結果

問題 No.1753 Don't cheat.
ユーザー zkouzkou
提出日時 2021-06-19 17:05:07
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,298 ms / 3,000 ms
コード長 2,812 bytes
コンパイル時間 381 ms
コンパイル使用メモリ 87,076 KB
実行使用メモリ 87,424 KB
最終ジャッジ日時 2023-08-30 06:18:17
合計ジャッジ時間 30,460 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge13
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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 72 ms
71,424 KB
testcase_01 AC 71 ms
71,416 KB
testcase_02 AC 72 ms
71,308 KB
testcase_03 AC 72 ms
71,268 KB
testcase_04 AC 71 ms
71,528 KB
testcase_05 AC 71 ms
71,272 KB
testcase_06 AC 72 ms
71,152 KB
testcase_07 AC 1,220 ms
86,948 KB
testcase_08 AC 1,270 ms
87,364 KB
testcase_09 AC 742 ms
83,092 KB
testcase_10 AC 1,239 ms
86,940 KB
testcase_11 AC 773 ms
83,604 KB
testcase_12 AC 1,183 ms
86,624 KB
testcase_13 AC 882 ms
83,768 KB
testcase_14 AC 1,089 ms
85,472 KB
testcase_15 AC 1,199 ms
86,576 KB
testcase_16 AC 931 ms
84,720 KB
testcase_17 AC 1,287 ms
87,424 KB
testcase_18 AC 1,156 ms
86,048 KB
testcase_19 AC 949 ms
84,444 KB
testcase_20 AC 1,204 ms
86,516 KB
testcase_21 AC 875 ms
83,384 KB
testcase_22 AC 1,116 ms
85,600 KB
testcase_23 AC 785 ms
83,380 KB
testcase_24 AC 1,250 ms
86,648 KB
testcase_25 AC 981 ms
84,816 KB
testcase_26 AC 1,294 ms
87,352 KB
testcase_27 AC 1,297 ms
87,320 KB
testcase_28 AC 1,294 ms
87,048 KB
testcase_29 AC 1,298 ms
87,372 KB
testcase_30 AC 1,284 ms
87,008 KB
testcase_31 AC 1,291 ms
87,348 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

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)
0