結果
問題 | No.2237 Xor Sum Hoge |
ユーザー | shobonvip |
提出日時 | 2023-03-03 22:02:47 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 4,017 ms / 10,000 ms |
コード長 | 5,997 bytes |
コンパイル時間 | 317 ms |
コンパイル使用メモリ | 82,616 KB |
実行使用メモリ | 277,676 KB |
最終ジャッジ日時 | 2024-09-17 23:03:38 |
合計ジャッジ時間 | 111,376 ms |
ジャッジサーバーID (参考情報) |
judge5 / 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 | 3,762 ms
271,336 KB |
testcase_01 | AC | 2,071 ms
260,608 KB |
testcase_02 | AC | 2,052 ms
260,916 KB |
testcase_03 | AC | 2,044 ms
261,012 KB |
testcase_04 | AC | 2,070 ms
260,828 KB |
testcase_05 | AC | 2,074 ms
261,392 KB |
testcase_06 | AC | 1,999 ms
261,648 KB |
testcase_07 | AC | 2,067 ms
261,384 KB |
testcase_08 | AC | 2,054 ms
261,504 KB |
testcase_09 | AC | 2,067 ms
261,400 KB |
testcase_10 | AC | 2,047 ms
261,120 KB |
testcase_11 | AC | 2,075 ms
263,612 KB |
testcase_12 | AC | 3,713 ms
270,040 KB |
testcase_13 | AC | 4,017 ms
271,104 KB |
testcase_14 | AC | 3,692 ms
275,024 KB |
testcase_15 | AC | 3,785 ms
269,044 KB |
testcase_16 | AC | 3,809 ms
270,524 KB |
testcase_17 | AC | 3,780 ms
272,324 KB |
testcase_18 | AC | 3,681 ms
269,084 KB |
testcase_19 | AC | 3,705 ms
265,696 KB |
testcase_20 | AC | 3,996 ms
272,932 KB |
testcase_21 | AC | 3,834 ms
273,128 KB |
testcase_22 | AC | 3,794 ms
270,828 KB |
testcase_23 | AC | 3,784 ms
274,580 KB |
testcase_24 | AC | 3,712 ms
270,152 KB |
testcase_25 | AC | 3,822 ms
273,180 KB |
testcase_26 | AC | 3,838 ms
273,424 KB |
testcase_27 | AC | 3,799 ms
271,620 KB |
testcase_28 | AC | 3,727 ms
275,204 KB |
testcase_29 | AC | 3,715 ms
270,808 KB |
testcase_30 | AC | 3,842 ms
277,676 KB |
testcase_31 | AC | 1,981 ms
261,836 KB |
testcase_32 | AC | 2,022 ms
261,864 KB |
testcase_33 | AC | 2,028 ms
262,720 KB |
testcase_34 | AC | 2,003 ms
261,956 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) # ---- mod = 998244353 N = 3 * 10**5 + 5 fact = [1]*(N+1) factinv = [1]*(N+1) for i in range(2, N+1): fact[i] = fact[i-1] * i % mod factinv[-1] = pow(fact[-1], mod-2, mod) for i in range(N-1, 1, -1): factinv[i] = factinv[i+1] * (i+1) % mod def cmb(a, b): if (a < b) or (b < 0): return 0 return fact[a] * factinv[b] % mod * factinv[a-b] % mod n,b,c = map(int,input().split()) # 下から決めていく # dp[i][j] : 下から i 桁決めたとき, 余りが j (かならず 1.2×10^5 以下) dp = [[0] * 120001 for i in range(80)] dp[0][0] = 1 # 0, cmb(n, 1), cmb(n, 2), ..., n を加算する! ar0 = [0] * (n+1) ar1 = [0] * (n+1) for i in range(n+1): if i % 2 == 0: ar0[i] = cmb(n, i) else: ar1[i] = cmb(n, i) for num in range(79): for i in range(120001): dp[num+1][i//2] += dp[num][i] dp[num+1][i//2] %= mod if (c >> num) & 1: dp[num+1] = convolution(dp[num+1], ar1)[:120001] else: dp[num+1] = convolution(dp[num+1], ar0)[:120001] for i in range(120001): if (i & 1) != (b >> num) & 1: dp[num+1][i] = 0 if i > (b >> num): dp[num+1][i] = 0 print(dp[79][0])