結果

問題 No.1364 [Renaming] Road to Cherry from Zelkova
ユーザー bond_cmprogbond_cmprog
提出日時 2021-01-23 19:27:39
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 814 ms / 2,500 ms
コード長 11,486 bytes
コンパイル時間 2,807 ms
コンパイル使用メモリ 216,120 KB
最終ジャッジ日時 2025-01-18 07:38:04
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 # 

#include <bits/stdc++.h>
#define REP(i, n) for(int i = 0;i < n;i++)
#define ll long long
using namespace std;
typedef pair<int, int> P;
typedef pair<ll,ll> LP;
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
const int INF = 1000000000;
const ll LINF = 1000000000000000000;//1e18
const double PI = acos(-1.0);
const double EPS = 1e-10;

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

/*  ----------------------- DEBUG FUNCTION ---------------------------- */
#define DUMPOUT cerr
void dump_function() { DUMPOUT << ' '; }
void dump_function(bool a) { DUMPOUT << a; }
void dump_function(int a) { DUMPOUT << a; }
void dump_function(long long a) { DUMPOUT << a; }
void dump_function(char a) { DUMPOUT << a; }
void dump_function(string &a) { DUMPOUT << a; }
void dump_function(double a) { DUMPOUT << a; }
template <class T> void dump_function(const vector<T> &);
template <class T, size_t size> void dump_function(const array<T, size> &);
template <class T, class L> void dump_function(const pair<T, L> &p);
template <class T, size_t size> void dump_function(const T (&)[size]);
template <class T> void dump_function(const vector<T> &a) {
    if(a.empty()) return;
    dump_function(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        DUMPOUT << " ";
        dump_function(*i);
    }
    DUMPOUT << endl;
}
template <class T> void dump_function(const deque<T> &a) {
    if(a.empty()) return;
    dump_function(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        DUMPOUT << " ";
        dump_function(*i);
    }
}
template <class T, size_t size> void dump_function(const array<T, size> &a) {
    dump_function(a[0]);
    for(auto i = a.begin(); ++i != a.end();) {
        DUMPOUT << " ";
        dump_function(*i);
    }
}
template <class T, class L> void dump_function(const pair<T, L> &p) {
    DUMPOUT << '(';
    dump_function(p.first);
    DUMPOUT << ",";
    dump_function(p.second);
    DUMPOUT << ')';
}
template <class T> void dump_function(set<T> &x) {
    for(auto e : x) dump_function(e), DUMPOUT << " ";
    DUMPOUT << endl;
}
template <class T> void dump_function(multiset<T> &x) {
    for(auto e : x) dump_function(e), DUMPOUT << " ";
    DUMPOUT << endl;
}
template <class T, size_t size> void dump_function(const T (&a)[size]) {
    dump_function(a[0]);
    for(auto i = a; ++i != end(a);) {
        DUMPOUT << " ";
        dump_function(*i);
    }
}
template <class T> void dump_function(const T &a) { DUMPOUT << a; }
int dump_out() {
    DUMPOUT << '\n';
    return 0;
}
template <class T> int dump_out(const T &t) {
    dump_function(t);
    DUMPOUT << '\n';
    return 0;
}
template <class Head, class... Tail> int dump_out(const Head &head, const Tail &... tail) {
    dump_function(head);
    DUMPOUT << ' ';
    dump_out(tail...);
    return 0;
}

#ifdef DEBUG_
#define dump(x)                                                                                                                                               \
    DUMPOUT << #x << ": ";                                                                                                                                        \
    dump_function(x);                                                                                                                                                  \
    DUMPOUT << endl;
void dumps() {}
template <class T> void dumps(const T &t) {
    dump_function(t);
    DUMPOUT << " ";
}
template <class Head, class... Tail> void dumps(const Head &head, const Tail &... tail) {
    dump_function(head);
    DUMPOUT << ' ';
    dump_out(tail...);
}
#else
#define dump(x)
template <class... T> void dumps(const T &...) {}
#endif
/*  ----------------------- DEBUG FUNCTION ---------------------------- */

template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() const { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(r, n / 2);
        t = t * t;
        if (n & 1) t = t * r;
        return t;
    }
    friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        return Fp<MOD>(u);
    }
};


template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
    constexpr T perm(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[n-k];
    }
};

/* ----------------------------- MOD ----------------------------------- */
const int MOD = 1000000007;
const int MOD2 = 998244353;
using mint = Fp<MOD>;
BiCoef<mint> bc;
using vec = vector<int>;
using mat = vector<vec>;
/* ----------------------------- MOD ----------------------------------- */

/*  ----------------------- AtCoder Library ---------------------------- */
// #include <atcoder/all>
// using namespace atcoder;
/*  ----------------------- AtCoder Library ---------------------------- */

class StronglyConnectedComponents{
    int nodeNum;
    int size;
public:
    vector<vector<int>> edge,revEdge;
    vector<vector<int>> graph;
    vector<int> label,visited,order;
    // 帰りがけ順に番号を振っていく
    void dfs(int cur){
        visited[cur] = 1;
        for(int next:edge[cur]) if(!visited[next]) dfs(next);
        order.push_back(cur);
    }
    // 通ることが出来た頂点に番号を振っていく
    void revDfs(int cur,int labelId){
        visited[cur] = 1;
        label[cur] = labelId;
        for(int next:revEdge[cur]) if(!visited[next]) revDfs(next,labelId);
    }

	StronglyConnectedComponents(const int& nodeNum) :
    nodeNum(nodeNum), edge(nodeNum), revEdge(nodeNum), label(nodeNum), visited(nodeNum) {}

    void make_edge(const int from,const int to) {
        edge[from].push_back(to);
        revEdge[to].push_back(from);
    }

    void solve(void) {
        for(int i = 0; i < nodeNum; ++i) visited[i] = 0;
        for(int i = 0; i < nodeNum; ++i) if(!visited[i]) dfs(i);
        for(int i = 0; i < nodeNum; ++i) visited[i] = 0;
        reverse(order.begin(),order.end());
        int labelId = 0;
        for(int i:order) if(!visited[i]) revDfs(i,labelId++);
        size = labelId;
        make_graph();
    }

    // 強連結成分で縮約したグラフを作る
    void make_graph(){
        graph.resize(size);
        for(int i = 0; i < edge.size(); i++){
            for(auto to : edge[i]){
                if(getLabel(i) == getLabel(to)) continue;
                graph[getLabel(i)].push_back(getLabel(to));
            }
        }
    }

    vector<vector<int>> topological_sort(void){
        vector<vector<int>> ret(size);
        for(int i = 0; i < nodeNum; i++) ret[label[i]].emplace_back(i);
        return ret;
    }

    void print(void) {
        for(auto labelId:label) cout << labelId << " ";
        cout << endl;
    }
    // vが属している強連結成分のラベル（トポロジカル順序）
    int getLabel(int v){
        return label[v];
    }

    int getSize(){
        return size;
    }
};

void solve(){
    int N, M;
    cin >> N >> M;
    StronglyConnectedComponents scc(N+1), rscc(N+1);
    vector<vector<tuple<int, ll, ll>>> edge(N+1), redge(N+1);
    REP(i,M){
        int u, v, l, a;
        cin >> u >> v >> l >> a;
        scc.make_edge(u,v);
        rscc.make_edge(v, u);
        edge[u].emplace_back(v, l, a);
        redge[v].emplace_back(u, l, a);
    }

    scc.solve();
    auto topo = scc.topological_sort();
    vector<mint> dp(N+1);
    vector<int> inf(N+1);
    int is_zero = 0;
    dp[0] = 1;
    for(auto v : topo){
        for(auto e : v) if(e == 0) is_zero = 1;
        if(!is_zero) continue;
        for(auto from : v){
            if(v.size() != 1) inf[from] = 1;
            for(auto [nv, l, a] : edge[from]){
                inf[nv] |= inf[from];
                if(inf[nv]) continue;
                dp[nv] += dp[from] * a;
            }
        }
    }
    if(inf[N]){
        cout << "INF" << endl;
        return;
    }
    vector<mint> rdp(N+1);
    rscc.solve();
    auto rtopo = rscc.topological_sort();
    rdp[N] = 1;
    mint ans = 0;
    for(auto v : rtopo){
        for(auto from : v){
            for(auto [nv, l, a] : redge[from]){
                rdp[nv] += rdp[from] * a;
                ans += dp[nv] * rdp[from] * a * l;
            }
        }
    }
    cout << ans << endl;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    solve();
    // int T; cin >> T; REP(t,T) solve();
}
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