結果

問題 No.1301 Strange Graph Shortest Path
コンテスト
ユーザー kcvlex
提出日時 2020-11-27 22:29:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 878 ms / 3,000 ms
コード長 10,064 bytes
コンパイル時間 2,058 ms
コンパイル使用メモリ 169,572 KB
最終ジャッジ日時 2025-01-16 07:52:35
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2
other AC * 33
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 <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#include <variant>

#define endl codeforces

#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)

using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
using size_type = ssize_t;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

template <typename T, std::size_t Head, std::size_t... Tail> 
struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail...>::type, Head>; };

template <typename T, std::size_t Head> 
struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };

template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;

template <typename T, typename F, typename... Args> 
void fill_seq(T &t, F f, Args... args) { 
    if constexpr (std::is_invocable<F, Args...>::value) { 
        t = f(args...); 
    } else { 
        for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); 
    } 
}

template <typename T> vec<T> make_v(size_type sz) { return vec<T>(sz); }

template <typename T, typename... Tail> 
auto make_v(size_type hs, Tail&&... ts) { 
    auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); 
    return vec<decltype(v)>(hs, v); 
}

namespace init__ { 
struct InitIO { 
    InitIO() { 
        std::cin.tie(nullptr); 
        std::ios_base::sync_with_stdio(false); 
        std::cout << std::fixed << std::setprecision(30); 
    } 
} init_io; 
}

template <typename T>
T ceil_pow2(T bound) {
    T ret = 1;
    while (ret < bound) ret *= 2;
    return ret;
}

template <typename T>
T ceil_div(T a, T b) { return a / b + !!(a % b); }



namespace graph {

using Node = ll;
using Weight = ll;
using Edge = std::pair<Node, Weight>;

template <bool Directed>
struct Graph : public vvec<Edge> {
    using vvec<Edge>::vvec;

    void add_edge(Node f, Node t, Weight w = 1) {
        (*this)[f].emplace_back(t, w);
        if (!Directed) (*this)[t].emplace_back(f, w);
    }

    Graph<Directed> build_inv() const {
        Graph<Directed> ret(this->size());
        for (Node i = 0; i < this->size(); i++) {
            for (const Edge &e : (*this)[i]) {
                Node j;
                Weight w;
                std::tie(j, w) = e;
                if (!Directed && j < i) continue;
                ret.add_edge(j, i, w);
            }
        }

        return ret;
    }
};

template <typename Iterator>
class dst_iterator {
    Iterator ite;

public:
    dst_iterator(Iterator ite) : ite(ite) { }

    bool operator ==(const dst_iterator<Iterator> &oth) const {
        return ite == oth.ite;
    }

    bool operator !=(const dst_iterator<Iterator> &oth) const {
        return !(*this == oth);
    }

    bool operator <(const dst_iterator<Iterator> &oth) const {
        return ite < oth.ite;
    }

    bool operator >(const dst_iterator<Iterator> &oth) const {
        return ite > oth.ite;
    }

    bool operator <=(const dst_iterator<Iterator> &oth) const {
        return ite <= oth.ite;
    }

    bool operator >=(const dst_iterator<Iterator> &oth) const {
        return ite >= oth.ite;
    }

    const Node& operator *() {
        return ite->first;
    }

    const Node& operator *() const {
        return ite->first;
    }

    dst_iterator operator ++() {
        ++ite;
        return ite;
    }
};

class dst_iteration {
    using ite_type = vec<Edge>::const_iterator;
    const vec<Edge> &edges;

public:
    dst_iteration(const vec<Edge> &edges) : edges(edges) { }

    auto begin() const {
        return dst_iterator<ite_type>(edges.cbegin());
    }

    auto end() const {
        return dst_iterator<ite_type>(edges.cend());
    }
};

class dst_reverse_iteration {
    using ite_type = vec<Edge>::const_reverse_iterator;
    const vec<Edge> &edges;

public:
    dst_reverse_iteration(const vec<Edge> &edges) : edges(edges) { }

    auto begin() const {
        return dst_iterator<ite_type>(edges.crbegin());
    }

    auto end() const {
        return dst_iterator<ite_type>(edges.crend());
    }
};

dst_iteration dst(const vec<Edge> &edges) {
    return dst_iteration(edges);
}

dst_reverse_iteration rdst(const vec<Edge> &edges) {
    return dst_reverse_iteration(edges);
}

}

namespace graph {

using Capacity = ll;

struct FlowEdge : public std::tuple<Node, Capacity, ll, Weight> {
    using std::tuple<Node, Capacity, ll, Weight>::tuple;

    Node& to() {
        return std::get<0>(*this);
    }

    const Node& to() const {
        return std::get<0>(*this);
    }

    Capacity& cap() {
        return std::get<1>(*this);
    }

    const Capacity& cap() const {
        return std::get<1>(*this);
    }

    ll& rev_idx() {
        return std::get<2>(*this);
    }

    const ll& rev_idx() const {
        return std::get<2>(*this);
    }

    Weight& weight() {
        return std::get<3>(*this);
    }

    const Weight& weight() const {
        return std::get<3>(*this);
    }
};

template <bool Directed>
struct FlowGraph : public vvec<FlowEdge> {
    using vvec<FlowEdge>::vvec;

    void add_edge(Node f, Node t, Capacity c = 1, Weight w = 1) {
        add_edge_with_rev(f, t, c, w);
        if (!Directed) add_edge_with_rev(t, f, c, w);
    }

private:
    void add_edge_with_rev(Node f, Node t, Capacity c, Weight w) {
        FlowEdge fe(t, c, (ll)((*this)[t].size()), w);
        (*this)[f].push_back(fe);
        FlowEdge rfe(f, Capacity(), (ll)((*this)[f].size()) - 1, -w);
        (*this)[t].push_back(rfe);
    }
};

}

namespace flow {

using graph::Node;
using graph::Weight;
using graph::Capacity;

template <typename FlowGraph>
class MinCostFlow {
    using prev_node_t = std::pair<Node, ll>;
    using pq_ele_t = std::pair<Weight, Node>;
    FlowGraph fgraph;
    const Weight dinf = 5e15;
    vec<Weight> dists, potential;
    vec<prev_node_t> pnode;

    void dijk(Node start) {
        std::priority_queue<pq_ele_t, vec<pq_ele_t>, std::greater<pq_ele_t>> pq;
        std::fill(ALL(dists), dinf);
        dists[start] = 0;
        pq.emplace(0, start);
        while (pq.size()) {
            Weight d;
            Node from;
            std::tie(d, from) = pq.top();
            pq.pop();
            if (dists[from] < d) continue;
            for (ll i = 0; i < fgraph[from].size(); i++) {
                const auto &edge = fgraph[from][i];
                auto to = edge.to();
                Weight dnxt = d + edge.weight() + potential[from] - potential[to];
                if (edge.cap() <= 0 || dists[to] <= dnxt) continue;
                dists[to] = dnxt;
                pnode[to] = prev_node_t(from, i);
                pq.emplace(dnxt, to);
            }
        }
    }

public:

    MinCostFlow(const FlowGraph &fgraph)
        : fgraph(fgraph), dists(fgraph.size()), 
          potential(fgraph.size(), 0), pnode(fgraph.size())
    {
    }

    Weight solve(Node start, Node goal, Capacity flow) {
        Weight ret = 0;
        while (0 < flow) {
            dijk(start);
            if (dists[goal] == dinf) return -1;
            for (ll i = 0; i < fgraph.size(); i++) potential[i] += dists[i];

            Capacity max_flow = flow;
            for (Node cur = goal; cur != start; cur = pnode[cur].first) {
                Node pre;
                ll pidx;
                std::tie(pre, pidx) = pnode[cur];
                const auto &edge = fgraph[pre][pidx];
                chmin(max_flow, edge.cap());
            }

            if (max_flow == 0) return -1;
            flow -= max_flow;
            ret += max_flow * potential[goal];
            for (Node cur = goal; cur != start; cur = pnode[cur].first) {
                Node pre;
                ll pidx;
                std::tie(pre, pidx) = pnode[cur];
                auto &edge = fgraph[pre][pidx];
                edge.cap() -= max_flow;
                auto &redge = fgraph[cur][edge.rev_idx()];
                redge.cap() += max_flow;
            }
        }

        return ret;
    }

    const FlowGraph& get_graph() const {
        return fgraph;
    }
};

}

int main() {
    ll n, m;
    std::cin >> n >> m;
    using raw_edge = std::tuple<ll, ll, ll, ll>;
    vec<raw_edge> edges(m);
    for (auto &[ u, v, c, d ] : edges) {
        std::cin >> u >> v >> c >> d;
        u--; v--;
    }

    graph::FlowGraph<true> fg(n + 2 * m);
    for (ll i = 0; i < m; i++) {
        auto [ u, v, c , d ] = edges[i];
        ll src = n + 2 * i;
        ll dst = src + 1;
        fg.add_edge(u, src, 2, 0);
        fg.add_edge(v, src, 2, 0);
        fg.add_edge(dst, u, 2, 0);
        fg.add_edge(dst, v, 2, 0);
        fg.add_edge(src, dst, 1, c);
        fg.add_edge(src, dst, 1, d);
    }

    flow::MinCostFlow<decltype(fg)> mcf(fg);
    std::cout << mcf.solve(0, n - 1, 2) << "\n";
    return 0;
}
0