#992729 (C++17) No.114 遠い未来

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問題	No.114 遠い未来
コンテスト
ユーザー	Nachia
提出日時	2024-07-05 00:41:30
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	2,104 ms / 5,000 ms
コード長	13,160 bytes
コンパイル時間	1,760 ms
コンパイル使用メモリ	133,912 KB
最終ジャッジ日時	2025-02-22 02:07:36
ジャッジサーバーID （参考情報）	judge4 / judge3
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 * 25
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ソースコード

raw source code
#include <vector>
#include <utility>
#include <cassert>
#include <algorithm>

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia

namespace nachia {

struct DsuFast{
private:
    std::vector<int> w;
public:
    DsuFast(int n = 0) : w(n, -1) {}
    int leader(int u){
        if(w[u] < 0) return u;
        return w[u] = leader(w[u]);
    }
    int operator[](int u){ return leader(u); }
    int merge(int u, int v){
        u = leader(u);
        v = leader(v);
        if(u == v) return u;
        if(-w[u] < -w[v]) std::swap(u, v);
        w[u] += w[v];
        w[v] = u;
        return u;
    }
    int size(int u){ return -w[leader(u)]; }
    bool same(int u, int v){ return leader(u) == leader(v); }
};

} // namespace nachia
#include <queue>

namespace nachia{

template<class Weight>
struct MultipleTimeDijkstra{
private:
    template<class T>
    using nega_queue = std::priority_queue<T, std::vector<T>, std::greater<T>>;

    struct IncidentEdge{
        int to;
        int e;
        Weight w;
    };
    std::vector<std::vector<IncidentEdge>> inci;
    int n;
    int m;
    Weight inf;
public:
    MultipleTimeDijkstra(
        Graph _graph,
        std::vector<Weight> _weight,
        Weight _inf
    )
        : n(_graph.numVertices())
        , m(_graph.numEdges())
        , inf(_inf)
    {
        inci.resize(n);
        for(int e=0; e<m; e++){
            auto [u,v] = _graph[e];
            inci[u].push_back({ v, e, _weight[e] });
            inci[v].push_back({ u, e, _weight[e] });
        }
    }

    std::vector<int> solve(std::vector<Weight>& w){
        if(n == 0) return {};
        std::vector<int> res(n, -1);
        if(m/n <= 5){
            std::vector<int> vis(n, 0);
            for(int t=0; t<n; t++){
                int v = -1;
                for(int s=0; s<n; s++) if(vis[s] == 0) if(v == -1 || w[s] < w[v]) v = s;
                for(auto& evx : inci[v]){
                    Weight nxd = w[v] + evx.w;
                    int x = evx.to;
                    if(!(nxd < w[x])) continue;
                    w[x] = nxd;
                    res[x] = evx.e;
                }
                vis[v] = 1;
            }
        } else {
            nega_queue<std::pair<Weight, int>> que;
            for(int v=0; v<n; v++) que.push({ w[v], v });
            while(!que.empty()){
                auto [wv,v] = que.top(); que.pop();
                if(w[v] < wv) continue;
                for(auto& evx : inci[v]){
                    Weight nxd = w[v] + evx.w;
                    int x = evx.to;
                    if(!(nxd < w[x])) continue;
                    w[x] = nxd;
                    que.push({ nxd, x });
                    res[x] = evx.e;
                }
            }
        }
        return res;
    }
};

struct MinimumSteinerTree{
    using Weight = long long;

    Graph graph;
    std::vector<int> terminals;
    std::vector<Weight> weight;
    Weight inf;

    std::vector<std::vector<std::pair<int,Weight>>> dp;

private:
    template<class T>
    using nega_queue = std::priority_queue<T, std::vector<T>, std::greater<T>>;
public:

    MinimumSteinerTree(
        Graph _graph,
        std::vector<int> _terminals,
        std::vector<Weight> _weight,
        Weight _inf
    )
        : graph(std::move(_graph))
        , terminals(std::move(_terminals))
        , weight(std::move(_weight))
        , inf(_inf)
    {
        int n = graph.numVertices();
        int m = graph.numEdges();
        int k = int(terminals.size());
        dp.assign(1<<k, std::vector<std::pair<int,Weight>>(n, std::make_pair(-m-1, inf)));
        auto zero = Weight(0);
        for(int i=0; i<n; i++) dp[0][i] = std::make_pair(-n-1, zero);

        auto dijkstra = MultipleTimeDijkstra<Weight>(graph, weight, inf);
        auto check = [&](int i, int v, int pre, Weight w){
            if(w < dp[i][v].second) dp[i][v] = { pre, w };
        };

        for(int i=0; i<(1<<k); i++){
            {
                std::vector<Weight> F(n);
                for(int v=0; v<n; v++) F[v] = dp[i][v].second;
                auto P = dijkstra.solve(F);
                for(int v=0; v<n; v++) if(P[v] >= 0) dp[i][v] = { -P[v] - 1, F[v] };
            }
            for(int kk=0; kk<k; kk++) if(!(i&(1<<k))){
                auto v = terminals[kk];
                check(i|(1<<kk), v, dp[i][v].first, dp[i][v].second);
            }
            int j0 = 1;
            while(j0 <= i) j0 <<= 1;
            for(int j=(j0-1)&~i; j>0; j=((j-1)&~i)) for(int v=0; v<n; v++){
                check(i|j, v, j, dp[i][v].second + dp[j][v].second);
            }
        }
    }

    Weight minWeight(int mask){
        if(mask == 0) return Weight(0);
        int k=0; while(!(mask & (1<<k))) k++;
        return dp[mask][terminals[k]].second;
    }
};

template<class Weight>
std::vector<int> MinimumSteinerTreeExhaustiveMstMethod(
    const Graph& graph,
    const std::vector<Weight>& weight,
    const std::vector<int>& excluded
){
    assert(excluded.size() <= 30);
    struct Edge {
        int u;
        int v;
        int e;
        Weight w;
    };
    int n = graph.numVertices();
    int m = graph.numEdges();
    int k = excluded.size();
    std::vector<Edge> edges(m);
    for(int e=0; e<m; e++){
        edges[e] = { graph[e].from, graph[e].to, e, weight[e] };
    }
    std::sort(edges.begin(), edges.end(), [](const Edge& l, const Edge& r){ return l.w < r.w; });
    std::vector<int> is_ex(n);
    std::pair<Weight, int> anslight = { Weight(0), -1 };
    for(int f=0; f<(1<<k); f++){
        int exc = n-1;
        for(int i=0; i<k; i++){
            int q = (f >> i) & 1;
            exc -= q;
            is_ex[excluded[i]] = q;
        }
        DsuFast dsu(n);
        Weight wsum = Weight(0);
        int cnt = 0;
        for(auto& e : edges){
            if(is_ex[e.u] || is_ex[e.v]) continue;
            if(dsu.same(e.u, e.v)) continue;
            dsu.merge(e.u, e.v);
            cnt++;
            wsum += e.w;
        }
        if(cnt != exc) continue;
        if(f == 0 || wsum < anslight.first) anslight = { wsum, f };
    }
    std::vector<int> selectedEdges;
    {
        int f = anslight.second;
        for(int i=0; i<k; i++) is_ex[excluded[i]] = ((f >> i) & 1);
        DsuFast dsu(n);
        for(auto& e : edges){
            if(is_ex[e.u] || is_ex[e.v]) continue;
            if(dsu.same(e.u, e.v)) continue;
            dsu.merge(e.u, e.v);
            selectedEdges.push_back(e.e);
        }
    }
    return selectedEdges;
}

} // namespace nachia
#include <iostream>
#include <string>
#include <array>
#include <cmath>

int main(){
    using namespace std;
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N, M, T; cin >> N >> M >> T;
    nachia::Graph graph(N, true);
    vector<long long> weight;
    for(int i=0; i<M; i++){
        int u,v,c; cin >> u >> v >> c; u--; v--;
        graph.addEdge(u,v);
        weight.push_back(c);
    }
    vector<int> terminals(T);
    for(int t=0; t<T; t++){
        int a; cin >> a;
        terminals[t] = a-1;
    }
    if(T <= 16){
        auto st = nachia::MinimumSteinerTree(graph, terminals, weight, 1001001001001);
        cout << st.minWeight((1<<T)-1) << endl;
    } else {
        vector<int> mask(N);
        for(int t : terminals) mask[t] = 1;
        vector<int> ex;
        for(int i=0; i<N; i++) if(!mask[i]) ex.push_back(i);
        auto edges = nachia::MinimumSteinerTreeExhaustiveMstMethod(graph, weight, ex);
        long long ans = 0;
        for(int e : edges) ans += weight[e];
        cout << ans << endl;
    }
    return 0;
}
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結果

ソースコード
