結果
| 問題 |
No.2215 Slide Subset Sum
|
| コンテスト | |
| ユーザー |
 Shirotsume
|
| 提出日時 | 2023-02-05 20:19:48 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 9,147 bytes |
| コンパイル時間 | 284 ms |
| コンパイル使用メモリ | 82,376 KB |
| 実行使用メモリ | 111,532 KB |
| 最終ジャッジ日時 | 2024-07-04 06:49:30 |
| 合計ジャッジ時間 | 6,532 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | -- * 2 |
| other | AC * 1 TLE * 1 -- * 43 |
ソースコード
import sys
from collections import deque, Counter
input = lambda: sys.stdin.readline().rstrip()
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
inf = 2 ** 63 - 1
mod = 998244353
"""
Reference
https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
https://github.com/atcoder/ac-library/blob/master/document_en/convolution.md
https://github.com/atcoder/ac-library/blob/master/document_ja/convolution.md
"""
mod = 998244353
def primitive_root(m):
if m == 2:
return 1
if m == 167772161:
return 3
if m == 469762049:
return 3
if m == 754974721:
return 11
if m == 998244353:
return 3
divs = [0] * 20
divs[0] = 2
cnt = 1
x = (m - 1) // 2
while x % 2 == 0:
x //= 2
i = 3
while i * i <= x:
if x % i == 0:
divs[cnt] = i
cnt += 1
while x % i == 0:
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while True:
ok = True
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1:
ok = False
break
if ok:
return g
g += 1
class FFT_INFO:
def __init__(self):
self.g = primitive_root(mod)
self.rank2 = ((mod - 1) & (1 - mod)).bit_length() - 1
self.root = [0] * (self.rank2 + 1)
self.root[self.rank2] = pow(self.g, (mod - 1) >> self.rank2, mod)
self.iroot = [0] * (self.rank2 + 1)
self.iroot[self.rank2] = pow(self.root[self.rank2], mod - 2, mod)
for i in range(self.rank2 - 1, -1, -1):
self.root[i] = self.root[i + 1] * self.root[i + 1] % mod
self.iroot[i] = self.iroot[i + 1] * self.iroot[i + 1] % mod
self.rate2 = [0] * max(0, self.rank2 - 1)
self.irate2 = [0] * max(0, self.rank2 - 1)
prod = 1
iprod = 1
for i in range(self.rank2 - 1):
self.rate2[i] = self.root[i + 2] * prod % mod
self.irate2[i] = self.iroot[i + 2] * iprod % mod
prod *= self.iroot[i + 2]
prod %= mod
iprod *= self.root[i + 2]
iprod %= mod
self.rate3 = [0] * max(0, self.rank2 - 2)
self.irate3 = [0] * max(0, self.rank2 - 2)
prod = 1
iprod = 1
for i in range(self.rank2 - 2):
self.rate3[i] = self.root[i + 3] * prod % mod
self.irate3[i] = self.iroot[i + 3] * iprod % mod
prod *= self.iroot[i + 3]
prod %= mod
iprod *= self.root[i + 3]
iprod %= mod
info = FFT_INFO()
def butterfly(a):
n = len(a)
h = (n - 1).bit_length()
length = 0
while length < h:
if h - length == 1:
p = 1 << (h - length - 1)
rot = 1
for s in range(1 << length):
offset = s << (h - length)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot % mod
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) % mod
if s + 1 != (1 << length):
rot *= info.rate2[(~s & -~s).bit_length() - 1]
rot %= mod
length += 1
else:
# 4-base
p = 1 << (h - length - 2)
rot = 1
imag = info.root[2]
for s in range(1 << length):
rot2 = rot * rot % mod
rot3 = rot2 * rot % mod
offset = s << (h - length)
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) % mod * imag
a[i + offset] = (a0 + a2 + a1 + a3) % mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % mod
a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % mod
if s + 1 != (1 << length):
rot *= info.rate3[(~s & -~s).bit_length() - 1]
rot %= mod
length += 2
def butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
length = h # a[i, i+(n<<length), i+2*(n>>length), ...] is transformed
while length:
if length == 1:
p = 1 << (h - length)
irot = 1
for s in range(1 << (length - 1)):
offset = s << (h - length + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) * irot % mod
if s + 1 != (1 << (length - 1)):
irot *= info.irate2[(~s & -~s).bit_length() - 1]
irot %= mod
length -= 1
else:
# 4-base
p = 1 << (h - length)
irot = 1
iimag = info.iroot[2]
for s in range(1 << (length - 2)):
irot2 = irot * irot % mod
irot3 = irot2 * irot % mod
offset = s << (h - length + 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 % mod
a[i + offset] = (a0 + a1 + a2 + a3) % mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
a[i + offset + 2 * p] = (a0 + a1 - a2 - a3) * irot2 % mod
a[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3 % mod
if s + 1 != (1 << (length - 2)):
irot *= info.irate3[(~s & -~s).bit_length() - 1]
irot %= mod
length -= 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] %= mod
else:
for i in range(n):
for j in range(m):
ans[i + j] += a[i] * b[j]
ans[i + j] %= 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] %= mod
butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, mod - 2, mod)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= mod
return a
def convolution(a, b):
n = len(a)
m = len(b)
if not n or not m:
return []
if min(n, m) <= 60:
return convolution_naive(a, b)
return convolution_fft(a, b)
n, m, k = mi()
a = li()
#以降, k を MAXI とおく
MAXI = k
#生の値を持つstack2つと、dpテーブルを持つstack2つを用意
valuetop = []
valuebottom = []
dptop = []
dpbottom = []
#番兵として、空集合に対応するdpテーブルを用意する
X = [0] * MAXI
X[0] = 1
dptop.append(X)
dpbottom.append(X)
def push(x):
#queueへのpush操作。bottomに値を追加してdpを更新するだけ
valuebottom.append(x)
ndp = [0] * MAXI
for v in range(MAXI):
ndp[(v+x)%MAXI] += dpbottom[-1][v]
ndp[v] += dpbottom[-1][v]
ndp[(v+x)%MAXI] %= mod
ndp[v] %= mod
dpbottom.append(ndp)
def pop():
#queueからのpop操作。topのstackに値が入っていればそこからpop。入っていなければ、今bottomにある要素を全部出して反転させてtopに入れる。
#各要素について、範囲外→top→bottom→範囲外（途中で終わる可能性もある）と移動するので、計算量は償却O(NK)
if not valuetop:
valuebottom.reverse()
for x in valuebottom:
ndp = [0] * MAXI
for v in range(MAXI):
ndp[(v+x)%MAXI] += dptop[-1][v]
ndp[v] += dptop[-1][v]
ndp[(v+x)%MAXI] %= mod
ndp[v] %= mod
dptop.append(ndp)
valuetop.append(x)
while valuebottom:
valuebottom.pop()
while len(dpbottom) > 1:
dpbottom.pop()
dptop.pop()
valuetop.pop()
def fold():
#2つのテーブルdptopとdpbottomの結果を統合する。計算量O(K)
d = convolution(dptop[-1], dpbottom[-1])
ans = (d[0] + d[k]) % mod
return ans
for i in range(m):
push(a[i])
ans = []
ans.append(fold())
for i in range(m, n):
pop()
push(a[i])
ans.append(fold())
for v in ans:
print((v-1) % mod)