結果
| 問題 | No.1302 Random Tree Score |
| ユーザー |
 tpyneriver
|
| 提出日時 | 2020-10-29 21:06:21 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 2,398 ms / 3,000 ms |
| コード長 | 9,173 bytes |
| コンパイル時間 | 2,091 ms |
| コンパイル使用メモリ | 86,900 KB |
| 実行使用メモリ | 241,208 KB |
| 最終ジャッジ日時 | 2023-09-29 04:05:54 |
| 合計ジャッジ時間 | 23,299 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge15 |
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 | 82 ms
77,636 KB |
| testcase_01 | AC | 83 ms
77,696 KB |
| testcase_02 | AC | 659 ms
113,464 KB |
| testcase_03 | AC | 1,238 ms
157,716 KB |
| testcase_04 | AC | 657 ms
113,128 KB |
| testcase_05 | AC | 2,375 ms
239,704 KB |
| testcase_06 | AC | 2,371 ms
240,004 KB |
| testcase_07 | AC | 661 ms
114,300 KB |
| testcase_08 | AC | 1,270 ms
160,772 KB |
| testcase_09 | AC | 2,382 ms
241,208 KB |
| testcase_10 | AC | 2,304 ms
232,924 KB |
| testcase_11 | AC | 637 ms
111,552 KB |
| testcase_12 | AC | 2,338 ms
237,084 KB |
| testcase_13 | AC | 85 ms
77,828 KB |
| testcase_14 | AC | 2,387 ms
240,848 KB |
| testcase_15 | AC | 2,398 ms
240,704 KB |
| testcase_16 | AC | 83 ms
77,776 KB |
ソースコード
#Convolution_998244353
MOD = 998244353
ROOT = 3
sum_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 = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD
arr[i + offset + p] = (l - r) % MOD
now *= sum_e[(~s & -~s).bit_length() - 1]
now %= MOD
def 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 = 1
for 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) % MOD
arr[i + offset + p] = (MOD + l - r) * inow % MOD
inow *= sum_ie[(~s & -~s).bit_length() - 1]
inow %= MOD
def 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, 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)
butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD
butterfly_inv(a)
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 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] %= MOD
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly(a)
for i in range(z):
a[i] *= a[i]
a[i] %= MOD
butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, MOD - 2, MOD)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD
return a
def 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 = 1
tmp = [r]
while m < n:
tmp += [0] * m
m *= 2
tmp = sub(times(tmp, 2), multiply(a[:m], square(tmp.copy())[:m]))
res = tmp[:n]
return res
def differentiate(a):
n = len(a)
res = [0] * n
for i in range(1, n):
res[i - 1] = a[i] * i % MOD
return res
def integrate(a):
n = len(a)
res = [0] * n
for i in range(n - 1):
res[i + 1] = a[i] * pow(i + 1, MOD - 2, MOD) % MOD
return res
def log(a):
#assert a[0] == 1
n = len(a)
return integrate(multiply(differentiate(a), inverse(a))[:n])
def exp(a):
#assert a[0] == 0
n = len(a)
res = [1]
g = [1]
q = differentiate(a)
m = 1
while m < n:
g = sub(times(g, 2), multiply(res, square(g)[:m]))
g += [0] * m
res += [0] * m
m *= 2
w = 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_998244353
MOD = 998244353
ROOT = 3
sum_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 = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD
arr[i + offset + p] = (l - r) % MOD
now *= sum_e[(~s & -~s).bit_length() - 1]
now %= MOD
def 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 = 1
for 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) % MOD
arr[i + offset + p] = (MOD + l - r) * inow % MOD
inow *= sum_ie[(~s & -~s).bit_length() - 1]
inow %= MOD
def 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, 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)
butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD
butterfly_inv(a)
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 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] %= MOD
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly(a)
for i in range(z):
a[i] *= a[i]
a[i] %= MOD
butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, MOD - 2, MOD)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD
return a
def 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 = 1
tmp = [r]
while m < n:
tmp += [0] * m
m *= 2
tmp = sub(times(tmp, 2), multiply(a[:m], square(tmp.copy())[:m]))
res = tmp[:n]
return res
def differentiate(a):
n = len(a)
res = [0] * n
for i in range(1, n):
res[i - 1] = a[i] * i % MOD
return res
def integrate(a):
n = len(a)
res = [0] * n
for i in range(n - 1):
res[i + 1] = a[i] * pow(i + 1, MOD - 2, MOD) % MOD
return res
def log(a):
#assert a[0] == 1
n = len(a)
return integrate(multiply(differentiate(a), inverse(a))[:n])
def exp(a):
#assert a[0] == 0
n = len(a)
res = [1]
g = [1]
q = differentiate(a)
m = 1
while m < n:
g = sub(times(g, 2), multiply(res, square(g)[:m]))
g += [0] * m
res += [0] * m
m *= 2
w = 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]*limit
for i in range(2,limit):
fac[i] = i * fac[i-1]%MOD
faci = [0]*limit
faci[-1] = pow(fac[-1], MOD -2, MOD)
for i in range(limit-2, -1, -1):
faci[i] = faci[i+1] * (i + 1) % MOD
return fac, faci
fac, faci = make_fac(134139)
import sys
readline = sys.stdin.readline
N = 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)