結果
| 問題 | No.287 場合の数 |
| ユーザー |
 strangerxxx
|
| 提出日時 | 2022-12-20 18:31:58 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 389 ms / 5,000 ms |
| コード長 | 8,365 bytes |
| コンパイル時間 | 207 ms |
| コンパイル使用メモリ | 82,176 KB |
| 実行使用メモリ | 80,776 KB |
| 最終ジャッジ日時 | 2024-11-18 01:58:12 |
| 合計ジャッジ時間 | 8,941 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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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 | 303 ms
79,732 KB |
| testcase_01 | AC | 57 ms
65,152 KB |
| testcase_02 | AC | 102 ms
76,416 KB |
| testcase_03 | AC | 380 ms
80,272 KB |
| testcase_04 | AC | 384 ms
80,148 KB |
| testcase_05 | AC | 299 ms
79,904 KB |
| testcase_06 | AC | 291 ms
79,780 KB |
| testcase_07 | AC | 308 ms
79,872 KB |
| testcase_08 | AC | 300 ms
80,100 KB |
| testcase_09 | AC | 298 ms
79,740 KB |
| testcase_10 | AC | 389 ms
80,272 KB |
| testcase_11 | AC | 285 ms
79,484 KB |
| testcase_12 | AC | 375 ms
80,116 KB |
| testcase_13 | AC | 295 ms
79,008 KB |
| testcase_14 | AC | 296 ms
79,976 KB |
| testcase_15 | AC | 295 ms
80,492 KB |
| testcase_16 | AC | 297 ms
79,604 KB |
| testcase_17 | AC | 380 ms
80,016 KB |
| testcase_18 | AC | 295 ms
79,996 KB |
| testcase_19 | AC | 378 ms
80,776 KB |
| testcase_20 | AC | 292 ms
79,720 KB |
| testcase_21 | AC | 298 ms
79,784 KB |
| testcase_22 | AC | 292 ms
79,968 KB |
| testcase_23 | AC | 296 ms
79,712 KB |
| testcase_24 | AC | 293 ms
79,744 KB |
ソースコード
MOD1 = 998244353
MOD2 = 985661441
MOD3 = 943718401
MOD4 = 935329793
MOD5 = 918552577
mod1 = lambda : MOD1
mod2 = lambda : MOD2
mod3 = lambda : MOD3
mod4 = lambda : MOD4
mod5 = lambda : MOD5
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:
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1: break
else:
return g
g += 1
def popcount(x):
x = ((x >> 1) & 0x55555555) + (x & 0x55555555)
x = ((x >> 2) & 0x33333333) + (x & 0x33333333)
x = ((x >> 4) & 0x0f0f0f0f) + (x & 0x0f0f0f0f)
x = ((x >> 8) & 0x00ff00ff) + (x & 0x00ff00ff)
x = ((x >> 16) & 0x0000ffff) + (x & 0x0000ffff)
return x
def tzcount(x):
return popcount(~x & (x - 1))
def build_ntt(mod):
g = primitive_root(mod())
rank2 = tzcount(mod() - 1)
root = [0] * (rank2 + 1)
iroot = [0] * (rank2 + 1)
rate2 = [0] * max(0, rank2 - 1)
irate2 = [0] * max(0, rank2 - 1)
rate3 = [0] * max(0, rank2 - 2)
irate3 = [0] * max(0, rank2 - 2)
root[rank2] = pow(g, (mod() - 1) >> rank2, mod())
iroot[rank2] = pow(root[rank2], mod() - 2, mod())
for i in range(rank2)[::-1]:
root[i] = root[i + 1] * root[i + 1]
root[i] %= mod()
iroot[i] = iroot[i + 1] * iroot[i + 1]
iroot[i] %= mod()
prod = 1
iprod = 1
for i in range(rank2 - 1):
rate2[i] = root[i + 2] * prod % mod()
irate2[i] = iroot[i + 2] * iprod % mod()
prod *= iroot[i + 2]
prod %= mod()
iprod *= root[i + 2]
iprod %= mod()
prod = 1
iprod = 1
for i in range(rank2 - 2):
rate3[i] = root[i + 3] * prod % mod()
irate3[i] = iroot[i + 3] * iprod % mod()
prod *= iroot[i + 3]
prod %= mod()
iprod *= root[i + 3]
iprod %= mod()
return root, iroot, rate2, irate2, rate3, irate3
def butterfly(a, mod, rate2, irate2, rate3, irate3, imag, iimag):
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 % mod()
a[i + offset] = (l + r) % mod()
a[i + offset + p] = (l - r) % mod()
if s + 1 != 1 << len_:
rot *= rate2[(~s & -~s).bit_length() - 1]
rot %= mod()
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % mod()
rot3 = rot2 * rot % 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) % mod() * imag
a[i + offset] = (a0 + a2 + a1 + a3) % mod()
a[i + offset + p] = (a0 + a2 - a1 - a3) % mod()
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod()
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod()
if s + 1 != 1 << len_:
rot *= rate3[(~s & -~s).bit_length() - 1]
rot %= mod()
len_ += 2
def butterfly_inv(a, mod, rate2, irate2, rate3, irate3, imag, iimag):
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) % mod()
a[i + offset + p] = (l - r) * irot % mod()
if s + 1 != (1 << (len_ - 1)):
irot *= irate2[(~s & -~s).bit_length() - 1]
irot %= mod()
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % mod()
irot3 = irot2 * irot % 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) * iimag % mod()
a[i + offset] = (a0 + a1 + a2 + a3) % mod()
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod()
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod()
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod()
if s + 1 != (1 << (len_ - 2)):
irot *= irate3[(~s & -~s).bit_length() - 1]
irot %= mod()
len_ -= 2
def convolution(a, b, mod):
root, iroot, rate2, irate2, rate3, irate3 = build_ntt(mod)
imag = root[2]
iimag = iroot[2]
n = len(a)
m = len(b)
if not n or not m: return []
if min(n, m) <= 100:
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] %= mod()
return res
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly(a, mod, rate2, irate2, rate3, irate3, imag, iimag)
butterfly(b, mod, rate2, irate2, rate3, irate3, imag, iimag)
for i in range(z):
a[i] *= b[i]
a[i] %= mod()
butterfly_inv(a, mod, rate2, irate2, rate3, irate3, imag, iimag)
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 inv_gcd(a, b):
a %= b
if a == 0: return b, 0
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u
s, t = t, s
m0, m1 = m1, m0
if m0 < 0: m0 += b // s
return s, m0
def gcd(x, y):
while y:
x, y = y, x % y
return x
def crt(r, m):
assert len(r) == len(m)
n = len(r)
r0 = 0
m0 = 1
for i in range(n):
assert 1 <= m[i]
r1 = r[i] % m[i]
m1 = m[i]
if m0 < m1:
r0, r1 = r1, r0
m0, m1 = m1, m0
if m0 % m1 == 0:
if r0 % m1 != r1: return 0, 0
continue
g, im = inv_gcd(m0, m1)
u1 = m1 // g
if (r1 - r0) % g: return 0, 0
x = (r1 - r0) // g * im % u1
r0 += x * m0
m0 *= u1
if (r0 < 0): r0 += m0
return r0, m0
def convolution_64bit(a, b):
n = len(a)
m = len(b)
mask = 18446744073709551615
mods = (MOD1, MOD2, MOD3, MOD4, MOD5)
c1 = convolution([v % MOD1 for v in a], [v % MOD1 for v in b], mod1)[:n + m - 1]
c2 = convolution([v % MOD2 for v in a], [v % MOD2 for v in b], mod2)[:n + m - 1]
c3 = convolution([v % MOD3 for v in a], [v % MOD3 for v in b], mod3)[:n + m - 1]
c4 = convolution([v % MOD4 for v in a], [v % MOD4 for v in b], mod4)[:n + m - 1]
c5 = convolution([v % MOD5 for v in a], [v % MOD5 for v in b], mod5)[:n + m - 1]
res = [0] * (n + m - 1)
for i, v in enumerate(zip(c1, c2, c3, c4, c5)):
cr, cm = crt(v, mods)
res[i] = cr & mask
return res
n = int(input())
x = [1] * (n + 1) + [0] * (5 * n)
ans = x[:]
for _ in range(7):
ans = convolution_64bit(ans, x[:])[:6 * n + 1]
print(ans[6 * n])