結果
| 問題 | No.2062 Sum of Subset mod 999630629 |
| ユーザー |
 zkou
|
| 提出日時 | 2022-08-26 23:18:41 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 7,975 bytes |
| コンパイル時間 | 161 ms |
| コンパイル使用メモリ | 82,176 KB |
| 実行使用メモリ | 268,652 KB |
| 最終ジャッジ日時 | 2024-10-14 01:09:08 |
| 合計ジャッジ時間 | 30,857 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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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 | 137 ms
147,200 KB |
| testcase_01 | AC | 136 ms
146,944 KB |
| testcase_02 | AC | 140 ms
146,944 KB |
| testcase_03 | AC | 137 ms
146,816 KB |
| testcase_04 | AC | 139 ms
146,816 KB |
| testcase_05 | AC | 137 ms
146,816 KB |
| testcase_06 | AC | 137 ms
146,944 KB |
| testcase_07 | AC | 138 ms
146,944 KB |
| testcase_08 | AC | 163 ms
168,704 KB |
| testcase_09 | AC | 157 ms
164,352 KB |
| testcase_10 | AC | 156 ms
162,560 KB |
| testcase_11 | AC | 506 ms
182,144 KB |
| testcase_12 | AC | 512 ms
183,040 KB |
| testcase_13 | AC | 345 ms
178,688 KB |
| testcase_14 | AC | 514 ms
183,296 KB |
| testcase_15 | AC | 243 ms
174,592 KB |
| testcase_16 | AC | 575 ms
181,504 KB |
| testcase_17 | AC | 521 ms
182,144 KB |
| testcase_18 | AC | 354 ms
178,688 KB |
| testcase_19 | AC | 286 ms
174,464 KB |
| testcase_20 | AC | 400 ms
176,256 KB |
| testcase_21 | AC | 433 ms
177,792 KB |
| testcase_22 | AC | 356 ms
176,256 KB |
| testcase_23 | AC | 159 ms
166,656 KB |
| testcase_24 | AC | 159 ms
166,784 KB |
| testcase_25 | AC | 2,847 ms
268,416 KB |
| testcase_26 | AC | 2,851 ms
268,496 KB |
| testcase_27 | AC | 2,832 ms
268,652 KB |
| testcase_28 | AC | 2,942 ms
268,388 KB |
| testcase_29 | AC | 2,330 ms
260,104 KB |
| testcase_30 | AC | 1,987 ms
259,624 KB |
| testcase_31 | TLE | - |
ソースコード
# For the sake of speed,
# this convolution is specialized to mod 998244353.
_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (
911660635,
509520358,
369330050,
332049552,
983190778,
123842337,
238493703,
975955924,
603855026,
856644456,
131300601,
842657263,
730768835,
942482514,
806263778,
151565301,
510815449,
503497456,
743006876,
741047443,
56250497,
867605899,
)
_fft_irate2 = (
86583718,
372528824,
373294451,
645684063,
112220581,
692852209,
155456985,
797128860,
90816748,
860285882,
927414960,
354738543,
109331171,
293255632,
535113200,
308540755,
121186627,
608385704,
438932459,
359477183,
824071951,
103369235,
)
_fft_rate3 = (
372528824,
337190230,
454590761,
816400692,
578227951,
180142363,
83780245,
6597683,
70046822,
623238099,
183021267,
402682409,
631680428,
344509872,
689220186,
365017329,
774342554,
729444058,
102986190,
128751033,
395565204,
)
_fft_irate3 = (
509520358,
929031873,
170256584,
839780419,
282974284,
395914482,
444904435,
72135471,
638914820,
66769500,
771127074,
985925487,
262319669,
262341272,
625870173,
768022760,
859816005,
914661783,
430819711,
272774365,
530924681,
)
def _butterfly(a):
n = len(a)
h = (n - 1).bit_length()
len_ = 0
while len_ < h:
if h - len_ == 1:
p = 1 << (h - len_ - 1)
rot = 1
for s in range(1 << len_):
offset = s << (h - len_)
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
if s + 1 != (1 << len_):
rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % _fft_mod
rot3 = rot2 * rot % _fft_mod
offset = s << (h - len_)
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 * _fft_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
if s + 1 != (1 << len_):
rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 2
def _butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
len_ = h
while len_:
if len_ == 1:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 1)):
offset = s << (h - len_ + 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
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % _fft_mod
irot3 = irot2 * irot % _fft_mod
offset = s << (h - len_ + 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) * _fft_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
)
if s + 1 != (1 << (len_ - 2)):
irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 2
def _convolution_naive(a, b):
n = len(a)
m = len(b)
ans = [0] * (n + m - 1)
if n < m:
for j in range(m):
for i in range(n):
ans[i + j] += a[i] * b[j]
ans[i + j] %= _fft_mod
else:
for i in range(n):
for j in range(m):
ans[i + j] += a[i] * b[j]
ans[i + j] %= _fft_mod
return ans
def _convolution_fft(a, b):
a = a.copy()
b = b.copy()
n = len(a)
m = len(b)
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
b += [0] * (z - m)
_butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= _fft_mod
_butterfly_inv(a)
a = a[: n + m - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= _fft_mod
return a
def _convolution_square(a):
a = a.copy()
n = len(a)
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
for i in range(z):
a[i] *= a[i]
a[i] %= _fft_mod
_butterfly_inv(a)
a = a[: 2 * n - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= _fft_mod
return a
def convolution(a, b):
"""It calculates (+, x) convolution in mod 998244353.
Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],
it calculates the array c of length n + m - 1, defined by
> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
It returns an empty list if at least one of a and b are empty.
Constraints
-----------
> len(a) + len(b) <= 8388609
Complexity
----------
> O(n log n), where n = len(a) + len(b).
"""
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 60:
return _convolution_naive(a, b)
if a is b:
return _convolution_square(a)
return _convolution_fft(a, b)
MOD = 998244353
table_len = 10**6 + 10
fac = [1, 1]
for i in range(2, table_len):
fac.append(fac[-1] * i % MOD)
finv = [0] * table_len
finv[-1] = pow(fac[-1], MOD - 2, MOD)
for i in range(table_len - 1, 0, -1):
finv[i - 1] = finv[i] * i % MOD
def comb(n, k):
if k < 0 or n < 0 or n - k < 0:
return 0
return fac[n] * finv[k] % MOD * finv[n - k] % MOD
from collections import Counter
P1 = 998244353
P2 = 999630629
# N = 10**5
# As = [10000] * N
N = int(input())
As = list(map(int, input().split()))
answer = pow(2, N - 1, P1) * sum(As) % P1
# #{ S | P2 <= \sum_{i \in S} A_i }
# = #{ S' | sum(As) - P2 >= \sum_{i \in S'} A_i }
weight_ub = sum(As) - P2 + 1
if weight_ub < 0:
print(answer)
exit()
prod = [1]
for A, count in Counter(As).items():
f = [0] * (weight_ub)
for i in range(0, weight_ub, A):
f[i] = comb(count, i // A)
prod = convolution(prod, f)[:weight_ub]
answer -= P2 * (sum(prod) % P1) % P1
answer %= P1
print(answer)