#510008 (C++17(gcc12)) No.1112 冥界の音楽

• 問題: No.1112 冥界の音楽
• ユーザー: iiljj
• 提出日時: 2020-07-10 22:27:02
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 10,795 bytes
• コンパイル時間: 6,267 ms
• コンパイル使用メモリ: 246,948 KB
• 最終ジャッジ日時: 2025-01-11 18:46:38
• ジャッジサーバーID （参考情報）: judge3 / judge5

コンパイルメッセージ

main.cpp:238:14: error: expected unqualified-id before 'const'
  238 |     Mat<Num>(const ll h, ll w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
      |              ^~~~~
main.cpp:238:14: error: expected ')' before 'const'
  238 |     Mat<Num>(const ll h, ll w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
      |             ~^~~~~
      |              )
main.cpp:239:14: error: expected unqualified-id before 'const'
  239 |     Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
      |              ^~~~~
main.cpp:239:14: error: expected ')' before 'const'
  239 |     Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
      |             ~^~~~~
      |              )
main.cpp:240:45: error: invalid declarator before 'init'
  240 |     Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
      |                                             ^~~~
main.cpp:240:44: error: expected ')' before 'init'
  240 |     Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
      |             ~                              ^~~~~
      |                                            )
main.cpp: In function 'void solve()':
main.cpp:323:11: error: could not convert 'sz' from 'll' {aka 'long long int'} to 'std::vector<std::vector<mint, std::allocator<mint> >, std::allocator<std::vector<mint, std::allocator<mint> > > >'
  323 |     mat C(sz, sz), M(sz, 1);
      |           ^~
      |           |
      |           ll {aka long long int}
main.cpp:323:22: error: could not convert 'sz' from 'll' {aka 'long long int'} to 'std::vector<std::vector<mint, std::allocator<mint> >, std::allocator<std::vector<mint, std::allocator<mint> > > >'
  323 |     mat C(sz, sz), M(sz, 1);
      |                      ^~
      |                      |
      |                      ll {aka long long int}
main.cpp: In instantiation of 'Mat<Num> Mat<Num>::pow(ll) const [with Num = mint; ll = long long int]':
main.cpp:333:19:   required from here
main.cpp:2

ソースコード

/* #region Head */

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

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region mint */

// 自動で MOD を取る整数
struct mint {
    ll x;
    mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
    mint &operator+=(const mint a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator-=(const mint a) {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator*=(const mint a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    mint operator+(const mint a) const {
        mint res(*this);
        return res += a;
    }
    mint operator-(const mint a) const {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint a) const {
        mint res(*this);
        return res *= a;
    }
    // O(log(t))
    mint pow(ll t) const {
        if (!t) return 1;
        mint a = pow(t >> 1); // ⌊t/2⌋ 乗
        a *= a;               // ⌊t/2⌋*2 乗
        if (t & 1)            // ⌊t/2⌋*2 == t-1 のとき
            a *= *this;       // ⌊t/2⌋*2+1 乗 => t 乗
        return a;
    }

    // for prime mod
    mint inv() const {
        return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
    }
    mint &operator/=(const mint a) { return (*this) *= a.inv(); }
    mint operator/(const mint a) const {
        mint res(*this);
        return res /= a;
    }
    bool operator==(const mint a) const { return this->x == a.x; }
    bool operator==(const ll a) const { return this->x == a; }

    // mint 入力
    friend istream &operator>>(istream &is, mint &x) {
        is >> x.x;
        return is;
    }

    // mint 出力
    friend ostream &operator<<(ostream &os, mint x) {
        os << x.x;
        return os;
    }
};

/* #endregion */

/* #region Mat */

// 行列，==, !=, [] あたりは vector と一緒
template <class Num> class Mat : public vc<vc<Num>> {
  public:
    // using vc<vc<Num>>::vector;
    ll h, w;

    // コンストラクタ
    Mat<Num>(const ll h, ll w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
    Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
    Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
        for (auto iter = init.begin(); iter != init.end(); ++iter) this->emplace_back(*iter);
        h = this->size(), w = (*this)[0].size();
    }

    // 行列に別の行列を足す
    Mat &operator+=(const Mat &another) {
        assert(this->h == another.h && this->w == another.w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] += another[i][j];
        return *this;
    }

    // 行列から別の行列を引く
    Mat &operator-=(const Mat &another) {
        assert(this->h == another.h && this->w == another.w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] -= another[i][j];
        return *this;
    }

    // 行列に別の行列を右から掛ける
    Mat &operator*=(const Mat &another) {
        assert(w == another.h);
        Mat<Num> ret(this->h, another.w);
        REP(i, 0, this->h) REP(j, 0, another.w) REP(k, 0, this->w) ret[i][j] += (*this)[i][k] * another[k][j];
        *this = ret;
        return *this;
    }

    // 行列に別の行列を足す
    Mat operator+(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret += another;
    }

    // 行列から別の行列を引く
    Mat operator-(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret -= another;
    }

    // 行列に別の行列を右から掛ける
    Mat operator*(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret *= another;
    }

    // 行列の n 乗を計算する
    Mat pow(ll n) const {
        assert(this->h == this->w);
        Mat<Num> ret(this->h, this->w);
        Mat<Num> a(*this);
        REP(i, 0, this->h) ret[i][i] = 1;
        while (n) {
            if (n & 1) ret = a * ret;
            a = a * a, n >>= 1;
        }
        return ret;
    }

    template <class... T> Mat assign(T... nums) {
        vc<Num> num_list = vc<Num>{nums...};
        assert(SIZE(num_list) == this->h * this->w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num_list[this->w * i + j];
        return *this;
    }

    void fill(Num num) { REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num; }
};

/* #endregion */

// Problem
void solve() {
    ll k, m, n;
    cin >> k >> m >> n;
    vll p(m), q(m), r(m);
    REP(i, 0, m) {
        cin >> p[i] >> q[i] >> r[i];
        --p[i], --q[i], --r[i];
    }

    using mat = Mat<mint>;
    ll sz = k * k;
    mat C(sz, sz), M(sz, 1);
    C.fill(0), M.fill(0);
    auto idx = [&k](ll s, ll t) -> ll { return k * s + t; };
    REP(i, 0, m) {
        ll from = idx(p[i], q[i]);
        ll to = idx(q[i], r[i]);
        C[to][from] += 1;
        if (p[i] == 0) M[from][0] = 1;
        // dump(p[i], q[i], r[i], from, to);
    }
    mat CC = C.pow(n - 2);
    mat result = CC * M;

    mint ret = 0;
    REP(i, 0, k) ret += result[idx(i, 0)][0];
    cout << ret << endl;
}

// entry point
int main() {
    solve();
    return 0;
}