結果
| 問題 | No.2633 Subsequence Combination Score |
| ユーザー |
👑  potato167
|
| 提出日時 | 2024-02-17 01:00:59 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,124 ms / 2,000 ms |
| コード長 | 7,299 bytes |
| コンパイル時間 | 540 ms |
| コンパイル使用メモリ | 82,512 KB |
| 実行使用メモリ | 127,260 KB |
| 最終ジャッジ日時 | 2024-09-28 23:19:22 |
| 合計ジャッジ時間 | 47,513 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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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 | 1,055 ms
125,336 KB |
| testcase_01 | AC | 1,077 ms
125,276 KB |
| testcase_02 | AC | 1,066 ms
125,280 KB |
| testcase_03 | AC | 1,093 ms
126,088 KB |
| testcase_04 | AC | 1,056 ms
125,620 KB |
| testcase_05 | AC | 1,057 ms
125,816 KB |
| testcase_06 | AC | 1,081 ms
125,824 KB |
| testcase_07 | AC | 1,068 ms
125,804 KB |
| testcase_08 | AC | 1,078 ms
126,932 KB |
| testcase_09 | AC | 1,112 ms
126,716 KB |
| testcase_10 | AC | 1,088 ms
126,348 KB |
| testcase_11 | AC | 1,089 ms
126,256 KB |
| testcase_12 | AC | 1,071 ms
125,864 KB |
| testcase_13 | AC | 1,076 ms
125,704 KB |
| testcase_14 | AC | 1,074 ms
125,844 KB |
| testcase_15 | AC | 1,078 ms
126,368 KB |
| testcase_16 | AC | 1,077 ms
126,344 KB |
| testcase_17 | AC | 1,089 ms
125,972 KB |
| testcase_18 | AC | 1,072 ms
125,856 KB |
| testcase_19 | AC | 1,103 ms
126,704 KB |
| testcase_20 | AC | 1,078 ms
126,448 KB |
| testcase_21 | AC | 1,079 ms
126,452 KB |
| testcase_22 | AC | 1,085 ms
126,208 KB |
| testcase_23 | AC | 1,100 ms
126,844 KB |
| testcase_24 | AC | 1,090 ms
126,404 KB |
| testcase_25 | AC | 1,110 ms
126,064 KB |
| testcase_26 | AC | 1,069 ms
126,592 KB |
| testcase_27 | AC | 1,075 ms
126,536 KB |
| testcase_28 | AC | 1,074 ms
126,328 KB |
| testcase_29 | AC | 1,088 ms
125,284 KB |
| testcase_30 | AC | 1,069 ms
125,388 KB |
| testcase_31 | AC | 1,087 ms
125,340 KB |
| testcase_32 | AC | 1,079 ms
125,160 KB |
| testcase_33 | AC | 1,078 ms
126,716 KB |
| testcase_34 | AC | 1,094 ms
126,676 KB |
| testcase_35 | AC | 1,067 ms
127,260 KB |
| testcase_36 | AC | 1,078 ms
126,708 KB |
| testcase_37 | AC | 1,096 ms
126,364 KB |
| testcase_38 | AC | 1,124 ms
126,536 KB |
| testcase_39 | AC | 1,116 ms
126,612 KB |
| testcase_40 | AC | 1,071 ms
126,208 KB |
ソースコード
#https://atcoder.jp/contests/practice2/submissions/24974537
_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 % _fft_mod
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_ - 1)):
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] = (ans[i + j] + a[i] * b[j]) % _fft_mod
else:
for i in range(n):
for j in range(m):
ans[i + j] = (ans[i + j] + a[i] * b[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] = a[i] * b[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] = a[i] * iz % _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] = a[i] * iz % _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) <= 0:
return _convolution_naive(a, b)
if a is b:
return _convolution_square(a)
return _convolution_fft(a, b)
N=int(input())
A=list(map(int,input().split()))
mod=998244353
L=(1<<17)
B=[0]*L
for a in A:
B[a]+=1
dp=[0]*L
fact=[1]*L
for i in range(1,L): fact[i]=fact[i-1]*i%mod
fact_inv=[1]*L
fact_inv[L-1]=pow(fact[L-1],-1,mod)
for i in range(L-1,0,-1): fact_inv[i-1]=fact_inv[i]*i%mod
def f(l,r):
if l+1==r:
dp[l]+=fact_inv[l]
dp[l]*=(pow(2,B[l],mod)-1)
dp[l]%=mod
return dp[l]*fact[l]%mod
res=0
m=(l+r)//2
res+=f(l,m)
p=[0]*(m-l)
q=[0]*(r-l)
for i in range(m-l): p[i]=dp[i+l]
for i in range(r-l): q[i]=fact_inv[i]
p=convolution(p,q)
for i in range(r-m): dp[i+m]=(dp[i+m]+p[i+m-l])%mod
res+=f(m,r)
return res%mod
print(f(0,L))