結果

問題 No.3243 Multiplication 8 1
ユーザー 👑 loop0919
提出日時 2025-08-22 23:13:20
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 122 ms / 2,000 ms
コード長 3,256 bytes
コンパイル時間 2,122 ms
コンパイル使用メモリ 205,040 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-08-22 23:14:11
合計ジャッジ時間 2,886 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 4
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 # 

/*
[Original Python code — included per AtCoder rule]

MOD = 998244353


def power(A, e):
    result = [[1 if i == j else 0 for j in range(len(A))] for i in range(len(A))]

    while e:
        if e % 2:
            result = multiply(result, A)
        A = multiply(A, A)
        e //= 2

    return result


def multiply(A, B):
    return [[sum(x * y % MOD for x, y in zip(A_row, B_col)) % MOD for B_col in zip(*B)] for A_row in A]


def multiply_vector(M, v):
    return [sum(M[i][j] * v[j] % MOD for j in range(len(v))) % MOD for i in range(len(M))]


X = [
    [1, 1, 1, 1, 0, 0, 0],  # 1
    [1, 1, 1, 1, 0, 0, 0],  # -1 ok
    [0, 0, 1, 1, 1, 1, 0],  # 2
    [0, 0, 1, 1, 1, 1, 0],  # -2
    [1, 0, 0, 0, 1, 1, 1],  # 4
    [1, 0, 0, 0, 1, 1, 1],  # -4
    [1, 0, 0, 0, 0, 0, 1],  # -1 ng
]

Y = [
    [1, 1],
    [1, 1],
]


def solve():
    N = int(input())
    ans = multiply_vector(power(X, N), [1, 0, 0, 0, 0, 0, 0])[0]
    ans -= multiply_vector(power(Y, N), [1, 0])[0]
    print(ans % MOD)


if __name__ == "__main__":
    T = int(input())
    for _ in range(T):
        solve()
*/

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
const ll MOD = 998244353;

using Mat = vector<vector<ll>>;

static Mat identity(int n) {
    Mat I(n, vector<ll>(n, 0));
    for (int i = 0; i < n; ++i) I[i][i] = 1;
    return I;
}

static Mat multiply(const Mat& A, const Mat& B) {
    int n = (int)A.size();
    int m = (int)A[0].size();         // also B.size()
    int p = (int)B[0].size();
    Mat C(n, vector<ll>(p, 0));
    for (int i = 0; i < n; ++i) {
        for (int k = 0; k < m; ++k) {
            ll aik = A[i][k] % MOD;
            if (aik == 0) continue;
            for (int j = 0; j < p; ++j) {
                C[i][j] = (C[i][j] + aik * (B[k][j] % MOD)) % MOD;
            }
        }
    }
    return C;
}

static vector<ll> multiply_vector(const Mat& M, const vector<ll>& v) {
    int n = (int)M.size();
    int m = (int)v.size();
    vector<ll> res(n, 0);
    for (int i = 0; i < n; ++i) {
        ll s = 0;
        for (int j = 0; j < m; ++j) {
            s = (s + (M[i][j] % MOD) * (v[j] % MOD)) % MOD;
        }
        res[i] = s;
    }
    return res;
}

static Mat power(Mat A, long long e) {
    int n = (int)A.size();
    Mat R = identity(n);
    while (e) {
        if (e & 1) R = multiply(R, A);
        A = multiply(A, A);
        e >>= 1;
    }
    return R;
}

// Constants from the original code
const Mat X = {
    {1, 1, 1, 1, 0, 0, 0},  // 1
    {1, 1, 1, 1, 0, 0, 0},  // -1 ok
    {0, 0, 1, 1, 1, 1, 0},  // 2
    {0, 0, 1, 1, 1, 1, 0},  // -2
    {1, 0, 0, 0, 1, 1, 1},  // 4
    {1, 0, 0, 0, 1, 1, 1},  // -4
    {1, 0, 0, 0, 0, 0, 1},  // -1 ng
};

const Mat Y = {
    {1, 1},
    {1, 1},
};

void solve() {
    long long N;
    cin >> N;
    vector<ll> vX = {1, 0, 0, 0, 0, 0, 0};
    vector<ll> vY = {1, 0};

    ll a = multiply_vector(power(X, N), vX)[0];
    ll b = multiply_vector(power(Y, N), vY)[0];

    ll ans = (a - b) % MOD;
    if (ans < 0) ans += MOD;  // Python's `%` yields non-negative; emulate it
    cout << ans << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int T;
    if (!(cin >> T)) return 0;
    while (T--) solve();
    return 0;
}
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