#606863 (C++17) No.1340 おーじ君をさがせ

• 問題: No.1340 おーじ君をさがせ
• ユーザー: r1933
• 提出日時: 2021-01-17 17:15:19
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 47 ms / 2,000 ms
• コード長: 8,126 bytes
• コンパイル時間: 3,246 ms
• コンパイル使用メモリ: 221,172 KB
• 最終ジャッジ日時: 2025-01-18 01:46:07
• ジャッジサーバーID （参考情報）: judge4 / judge4

ファイルパターン	結果
sample	AC * 3
other	AC * 59

ソースコード

#pragma GCC optimize("Ofast")
#include "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define repc(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline istream& operator>>(istream &is, Container &vs) {
    for (auto &v: vs) is >> v;
    return is;
}

inline void output() { cout << "\n"; }
template <class Head, class... Tail>
inline void output(Head&& head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) cout << " ";
    output(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline ostream& operator<<(ostream &os, const Container &vs) {
    static constexpr const char *delim[] = {" ", ""};
    for (auto it = begin(vs); it != end(vs); ++it) {
        os << delim[it == begin(vs)] << *it;
    }
    return os;
}

template <class Iterator>
inline void join(const Iterator &Begin, const Iterator &End, const string &delim = "\n", const string &last = "\n") {
    for (auto it = Begin; it != End; ++it) {
        cout << ((it == Begin) ? "" : delim) << *it;
    }
    cout << last;
}

template <class T>
inline vector<T> makeVector(const T &init_value, size_t sz) {
    return vector<T>(sz, init_value);
}

template <class T, class... Args>
inline auto makeVector(const T &init_value, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(init_value, args...))>(sz, makeVector<T>(init_value, args...));
}

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class Container>
struct reverse_t {
    Container &c;
    reverse_t(Container &c) : c(c) {}
    auto begin() { return c.rbegin(); }
    auto end() { return c.rend(); }
};

template <class Container>
auto reversed(Container &c) {
    return reverse_t<Container>(c);
}

template <class T>
inline bool chmax(T &a, const T &b) noexcept {
    return b > a && (a = b, true);
}

template <class T>
inline bool chmin(T &a, const T &b) noexcept {
    return b < a && (a = b, true);
}

template <class T>
inline T diff(const T &a, const T &b) noexcept {
    return a < b ? b - a : a - b;
}

void operator|=(vector<bool>::reference lhs, const bool rhs) {
    lhs = lhs | rhs;
}

void ioinit() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
    clog << fixed << setprecision(10);
}
// }}} End Header

// Matrix {{{
// template <class Tp>
// struct Addition {
//     Tp operator()(const Tp& lhs, const Tp& rhs) {
//         return lhs + rhs;
//     }
// };

template <class Tp>
struct Addition {
    Tp operator()(const Tp& lhs, const Tp& rhs) {
        return lhs | rhs;
    }
};

// template <class Tp>
// struct Addition {
//     Tp operator()(const Tp& lhs, const Tp& rhs) {
//         return lhs ^ rhs;
//     }
// };

// template <class Tp>
// struct Multiplication {
//     Tp operator()(const Tp& lhs, const Tp& rhs) {
//         return lhs * rhs;
//     }
// };

template <class Tp>
struct Multiplication { // Change identity!!!!
    Tp operator()(const Tp& lhs, const Tp& rhs) {
        return lhs & rhs;
    }
};

template <class Tp, typename Add = Addition<Tp>, typename Mul = Multiplication<Tp>>
class Matrix {
private:
    vector<vector<Tp>> A;
    Add add;
    Mul mul;

public:
    Matrix() = default;
    Matrix(size_t n, size_t m) : A(n, vector<Tp>(m, 0)) {}
    Matrix(size_t n) : A(n, vector<Tp>(n, 0)) {}
    Matrix(vector<vector<Tp>> A) : A(A) {}

    size_t height() const {
        return A.size();
    }
    size_t width() const {
        return A[0].size();
    }

    vector<Tp>& operator[](size_t k) {
        return A[k];
    }
    const vector<Tp>& operator[](size_t k) const {
        return A[k];
    }

    // static Matrix identity(size_t n) { // product
    //     Matrix res(n);
    //     for (size_t i = 0; i < n; ++i) res[i][i] = 1;
    //     return res;
    // }
    static Matrix identity(size_t n) { // logical product
        Matrix res(n);
        for (size_t i = 0; i < n; ++i) res[i][i] = -1;
        return res;
    }

    Matrix& operator+=(const Matrix& B) {
        const size_t n = height();
        const size_t m = width();
        assert(n == B.height() && m == B.width());
        for (size_t i = 0; i < n; ++i) {
            for (size_t j = 0; j < m; ++j) {
                A[i][j] += B[i][j];
            }
        }
        return *this;
    }
    Matrix& operator-=(const Matrix& B) {
        const size_t n = height();
        const size_t m = width();
        assert(n == B.height() && m == B.width());
        for (size_t i = 0; i < n; ++i) {
            for (size_t j = 0; j < m; ++j) {
                A[i][j] -= B[i][j];
            }
        }
        return *this;
    }
    Matrix& operator*=(const Matrix& B) {
        const size_t n = height();
        const size_t m = width();
        const size_t l = B.width();
        assert(m == B.height());
        vector<vector<Tp>> C(n, vector<Tp>(l, 0));
        for (size_t i = 0; i < n; ++i) {
            for (size_t j = 0; j < m; ++j) {
                for (size_t k = 0; k < l; ++k) {
                    C[i][k] = add(C[i][k], mul(A[i][j], B[j][k]));
                }
            }
        }
        A.swap(C);
        return *this;
    }
    Matrix operator+(const Matrix& B) const {
        return Matrix(A) += B;
    }
    Matrix operator-(const Matrix& B) const {
        return Matrix(A) -= B;
    }
    Matrix operator*(const Matrix& B) const {
        return Matrix(A) *= B;
    }

    Matrix pow(intmax_t e) const {
        Matrix res = identity(height());
        Matrix B(A);
        while (e > 0) {
            if (e & 1) res *= B;
            B *= B;
            e >>= 1;
        }
        return res;
    }
    Matrix pow(string e) const {
        Matrix res = identity(height());
        Matrix B(A);
        for (const char c: e) {
            res = res.pow(10) * B.pow(c - '0');
        }
        return res;
    }

    auto& data() {
        return A;
    }
    const auto& data() const {
        return A;
    }
};
// }}}

signed main() {
    ioinit();

    var(intmax_t, N, M, T);

    Matrix<intmax_t> A(N);
    rep(_, 0, M) {
        var(size_t, a, b);
        A[a][b] = 1;
    }

    // G_k[u][v] := k 回の移動で u -> v が可能か
    // G_{k1 + k2}[u][v] = ⋃_{w = 1}^N (G_k1[u][w] and G_k2[w][v])
    if (T == 0) {
        output(1);
    } else {
        A *= A.pow(T - 1);
        intmax_t res = 0;
        rep(j, 0, N) res += A[0][j];
        output(res);
    }
    return 0;
}