結果

問題 No.1301 Strange Graph Shortest Path
ユーザー haruki_Kharuki_K
提出日時 2020-11-27 22:59:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 225 ms / 3,000 ms
コード長 9,756 bytes
コンパイル時間 2,704 ms
コンパイル使用メモリ 215,388 KB
最終ジャッジ日時 2025-01-16 08:18:42
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 33
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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 double ld
#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 mp make_pair
#define fst first
#define snd second
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); }
// [a,b]
template <class Int> Int rand(Int a, Int b) { static mt19937_64 mt{random_device{}()}; return uniform_int_distribution<Int>(a,b)(mt); }
i64 irand(i64 a, i64 b) { return rand<i64>(a,b); }
u64 urand(u64 a, u64 b) { return rand<u64>(a,b); }
// <<<
// >>> min cost flow
template <class Flow, class Cost>
struct MinCostFlow { // Primal-Dual
    static constexpr Cost inf = numeric_limits<Cost>::max();
    static constexpr Flow EPS = 1e-10; //

    struct Edge {
        int32_t to, rev, id;
        Flow cap;
        Cost cost;
        Edge(int to, int rev, int id, Flow cap, Cost cost)
            : to(to), rev(rev), id(id), cap(cap), cost(cost) {}
    };
    vector<vector<Edge>> g;
    vector<pair<int32_t,int32_t>> es;
    vector<Cost> h; // potential
    vector<int32_t> pv, pe; // previous vertex/edge index
    int V, E = 0, s = -1, t = -1;
    Flow next_cap = 0;
    Cost next_cost = 0;
    bool neg_edge = false;

    MinCostFlow(int V = 0) : g(V), h(V), pv(V, -1), pe(V, -1), V(V) {}
    void add_edge(int from, int to, Flow cap, Cost cost) {
        assert(from != to);
        es.emplace_back(from, g[from].size());
        g[from].emplace_back(to, g[to].size(), E, cap, cost);
        g[to].emplace_back(from, g[from].size()-1, E, 0, -cost);
        E++;
        if (cost < -EPS) neg_edge = true;
    }

    struct edge_t {
        int32_t from, to;
        Flow flow, cap;
        Cost cost;
    };
    Edge& internal_edge(int id) {
        assert(0 <= id); assert(id < (int)es.size());
        int from, idx; tie(from, idx) = es[id];
        return g[from][idx];
    }
    edge_t edge(int id) const {
        assert(0 <= id); assert(id < (int)es.size());
        int32_t from, idx; tie(from, idx) = es[id];
        auto const& e = g[from][idx];
        auto const& r = g[e.to][e.rev];
        return { from, e.to, r.cap, e.cap+r.cap, e.cost };
    }
    vector<edge_t> edges() const {
        vector<edge_t> ret(E);
        rep (id,E) ret[id] = edge(id);
        return ret;
    }

    template <class T> static constexpr bool chmin(T &x, T const& y) {
        return x > y ? (x = y, true) : false;
    };
    void BellmanFord(int s) {
        fill(h.begin(), h.end(), inf);
        h[s] = 0;
        bool update = false;
        rep (_,V-1) {
            update = false;
            rep (x,V) if (h[x] < inf) {
                rep (i,g[x].size()) {
                    auto const& e = g[x][i];
                    if (e.cap > EPS && chmin(h[e.to], h[x] + e.cost)) {
                        pv[e.to] = x, pe[e.to] = i;
                        update = true;
                    }
                }
            }
            if (not update) break;
        }
        assert(not update); // todo: cancel negative loops
        neg_edge = false;
    }
    void Dijkstra(int s) { // use old h
        using P = pair<Cost,int32_t>;
        priority_queue<P, vector<P>, greater<P>> q;
        vector<Cost> d(V, inf);
        d[s] = 0;
        q.emplace(0, s);
        while (q.size()) {
            int val, x; tie(val, x) = q.top(); q.pop();
            if (d[x] < val) continue;
            rep (i,g[x].size()) {
                auto const& e = g[x][i];
                if (e.cap > EPS && chmin(d[e.to], d[x] + e.cost+h[x]-h[e.to])) {
                    pv[e.to] = x, pe[e.to] = i;
                    q.emplace(d[e.to], e.to);
                }
            }
        }
        rep (x,V) if (d[x] < inf) h[x] += d[x];
    }
    bool calc_next(int s = -1, int t = -1) {
        if (t < 0) s = this-> s, t = this->t;
        if (neg_edge) BellmanFord(s); else Dijkstra(s);
        if (h[t] >= inf) {
            next_cap = 0, next_cost = inf;
            return false;
        }
        next_cap = numeric_limits<Flow>::max();
        for (int x = t; x != s; x = pv[x]) chmin(next_cap, g[pv[x]][pe[x]].cap);
        next_cost = h[t];
        return next_cap > EPS;
    }
    void add_flow(Flow flow, int s = -1, int t = -1) {
        if (t < 0) s = this-> s, t = this->t;
        for (int x = t; x != s; x = pv[x]) {
            auto &e = g[pv[x]][pe[x]];
            e.cap -= flow;
            g[x][e.rev].cap += flow;
        }
    }
    pair<Cost, bool> min_cost_flow(int s, int t, Flow flow) {
        this->s = s, this->t = t;
        Cost cost = 0;
        while (flow > EPS) {
            if (not calc_next()) return { cost, false };
            auto f = min(flow, next_cap);
            add_flow(f);
            flow -= f;
            cost += f * next_cost;
        }
        return { cost, true };
    }

#ifdef LOCAL
    friend string to_s(MinCostFlow a) {
        string ret = "\n";
        ret += "V = " + to_s(a.V) + ", E = " + to_s(a.E) + "\n";
        ret += "s = " + to_s(a.s) + ", t = " + to_s(a.t) + "\n";
        for (auto const& p : a.es) {
            auto const& e = a.g[p.first][p.second];
            auto const& r = a.g[e.to][e.rev];
            ret += to_s(e.id) + " : ";
            ret += to_s(p.first) + "->" + to_s(e.to) + ", ";
            ret += "flow " + to_s(r.cap) + "/" + to_s(e.cap+r.cap) + ", ";
            ret += "cost " + to_s(e.cost) + "\n";
        }
        return ret;
    }
#endif

};
// <<<

int32_t main() {
    int n, m; cin >> n >> m;
    struct edge { int to, c, d; };
    MinCostFlow<int, int> g(n);
    rep (i,m) {
        int a, b, c, d; cin >> a >> b >> c >> d; --a, --b;
        g.add_edge(a, b, 1, c);
        g.add_edge(b, a, 1, c);
        g.add_edge(a, b, 1, d);
        g.add_edge(b, a, 1, d);
    }

    cout << g.min_cost_flow(0, n-1, 2).fst << endl;


}
0