結果
| 問題 | No.2369 Some Products |
| ユーザー |
 shobonvip
|
| 提出日時 | 2023-06-30 03:11:33 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,574 ms / 2,500 ms |
| コード長 | 6,129 bytes |
| コンパイル時間 | 388 ms |
| コンパイル使用メモリ | 87,152 KB |
| 実行使用メモリ | 469,752 KB |
| 最終ジャッジ日時 | 2023-09-21 14:20:50 |
| 合計ジャッジ時間 | 11,373 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge11 |
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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 | 76 ms
71,224 KB |
| testcase_01 | AC | 78 ms
71,032 KB |
| testcase_02 | AC | 1,574 ms
463,076 KB |
| testcase_03 | AC | 1,483 ms
469,580 KB |
| testcase_04 | AC | 1,484 ms
469,752 KB |
| testcase_05 | AC | 202 ms
102,524 KB |
| testcase_06 | AC | 1,263 ms
469,600 KB |
| testcase_07 | AC | 199 ms
104,956 KB |
| testcase_08 | AC | 334 ms
148,348 KB |
| testcase_09 | AC | 170 ms
86,896 KB |
| testcase_10 | AC | 547 ms
214,712 KB |
| testcase_11 | AC | 999 ms
373,676 KB |
| testcase_12 | AC | 153 ms
87,636 KB |
| testcase_13 | AC | 645 ms
245,548 KB |
| testcase_14 | AC | 734 ms
280,352 KB |
ソースコード
# FFT # code from: https://atcoder.jp/contests/practice2/submissions/24974537 # but changed a little _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): 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) # ---- def poly_inv(a, length = None): if length == None: M = len(a) else: M = length if M <= 0: return [] n = len(a) r = pow(a[0], _fft_mod-2, _fft_mod) m = 1 res = [r] while m < M: f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m)) g = res + [0]*m _butterfly(f) _butterfly(g) for i in range(2*m): f[i] = f[i] * g[i] % _fft_mod _butterfly_inv(f) f = f[m:] + [0]*m _butterfly(f) for i in range(2*m): f[i] = f[i] * g[i] % _fft_mod _butterfly_inv(f) iz = pow(2*m, _fft_mod-2, _fft_mod) iz = (-iz*iz) % _fft_mod for i in range(m): f[i] = f[i] * iz % _fft_mod res += f[:m] m <<= 1 return res[:M] mod = 998244353 n = int(input()) p = list(map(int,input().split())) f = [[0] * (n+1) for i in range(n+1)] f[0][0] = 1 for i in range(n): for j in range(n+1): f[i+1][j] += f[i][j] if j >= 1: f[i+1][j] += f[i][j-1] * p[i] f[i+1][j] %= mod g = [[0] * (n+1) for i in range(n+1)] g[0][0] = 1 for i in range(n): for j in range(n+1): g[i+1][j] = g[i][j] for j in range(1, n+1): g[i+1][j] += g[i+1][j-1] * (-p[i]) g[i+1][j] %= mod q = int(input()) for i in range(q): a, b, k = map(int,input().split()) a -= 1 ans = 0 for j in range(k+1): ans += f[b][j] * g[a][k-j] ans %= mod print(ans)