結果

問題 No.1112 冥界の音楽
コンテスト
ユーザー rokahikou1
提出日時 2020-11-26 17:46:06
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 19 ms / 2,000 ms
コード長 6,403 bytes
コンパイル時間 1,925 ms
コンパイル使用メモリ 179,200 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-23 20:54:58
合計ジャッジ時間 3,069 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 3
other AC * 34
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function 'int main()':
main.cpp:212:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  212 |     auto [K, M, N] = reads<ll, ll, ll>();
      |          ^
main.cpp:215:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  215 |         auto [p, q, r] = reads<int, int, int>();
      |              ^

ソースコード

diff # 

#include <bits/stdc++.h>
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define ALL(v) (v).begin(), (v).end()
#define LLA(v) (v).rbegin(), (v).rend()
#define PB push_back
#define MP(a, b) make_pair((a), (b))
using namespace std;
template <class T> inline vector<T> make_vec(size_t a, T val) {
    return vector<T>(a, val);
}
template <class... Ts> inline auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec(ts...))>(a, make_vec(ts...));
}
template <typename T> inline T read() {
    T t;
    cin >> t;
    return t;
}
template <typename T> inline vector<T> readv(size_t sz) {
    vector<T> ret(sz);
    rep(i, sz) cin >> ret[i];
    return ret;
}
template <typename... Ts> inline tuple<Ts...> reads() {
    return {read<Ts>()...};
}
template <typename T> struct edge {
    int to;
    T cost;
    edge(int t, T c) : to(t), cost(c) {}
};
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using Graph = vector<vector<int>>;
template <typename T> using WGraph = vector<vector<edge<T>>>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;

template <uint_fast64_t MOD> class ModInt {
    using u64 = uint_fast64_t;

  public:
    u64 val;

    ModInt(const u64 x = 0) : val((x + MOD) % MOD) {}
    constexpr u64 &value() { return val; }
    constexpr ModInt operator-() { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt &rhs) const {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt &rhs) const {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt &rhs) const {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt &rhs) const {
        return ModInt(*this) /= rhs;
    }
    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if(val >= MOD) {
            val -= MOD;
        }
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if(val < rhs.val) {
            val += MOD;
        }
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = val * rhs.val % MOD;
        return *this;
    }

    constexpr ModInt &operator/=(const ModInt &rhs) {
        *this *= rhs.inv();
        return *this;
    }

    constexpr bool operator==(const ModInt &rhs) {
        return this->val == rhs.val;
    }
    constexpr bool operator!=(const ModInt &rhs) {
        return this->val != rhs.val;
    }
    friend constexpr ostream &operator<<(ostream &os, const ModInt<MOD> &x) {
        return os << x.val;
    }
    friend constexpr istream &operator>>(istream &is, ModInt<MOD> &x) {
        return is >> x.val;
    }

    constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); }

    constexpr ModInt pow(ll e) const {
        u64 x = 1, p = val;
        while(e > 0) {
            if(e % 2 == 0) {
                p = (p * p) % MOD;
                e /= 2;
            } else {
                x = (x * p) % MOD;
                e--;
            }
        }
        return ModInt(x);
    }
};

using mint = ModInt<MOD>;

#include <cassert>
// 参考:https://ei1333.github.io/luzhiled/snippets/math/matrix.html
// (掛け算と累乗)https://yukicoder.me/submissions/523126
// 他は知らん
template <class T> struct Matrix {
    vector<vector<T>> A;
    Matrix() {}
    Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}
    Matrix(size_t n) : A(n, vector<T>(n, 0)) {}

    size_t height() const { return A.size(); }

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

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

    static Matrix I(size_t n) {
        Matrix mat(n);
        for(int i = 0; i < n; i++)
            mat[i][i] = 1;
        return mat;
    }

    Matrix &operator+=(const Matrix &B) {
        size_t h = height(), w = width();
        assert(h == B.height() && w == B.width);
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return *this;
    }

    Matrix &operator-=(const Matrix &B) {
        size_t h = height(), w = width();
        assert(h == B.height() && w == B.width);
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return *this;
    }

    Matrix &operator*=(const Matrix &B) {
        size_t h = height(), w = B.width(), p = width();
        assert(p == B.height());
        vector<vector<T>> C(h, vector<T>(w, 0));
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                for(int k = 0; k < p; k++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        return *this;
    }

    Matrix &operator^=(ll k) {
        Matrix B = Matrix::I(height());
        while(k > 0) {
            if(k & 1)
                B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        return *this;
    }

    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 ll k) const { return (Matrix(*this) ^= k); }

    friend ostream &operator<<(ostream &os, const Matrix &p) {
        size_t h = p.height(), w = p.width();
        for(int i = 0; i < h; i++) {
            os << "[";
            for(int j = 0; j < w; j++) {
                os << p[i][j] << (j + 1 == w ? "]\n" : ",");
            }
        }
        return os;
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    auto [K, M, N] = reads<ll, ll, ll>();
    Matrix<mint> mat(K * K, K * K), vec(K * K, 1);
    rep(i, M) {
        auto [p, q, r] = reads<int, int, int>();
        p--, q--, r--;
        mat[q * K + r][p * K + q] = 1;
        if(p == 0)
            vec[p * K + q][0] = 1;
    }
    auto res = (mat ^ (N - 2)) * vec;
    mint ans = 0;
    rep(i, K * K) {
        if(i % K == 0)
            ans += res[i][0];
    }
    cout << ans << endl;
}
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