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 | 408 ms / 5,000 ms |
コード長 | 8,365 bytes |
コンパイル時間 | 163 ms |
コンパイル使用メモリ | 82,304 KB |
実行使用メモリ | 81,032 KB |
最終ジャッジ日時 | 2024-04-29 02:53:41 |
合計ジャッジ時間 | 9,742 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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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 | 324 ms
79,852 KB |
testcase_01 | AC | 62 ms
65,280 KB |
testcase_02 | AC | 106 ms
76,496 KB |
testcase_03 | AC | 401 ms
80,148 KB |
testcase_04 | AC | 405 ms
80,144 KB |
testcase_05 | AC | 308 ms
79,724 KB |
testcase_06 | AC | 296 ms
79,644 KB |
testcase_07 | AC | 316 ms
79,740 KB |
testcase_08 | AC | 315 ms
79,708 KB |
testcase_09 | AC | 313 ms
79,864 KB |
testcase_10 | AC | 398 ms
80,148 KB |
testcase_11 | AC | 301 ms
79,620 KB |
testcase_12 | AC | 408 ms
80,008 KB |
testcase_13 | AC | 321 ms
79,132 KB |
testcase_14 | AC | 326 ms
79,732 KB |
testcase_15 | AC | 323 ms
79,724 KB |
testcase_16 | AC | 308 ms
79,476 KB |
testcase_17 | AC | 393 ms
80,016 KB |
testcase_18 | AC | 307 ms
79,740 KB |
testcase_19 | AC | 394 ms
81,032 KB |
testcase_20 | AC | 308 ms
79,468 KB |
testcase_21 | AC | 315 ms
79,856 KB |
testcase_22 | AC | 311 ms
79,724 KB |
testcase_23 | AC | 308 ms
79,580 KB |
testcase_24 | AC | 314 ms
79,860 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])