結果

問題 No.1364 [Renaming] Road to Cherry from Zelkova
ユーザー 👑 emthrmemthrm
提出日時 2021-01-22 23:43:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 167 ms / 2,500 ms
コード長 6,753 bytes
コンパイル時間 2,491 ms
コンパイル使用メモリ 224,796 KB
最終ジャッジ日時 2025-01-18 06:31:24
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 45
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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int MOD>
struct MInt {
  unsigned val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % MOD : x % MOD + MOD) {}
  static int get_mod() { return MOD; }
  static void set_mod(int divisor) { assert(divisor == MOD); }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= MOD) val -= MOD; return *this; }
  MInt &operator-=(const MInt &x) { if((val += MOD - x.val) >= MOD) val -= MOD; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % MOD; return *this; }
  MInt &operator/=(const MInt &x) {
    // assert(std::__gcd(static_cast<int>(x.val), MOD) == 1);
    unsigned a = x.val, b = MOD; int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      std::swap(a -= tmp * b, b);
      std::swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == MOD) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? MOD : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? MOD - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int MOD> MInt<MOD> abs(const MInt<MOD> &x) { return x; } }
template <int MOD>
struct Combinatorics {
  using ModInt = MInt<MOD>;
  int val;  // "val!" and "mod" must be disjoint.
  std::vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    for (int i = 1; i <= val; ++i) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    for (int i = 1; i <= val; ++i) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return 0;
    assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return 0;
    assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0) return 0;
    return k == 0 ? 1 : nCk(n + k - 1, k);
  }
};
using ModInt = MInt<MOD>;

std::vector<int> topological_sort(const std::vector<std::vector<int>> &graph) {
  int n = graph.size();
  std::vector<int> deg(n, 0);
  for (int i = 0; i < n; ++i) {
    for (int e : graph[i]) ++deg[e];
  }
  std::queue<int> que;
  for (int i = 0; i < n; ++i) {
    if (deg[i] == 0) que.emplace(i);
  }
  std::vector<int> res;
  while (!que.empty()) {
    int ver = que.front(); que.pop();
    res.emplace_back(ver);
    for (int e : graph[ver]) {
      if (--deg[e] == 0) que.emplace(e);
    }
  }
  return res.size() == n ? res : std::vector<int>();
}

int main() {
  int n, m; cin >> n >> m; ++n;
  vector<int> u(m), v(m), l(m), a(m); REP(i, m) cin >> u[i] >> v[i] >> l[i] >> a[i];
  vector<vector<int>> graph(n), rev(n);
  REP(i, m) {
    graph[u[i]].emplace_back(i);
    rev[v[i]].emplace_back(i);
  }
  vector<bool> reachn(n, false);
  reachn[n - 1] = true;
  queue<int> que({n - 1});
  while (!que.empty()) {
    int ver = que.front(); que.pop();
    for (int id : rev[ver]) {
      if (!reachn[u[id]]) {
        reachn[u[id]] = true;
        que.emplace(u[id]);
      }
    }
  }
  if (!reachn[0]) {
    cout << 0 << '\n';
    return 0;
  }
  vector<bool> reach0(n, false);
  reach0[0] = true;
  vector<vector<int>> dag(n), dag_r(n);
  vector<map<int, pair<ll, ModInt>>> g(n);
  que.emplace(0);
  while (!que.empty()) {
    int ver = que.front(); que.pop();
    for (int id : graph[ver]) {
      if (reachn[v[id]]) {
        dag[ver].emplace_back(v[id]);
        dag_r[v[id]].emplace_back(ver);
        g[ver][v[id]].first += a[id];
        g[ver][v[id]].second += 1LL * a[id] * l[id];
        if (!reach0[v[id]]) {
          reach0[v[id]] = true;
          que.emplace(v[id]);
        }
      }
    }
  }
  assert(reach0[n - 1]);
  vector<int> ts = topological_sort(dag);
  if (ts.empty()) {
    cout << "INF\n";
    return 0;
  }
  vector<ModInt> dp0(n, 0), dpn(n, 0);
  dp0[0] = 1;
  REP(_, n) {
    int i = ts[_];
    sort(ALL(dag[i]));
    dag[i].erase(unique(ALL(dag[i])), dag[i].end());
    for (int e : dag[i]) dp0[e] += dp0[i] * g[i][e].first;
  }
  // REP(i, n) cout << dp0[i] << " \n"[i + 1 == n];
  dpn[n - 1] = 1;
  for (int _ = n - 1; _ >= 0; --_) {
    int i = ts[_];
    sort(ALL(dag_r[i]));
    dag_r[i].erase(unique(ALL(dag_r[i])), dag_r[i].end());
    for (int e : dag_r[i]) dpn[e] += dpn[i] * g[e][i].first;
  }
  // REP(i, n) cout << dpn[i] << " \n"[i + 1 == n];
  ModInt ans = 0;
  REP(i, n) {
    for (int e : dag[i]) ans += dp0[i] * dpn[e] * g[i][e].second;
  }
  cout << ans << '\n';
  return 0;
}
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