not a or not b:
return []
if min(n, m) <= 40:
if n < m:
n, m = m, n
a, b = b, a
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= P
return res
z = 1 << ((n + m - 1).bit_length())
iz = pow(z, P - 2, P)
a += [0] * (z - n)
b += [0] * (z - m)
NTT.butterfly(a)
NTT.butterfly(b)
c = [a[i] * b[i] % P * iz % P for i in range(z)]
NTT.butterfly_inv(c)
return c[:n + m - 1]
n, x = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = list(map(int, input().split()))
if x == 0:
ans = sum(A[i] * B[i] % P * C[0] % P for i in range(n + 1)) + sum(A[i] * B[0] % P * C[i] % P for i in range(1, n + 1))
print(ans % P)
else:
def enumerate_powers(x, n):
x2 = x * x % P
pow_x2 = 1 # x ** (2i)
y = 1 # x ** (i(i + 1))
z = 1 # x ** t(i)
yield z
for _ in range(n):
yield z
pow_x2 = pow_x2 * x2 % P
y = y * pow_x2 % P
z = z * y % P
t = lambda k : (k - 1) * k * (k + 1) // 3
inv_x = pow(x, P - 2, P)
pows_inv_x = list(enumerate_powers(inv_x, n))
pows_x = list(enumerate_powers(x, n))
F = [B[i] * pows_inv_x[i] % P for i in range(n + 1)]
G = [C[i] * pows_inv_x[i] % P for i in range(n + 1)]
H = NTT.convolution(F, G)
ans = sum(A[i] * pows_x[i] % P * H[i] % P for i in range(n + 1))
print(ans % P)