結果

問題 No.1753 Don't cheat.
ユーザー zkou
提出日時 2021-06-19 17:05:07
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,309 ms / 3,000 ms
コード長 2,812 bytes
コンパイル時間 633 ms
コンパイル使用メモリ 82,248 KB
実行使用メモリ 85,892 KB
最終ジャッジ日時 2024-12-31 18:24:13
合計ジャッジ時間 29,652 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
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ファイルパターン 結果
sample AC * 2
other AC * 30
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ソースコード

diff #
プレゼンテーションモードにする

MOD = 998244353
half = pow(2, MOD - 2, MOD)
def int2frac(n, m=None, N = 10000, D = 10000):
"""
Return (r, s) s.t. r = s * n (mod m) if such a pair exists.
Otherwise, return (0, 0).
Parameters
----------
n: an integer that will be represented as a fraction.
m: A modulus used to represent n.
N: An upperbound of r, which is the numerator of n.
D: An upperbound of s, which is the denominator of n.
"""
def gcd(a, b):
while b:
a, b = b, a % b
return a
if m is None:
m = MOD
v = (m, 0)
w = (n, 1)
while w[0] > N:
q = v[0] // w[0]
v, w = w, (v[0] - q * w[0], v[1] - q * w[1])
if w[1] < 0:
w = (-w[0], -w[1])
if w[1] <= D and gcd(w[0], w[1]) == 1:
return w
else:
return (0, 0)
def fwht(a) -> None:
"""
In-place Fast Walsh–Hadamard Transform of array a.
Reference: https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform
"""
h = 1
while h < len(a):
for i in range(0, len(a), h * 2):
for j in range(i, i + h):
x = a[j]
y = a[j + h]
a[j] = (x + y) % MOD
a[j + h] = (x - y) % MOD
h *= 2
def ifwht(a) -> None:
"""
In-place Inverse Fast Walsh–Hadamard Transform of array a.
Reference: https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform
"""
h = 1
while h < len(a):
for i in range(0, len(a), h * 2):
for j in range(i, i + h):
x = a[j]
y = a[j + h]
a[j] = (x + y) * half % MOD
a[j + h] = (x - y) * half % MOD
h *= 2
N = int(input())
As = list(map(int, input().split()))
assert 1 <= N <= 2 * 10 ** 3
assert all(0 <= A <= 10 ** 5 for A in As)
assert N + 1 == len(As)
assert As[0]
sumAs = sum(As)
invsumAs = pow(sum(As), MOD - 2, MOD)
for i in range(N + 1):
As[i] *= invsumAs
As[i] %= MOD
# print([int2frac(A) for A in As])
z = 1 << N.bit_length()
A0 = [0] * z
A0[0] = As[0]
fwht(A0)
As_fwht = As + [0] * (z - N - 1)
fwht(As_fwht)
assert all((As[0] + 1 - As_fwht[k]) % MOD != 0 for k in range(z))
q = [pow(As[0] + 1 - As_fwht[k], MOD - 2, MOD) * A0[k] % MOD for k in range(z)]
ifwht(q)
ps = []
for x in range(1, N + 1):
A0 = [0] * z
A0[0] = As[x]
fwht(A0)
Ax = As + [0] * (z - N - 1)
Ax[0] = 0
Ax[x] = 0
fwht(Ax)
assert all((1 - Ax[k]) % MOD != 0 for k in range(z))
p = [pow(1 - Ax[k], MOD - 2, MOD) * A0[k] % MOD for k in range(z)]
ifwht(p)
ps.append(p)
# print(x, [int2frac(e) for e in p])
answer = q[0]
for p in ps:
for xor in range(z):
answer += p[xor] * q[xor] % MOD
answer %= MOD
print((1 - answer) % MOD)
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