#994483 (C++17(gcc12)) No.2810 Have Another Go (Hard)

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問題	No.2810 Have Another Go (Hard)
ユーザー	tokusakurai
提出日時	2024-07-12 22:46:53
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	2,613 ms / 3,000 ms
コード長	13,978 bytes
コンパイル時間	2,609 ms
コンパイル使用メモリ	215,148 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-12 22:48:31
合計ジャッジ時間	96,352 ms
ジャッジサーバーID （参考情報）	judge2 / judge1
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ファイルパターン	結果
other	AC * 61
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n) - 1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r) - 1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
void err_print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cerr << v[i] + x << ' ';
    cerr << endl;
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template <typename T, bool is_float = false>
struct Matrix {
    vector<vector<T>> A;
    int n, m;

    Matrix() = default;

    Matrix(int n) : A(n, vector<T>(n, 0)), n(n), m(n) {}

    Matrix(int n, int m) : A(n, vector<T>(m, 0)), n(n), m(m) {}

    Matrix(const vector<vector<T>> &A) : A(A), n((int)A.size()), m(A.empty() ? 0 : (int)A[0].size()) {}

    inline const vector<T> &operator[](int k) const { return A[k]; }

    inline vector<T> &operator[](int k) { return A[k]; }

    static Matrix I(int l) {
        Matrix ret(l, l);
        for (int i = 0; i < l; i++) ret[i][i] = 1;
        return ret;
    }

    Matrix &operator+=(const Matrix &B) {
        assert(n == B.n && m == B.m);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) A[i][j] += B[i][j];
        }
        return *this;
    }

    Matrix &operator-=(const Matrix &B) {
        assert(n == B.n && m == B.m);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) A[i][j] -= B[i][j];
        }
        return *this;
    }

    Matrix &operator*=(const Matrix &B) {
        assert(m == B.n);
        Matrix ret(n, B.m);
        for (int i = 0; i < n; i++) {
            for (int k = 0; k < m; k++) {
                for (int j = 0; j < B.m; j++) ret[i][j] += A[i][k] * B[k][j];
            }
        }
        swap(A, ret.A);
        m = B.m;
        return *this;
    }

    Matrix &operator/=(const Matrix &B) {
        *this *= B.inverse();
        return *this;
    }

    Matrix operator-() const {
        Matrix ret(n, m);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) ret[i][j] = -A[i][j];
        }
        return ret;
    }

    Matrix operator+(const Matrix &B) const { return Matrix(*this) += B; }

    Matrix operator-(const Matrix &B) const { return Matrix(*this) -= B; }

    Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }

    Matrix operator/(const Matrix &B) const { return Matrix(*this) /= B; }

    bool operator==(const Matrix &B) const { return A == B.A; }

    bool operator!=(const Matrix &B) const { return A != B.A; }

    Matrix pow(long long k) const {
        assert(n == m);
        Matrix now = *this, ret = I(n);
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    Matrix transpose() const {
        Matrix ret(m, n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) ret[j][i] = A[i][j];
        }
        return ret;
    }

    Matrix submatrix(vector<int> rs, vector<int> cs) {
        int sub_n = rs.size(), sub_m = cs.size();
        Matrix ret(sub_n, sub_m);
        for (int i = 0; i < sub_n; i++) {
            for (int j = 0; j < sub_m; j++) ret[i][j] = A[rs[i]][cs[j]];
        }
        return ret;
    }

    Matrix submatrix(int lr, int rr, int lc, int rc) {
        assert(0 <= lr && lr <= rr && rr <= n);
        assert(0 <= lc && lc <= rc && rc <= m);
        int sub_n = rr - lr, sub_m = rc - lc;
        Matrix ret(sub_n, sub_m);
        for (int i = 0; i < sub_n; i++) {
            for (int j = 0; j < sub_m; j++) ret[i][j] = A[lr + i][lc + j];
        }
        return ret;
    }

    static bool eq(const T &a, const T &b) {
        if constexpr (is_float) return abs(a - b) <= 1e-6;
        return a == b;
    }

    int get_pivot(int j, int i) {
        int pivot = i;
        for (int k = i + 1; k < n; k++) {
            if constexpr (is_float) {
                if (abs(A[k][j]) > abs(A[pivot][j])) pivot = k;
            } else {
                if (A[k][j] != 0) pivot = k;
            }
        }
        return pivot;
    }

    // 行基本変形を用いて簡約化を行い、(rank, det) の組を返す
    pair<int, T> row_reduction(vector<T> &b) {
        assert((int)b.size() == n);
        if (n == 0) return make_pair(0, m > 0 ? 0 : 1);
        int check = 0, rank = 0;
        T det = (n == m ? 1 : 0);
        for (int j = 0; j < m; j++) {
            int pivot = get_pivot(j, check);
            if (check != pivot) det = -det;
            swap(A[check], A[pivot]), swap(b[check], b[pivot]);
            if (eq(A[check][j], T(0))) {
                det = T(0);
                continue;
            }
            rank++;
            det *= A[check][j];
            T r = T(1) / A[check][j];
            for (int k = j + 1; k < m; k++) A[check][k] *= r;
            b[check] *= r;
            A[check][j] = T(1);
            for (int i = 0; i < n; i++) {
                if (i == check) continue;
                if (!eq(A[i][j], 0)) {
                    for (int k = j + 1; k < m; k++) A[i][k] -= A[i][j] * A[check][k];
                    b[i] -= A[i][j] * b[check];
                }
                A[i][j] = T(0);
            }
            if (++check == n) break;
        }
        return make_pair(rank, det);
    }

    pair<int, T> row_reduction() {
        vector<T> b(n, T(0));
        return row_reduction(b);
    }

    int rank() const { return Matrix(*this).row_reduction().first; }

    T determinant() const {
        assert(n == m);
        return Matrix(*this).row_reduction().second;
    }

    pair<bool, Matrix> inverse() {
        if (n != m) return make_pair(false, Matrix(0, 0));
        if (n == 0) return make_pair(true, Matrix(0, 0));
        vector<vector<T>> A_cpy = A;
        Matrix ret = I(n);
        for (int j = 0; j < n; j++) {
            int pivot = get_pivot(j, j);
            swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);
            if (eq(A[j][j], T(0))) return make_pair(false, Matrix(0, 0));
            T r = T(1) / A[j][j];
            for (int k = j + 1; k < n; k++) A[j][k] *= r;
            for (int k = 0; k < n; k++) ret[j][k] *= r;
            A[j][j] = T(1);
            for (int i = 0; i < n; i++) {
                if (i == j) continue;
                if (!eq(A[i][j], T(0))) {
                    for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];
                    for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];
                }
                A[i][j] = T(0);
            }
        }
        A = A_cpy;
        return make_pair(true, ret);
    }
};

using mat = Matrix<mint>;

void solve() {
    ll N, M, Q;
    cin >> N >> M >> Q;

    auto calc = [&](ll n) {
        if (n < 0) return mint(0);
        mat A(6, 6);
        rep(j, 6) A[j][0] = 1;
        rep(i, 5) A[i][i + 1] = 1;
        mat x(1, 6);
        x[0][0] = 1;
        x *= A.pow(n);
        return x[0][0];
    };

    // n-5 から n まで
    auto calc_range = [&](ll n) {
        if (n < 0) return vector<mint>(6, 0);
        mat A(6, 6);
        rep(j, 6) A[j][0] = 1;
        rep(i, 5) A[i][i + 1] = 1;
        mat x(1, 6);
        x[0][0] = 1;
        x *= A.pow(n);
        vector<mint> ret(6, 0);
        rep(i, 6) ret[i] = x[0][i];
        reverse(all(ret));
        return ret;
    };

    // n 以上になるまでの操作の場合の数
    auto calc2 = [&](ll n) {
        if (n <= 0) return mint(1);
        auto v = calc_range(n - 1);
        mint sum = 0;
        rep(i, 6) sum += v[i] * (i + 1);
        return sum;
    };

    mat A(5, 5);
    rep(i, 5) rep(j, 5) {
        rep2(k, 1, 7) {
            if (i + k <= 5) continue;
            A[i][j] += calc(N + j - (i + k));
        }
    }

    // rep(i, 5) print(A[i]);

    A = A.pow(M - 1);

    mint sum = calc2(N * M);

    // rep(i, 20) cout << calc(i) << endl;

    while (Q--) {
        ll y;
        cin >> y;

        mat x(1, 5);
        {
            auto v = calc_range(y - 1);
            rep(i, 5) x[0][i] = v[i + 1];
        }

        x *= A;
        mint ans = sum;

        rep(i, 5) {
            rep2(k, 1, 7) {
                if (i + k <= 5) continue;
                ll z = y - 5 + i + k;
                ans -= x[0][i] * calc2(N - z);
            }
        }

        cout << ans << '\n';
    }
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
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結果

ソースコード
