結果
問題 | No.1302 Random Tree Score |
ユーザー |
![]() |
提出日時 | 2020-10-29 21:06:21 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 2,329 ms / 3,000 ms |
コード長 | 9,173 bytes |
コンパイル時間 | 423 ms |
コンパイル使用メモリ | 82,500 KB |
実行使用メモリ | 240,764 KB |
最終ジャッジ日時 | 2024-07-21 22:39:47 |
合計ジャッジ時間 | 22,578 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
#Convolution_998244353MOD = 998244353ROOT = 3sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263,730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)def butterfly(arr):n = len(arr)h = (n - 1).bit_length()for ph in range(1, h + 1):w = 1 << (ph - 1)p = 1 << (h - ph)now = 1for s in range(w):offset = s << (h - ph + 1)for i in range(p):l = arr[i + offset]r = arr[i + offset + p] * nowarr[i + offset] = (l + r) % MODarr[i + offset + p] = (l - r) % MODnow *= sum_e[(~s & -~s).bit_length() - 1]now %= MODdef butterfly_inv(arr):n = len(arr)h = (n - 1).bit_length()for ph in range(1, h + 1)[::-1]:w = 1 << (ph - 1)p = 1 << (h - ph)inow = 1for s in range(w):offset = s << (h - ph + 1)for i in range(p):l = arr[i + offset]r = arr[i + offset + p]arr[i + offset] = (l + r) % MODarr[i + offset + p] = (MOD + l - r) * inow % MODinow *= sum_ie[(~s & -~s).bit_length() - 1]inow %= MODdef convolution(a, b):n = len(a)m = len(b)if not n or not m: return []if min(n, m) <= 50:if n < m:n, m = m, na, b = b, ares = [0] * (n + m - 1)for i in range(n):for j in range(m):res[i + j] += a[i] * b[j]res[i + j] %= MODreturn resz = 1 << (n + m - 2).bit_length()a += [0] * (z - n)b += [0] * (z - m)butterfly(a)butterfly(b)for i in range(z):a[i] *= b[i]a[i] %= MODbutterfly_inv(a)a = a[:n + m - 1]iz = pow(z, MOD - 2, MOD)for i in range(n + m - 1):a[i] *= iza[i] %= MODreturn adef autocorrelation(a):n = len(a)if not n: return []if n <= 50:res = [0] * (2 * n - 1)for i in range(n):for j in range(n):res[i + j] += a[i] * a[j]res[i + j] %= MODreturn resz = 1 << (2 * n - 2).bit_length()a += [0] * (z - n)butterfly(a)for i in range(z):a[i] *= a[i]a[i] %= MODbutterfly_inv(a)a = a[:2 * n - 1]iz = pow(z, MOD - 2, MOD)for i in range(2 * n - 1):a[i] *= iza[i] %= MODreturn adef add(a, b):return [(va + vb) % MOD for va, vb in zip(a, b)]def sub(a, b):return [(va - vb) % MOD for va, vb in zip(a, b)]def times(a, k):return [v * k % MOD for v in a]def multiply(a, b):return convolution(a.copy(), b.copy())def square(a):return autocorrelation(a.copy())def inverse(a):n = len(a)r = pow(a[0], MOD - 2, MOD)m = 1tmp = [r]while m < n:tmp += [0] * mm *= 2tmp = sub(times(tmp, 2), multiply(a[:m], square(tmp.copy())[:m]))res = tmp[:n]return resdef differentiate(a):n = len(a)res = [0] * nfor i in range(1, n):res[i - 1] = a[i] * i % MODreturn resdef integrate(a):n = len(a)res = [0] * nfor i in range(n - 1):res[i + 1] = a[i] * pow(i + 1, MOD - 2, MOD) % MODreturn resdef log(a):#assert a[0] == 1n = len(a)return integrate(multiply(differentiate(a), inverse(a))[:n])def exp(a):#assert a[0] == 0n = len(a)res = [1]g = [1]q = differentiate(a)m = 1while m < n:g = sub(times(g, 2), multiply(res, square(g)[:m]))g += [0] * mres += [0] * mm *= 2w = add(q[:m], multiply(g, sub(differentiate(res), multiply(res, q[:m])[:m]))[:m])res = add(res, multiply(res, sub(a[:m], integrate(w)))[:m])return res[:n]#Convolution_998244353MOD = 998244353ROOT = 3sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263,730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)def butterfly(arr):n = len(arr)h = (n - 1).bit_length()for ph in range(1, h + 1):w = 1 << (ph - 1)p = 1 << (h - ph)now = 1for s in range(w):offset = s << (h - ph + 1)for i in range(p):l = arr[i + offset]r = arr[i + offset + p] * nowarr[i + offset] = (l + r) % MODarr[i + offset + p] = (l - r) % MODnow *= sum_e[(~s & -~s).bit_length() - 1]now %= MODdef butterfly_inv(arr):n = len(arr)h = (n - 1).bit_length()for ph in range(1, h + 1)[::-1]:w = 1 << (ph - 1)p = 1 << (h - ph)inow = 1for s in range(w):offset = s << (h - ph + 1)for i in range(p):l = arr[i + offset]r = arr[i + offset + p]arr[i + offset] = (l + r) % MODarr[i + offset + p] = (MOD + l - r) * inow % MODinow *= sum_ie[(~s & -~s).bit_length() - 1]inow %= MODdef convolution(a, b):n = len(a)m = len(b)if not n or not m: return []if min(n, m) <= 50:if n < m:n, m = m, na, b = b, ares = [0] * (n + m - 1)for i in range(n):for j in range(m):res[i + j] += a[i] * b[j]res[i + j] %= MODreturn resz = 1 << (n + m - 2).bit_length()a += [0] * (z - n)b += [0] * (z - m)butterfly(a)butterfly(b)for i in range(z):a[i] *= b[i]a[i] %= MODbutterfly_inv(a)a = a[:n + m - 1]iz = pow(z, MOD - 2, MOD)for i in range(n + m - 1):a[i] *= iza[i] %= MODreturn adef autocorrelation(a):n = len(a)if not n: return []if n <= 50:res = [0] * (2 * n - 1)for i in range(n):for j in range(n):res[i + j] += a[i] * a[j]res[i + j] %= MODreturn resz = 1 << (2 * n - 2).bit_length()a += [0] * (z - n)butterfly(a)for i in range(z):a[i] *= a[i]a[i] %= MODbutterfly_inv(a)a = a[:2 * n - 1]iz = pow(z, MOD - 2, MOD)for i in range(2 * n - 1):a[i] *= iza[i] %= MODreturn adef add(a, b):return [(va + vb) % MOD for va, vb in zip(a, b)]def sub(a, b):return [(va - vb) % MOD for va, vb in zip(a, b)]def times(a, k):return [v * k % MOD for v in a]def multiply(a, b):return convolution(a.copy(), b.copy())def square(a):return autocorrelation(a.copy())def inverse(a):n = len(a)r = pow(a[0], MOD - 2, MOD)m = 1tmp = [r]while m < n:tmp += [0] * mm *= 2tmp = sub(times(tmp, 2), multiply(a[:m], square(tmp.copy())[:m]))res = tmp[:n]return resdef differentiate(a):n = len(a)res = [0] * nfor i in range(1, n):res[i - 1] = a[i] * i % MODreturn resdef integrate(a):n = len(a)res = [0] * nfor i in range(n - 1):res[i + 1] = a[i] * pow(i + 1, MOD - 2, MOD) % MODreturn resdef log(a):#assert a[0] == 1n = len(a)return integrate(multiply(differentiate(a), inverse(a))[:n])def exp(a):#assert a[0] == 0n = len(a)res = [1]g = [1]q = differentiate(a)m = 1while m < n:g = sub(times(g, 2), multiply(res, square(g)[:m]))g += [0] * mres += [0] * mm *= 2w = add(q[:m], multiply(g, sub(differentiate(res), multiply(res, q[:m])[:m]))[:m])res = add(res, multiply(res, sub(a[:m], integrate(w)))[:m])return res[:n]def make_fac(limit):fac = [1]*limitfor i in range(2,limit):fac[i] = i * fac[i-1]%MODfaci = [0]*limitfaci[-1] = pow(fac[-1], MOD -2, MOD)for i in range(limit-2, -1, -1):faci[i] = faci[i+1] * (i + 1) % MODreturn fac, facifac, faci = make_fac(134139)import sysreadline = sys.stdin.readlineN = int(readline())W = [1] + [(1 if i&1 else -1)*pow(i, i-1, MOD)*faci[i]%MOD for i in range(2, N+2)]print(exp(times(log(multiply([1]+W, inverse(autocorrelation(W)[:N]))[:N]), N-1))[N-2]*fac[N-2]*pow(N, (N-2)*(MOD-2)%(MOD-1), MOD)%MOD)