結果

問題 No.1364 [Renaming] Road to Cherry from Zelkova
コンテスト
ユーザー haruki_K
提出日時 2021-01-22 22:26:25
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 240 ms / 2,500 ms
コード長 12,507 bytes
コンパイル時間 2,582 ms
コンパイル使用メモリ 225,664 KB
最終ジャッジ日時 2025-01-18 04:40:49
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 # 

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define rng(x, l, r) begin(x) + (l), begin(x) + (r)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class A, class B> auto mp(A &&a, B &&b) { return make_pair(forward<A>(a), forward<B>(b)); }
template <class... T> auto mt(T&&... x) { return make_tuple(forward<T>(x)...); }
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
const int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
const int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
template <class A, class B> pair<A, B> operator+(pair<A, B> const& p, pair<A, B> const& q) { return { p.first + q.first, p.second + q.second }; }
template <class A, class B> pair<A, B> operator-(pair<A, B> const& p, pair<A, B> const& q) { return { p.first - q.first, p.second - q.second }; }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
// <<<
// >>> modint

template <uint32_t md>
class modint {
    static_assert(md < (1u<<31), "");
    using M = modint;
    using i64 = int64_t;
    uint32_t x;
public:
    static constexpr uint32_t mod = md;
    constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }
    constexpr i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    constexpr bool operator==(M r) const { return x == r.x; }
    constexpr bool operator!=(M r) const { return x != r.x; }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { return M()-*this; }
    constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }
    constexpr M& operator/=(M r) { return *this *= r.inv(); }
    constexpr M operator+(M r) const { return M(*this) += r; }
    constexpr M operator-(M r) const { return M(*this) -= r; }
    constexpr M operator*(M r) const { return M(*this) *= r; }
    constexpr M operator/(M r) const { return M(*this) /= r; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }
    constexpr M inv() const { assert(x > 0); return pow(md-2); }
    constexpr M pow(i64 n) const {
        assert(not (x == 0 && n == 0));
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
#ifdef LOCAL
    friend string to_s(M r) { return to_s(r.val(), mod); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};

// <<<
//constexpr int64_t MOD = 998244353;
constexpr int64_t MOD = 1e9+7;
using mint = modint<MOD>;
mint parity(int n) { return n & 1 ? -1 : +1; }
// >>> mod table
template <uint32_t mod> struct ModTable {
    vector<uint32_t> fact = {1, 1}, finv = {1, 1}, inv = {0, 1};
    void calc(int n) {
        int old = fact.size();
        if (n < old) return;
        fact.resize(n+1);
        finv.resize(n+1);
        inv.resize(n+1);
        for (uint32_t i = old; i <= n; i++) {
            fact[i] = uint64_t(fact[i-1])*i % mod;
            inv[i] = mod - uint64_t(inv[mod%i])*(mod/i) % mod;
            finv[i] = uint64_t(finv[i-1])*inv[i] % mod;
        }
    }
};
ModTable<MOD> mod_tab;

modint<MOD> fact(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.fact[n];
}
modint<MOD> finv(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.finv[n];
}
modint<MOD> comb(int n, int k) {
    if (n < 0 || k < 0 || n < k) return 0;
    return fact(n)*finv(k)*finv(n-k);
}
modint<MOD> perm(int n, int k) {
    assert(k >= 0); assert(n >= k);
    return fact(n)*finv(n-k);
}
// <<<
// >>> scc
#ifndef EDGE_INFO
#define EDGE_INFO
constexpr int dest(int v) { return v; }
template <class E, class = decltype(declval<E>().to)>
constexpr int dest(E const& e) { return e.to; }
constexpr int cost(int) { return 1; }
template <class E, class = decltype(declval<E>().cost)>
constexpr auto cost(E const& e) { return e.cost; }
template <class E> using cost_t = decltype(cost(declval<E>()));
#endif
template <class E> struct SCC {
    vector<vector<E>> const& g;
    vector<int32_t> ord, low, st;
    int32_t time = 0, pos = 0, sz = 0;
    SCC(vector<vector<E>> const& g) : g(g), ord(g.size()), low(g.size()), st(g.size()) {
        rep (v, g.size()) if (ord[v] == 0) dfs(v);
        for (auto &x : ord) x += sz;
    }
    void dfs(int32_t v) {
        low[v] = ord[v] = ++time; st[pos++] = v;
        for (auto const& e : g[v]) {
            if (ord[dest(e)] == 0) {
                dfs(dest(e));
                chmin(low[v], low[dest(e)]);
            } else if (ord[dest(e)] > 0) {
                chmin(low[v], ord[dest(e)]);
            }
        }
        if (low[v] == ord[v]) {
            sz++; do ord[st[--pos]] = -sz; while (st[pos] != v);
        }
    }

    // t-sorted id
    int id(int v) const { return ord[v]; }
    int size() const { return sz; }
    vector<vector<int>> groups() const {
        vector<vector<int>> grp(sz);
        rep (v, g.size()) grp[ord[v]].push_back(v);
        return grp;
    }

    // no multiple edges, no self-loops
    // no edge information
    vector<vector<int>> graph() const {
        vector<vector<int>> ret(size());
        rep (v, g.size()) {
            for (auto const& e : g[v]) {
                int x = id(v), y = id(dest(e));
                if (x != y) ret[x].push_back(y);
            }
        }
        for (auto &ls : ret) {
            sort(ls.begin(), ls.end());
            ls.erase(unique(ls.begin(), ls.end()), ls.end());
        }
        return ret;
    }
};
template <class E> auto get_scc(vector<vector<E>> const& g) { return SCC<E>(g); }

// <<<
// >>> bfs
#ifndef EDGE_INFO
#define EDGE_INFO
constexpr int dest(int v) { return v; }
template <class E, class = decltype(declval<E>().to)>
constexpr int dest(E const& e) { return e.to; }
constexpr int cost(int) { return 1; }
template <class E, class = decltype(declval<E>().cost)>
constexpr auto cost(E const& e) { return e.cost; }
template <class E> using cost_t = decltype(cost(declval<E>()));
#endif
template <class E>
vector<int> bfs(vector<vector<E>> const& g, int s, int inf) {
    vector<int> d(g.size(), inf);
    queue<int> q;
    d[s] = 0;
    q.push(s);
    while (q.size()) {
        int x = q.front(); q.pop();
        for (auto const& e : g[x]) {
            const int y = dest(e);
            if (chmin(d[y], d[x]+1)) q.push(y);
        }
    }
    return d;
}
// <<<

int32_t main() {
    int n, m; cin >> n >> m; n++;
    struct edge { int to, len, num; };
    vector<vector<edge>> g(n), rg(n);
    rep (i, m) {
        int x, y, L, N; cin >> x >> y >> L >> N;
        g[x].pb({y, L, N});
        rg[y].pb({x, L, N});
    }

    auto scc = get_scc(g);
    auto h = scc.graph();
    vector<vector<int>> rh(h.size());
    rep (i, h.size()) for (int j : h[i]) {
        rh[j].eb(i);
    }
    auto grp = scc.groups();
    auto ds = bfs(h, scc.id(0), INF);
    auto dt = bfs(rh, scc.id(n-1), INF);
    vector<int> alive(h.size(), 0);
    // dump(h, grp);
    // dump(ds);
    // dump(dt);
    rep (i, h.size()) {
        alive[i] = (ds[i] < INF and dt[i] < INF);
        if (alive[i] and sz(grp[i]) >= 2) {
            quit("INF");
        }
    }

    vector<int> ord(n);
    iota(all(ord), 0);
    sort(all(ord), [&](int x, int y) { return scc.id(x) < scc.id(y); });

    vector<mint> scnt(n);
    scnt[0] = 1;
    for (int x : ord) {
        if (not alive[scc.id(x)]) continue;
        for (auto [y, len, num] : g[x]) {
            if (not alive[scc.id(y)]) continue;
            scnt[y] += scnt[x] * num;
        }
    }

    reverse(all(ord));
    vector<mint> tcnt(n);
    tcnt[n-1] = 1;
    for (int x : ord) {
        if (not alive[scc.id(x)]) continue;
        for (auto [y, len, num] : rg[x]) {
            if (not alive[scc.id(y)]) continue;
            tcnt[y] += tcnt[x] * num;
        }
    }
    dump(scnt);
    dump(tcnt);

    mint ans = 0;
    rep (x, n) for (auto [y, len, num] : g[x]) {
        ans += scnt[x] * tcnt[y] * num * len;
    }
    cout << ans << "\n";

}
0