結果

問題 No.3087 University Coloring
ユーザー 👑 Nachia
提出日時 2025-04-04 21:36:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 95 ms / 2,000 ms
コード長 8,253 bytes
コンパイル時間 949 ms
コンパイル使用メモリ 89,592 KB
実行使用メモリ 9,148 KB
最終ジャッジ日時 2025-04-04 21:38:40
合計ジャッジ時間 5,016 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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 * 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 # 

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<i64(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <utility>
#include <cassert>

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() : m_n(0), m_e(0), m_isUndir(false) {}
    explicit Graph(int n, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    explicit Graph(int n, const std::vector<std::pair<int, int>>& edges, int 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, int 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

namespace nachia{

std::vector<int> MinimumSpanningForestKnownPriority(
    const nachia::Graph& graph,
    const std::vector<int>& edgePriorityOrdered = {}
){
    int m = graph.numEdges();
    auto dsu = nachia::DsuFast(graph.numVertices());
    std::vector<int> ans;
    bool f = !edgePriorityOrdered.empty();
    for(int i=0; i<m; i++){
        int e = f ? edgePriorityOrdered[i] : i;
        int v = graph[e].from;
        int w = graph[e].to;
        if(dsu.same(v,w)) continue;
        ans.push_back(e);
        dsu.merge(v,w);
    }
    return ans;
}

template<class Weight>
std::vector<int> MinimumSpanningForest(
    const nachia::Graph& graph,
    const std::vector<Weight>& weight
){
    int m = graph.numEdges();
    std::vector<int> P(m);
    for(int i=0; i<m; i++) P[i] = i;
    std::sort(P.begin(), P.end(), [&](int l, int r){ return weight[l] < weight[r]; });
    return MinimumSpanningForestKnownPriority(graph, P);
}

} // namespace nachia


void testcase(){
    i64 N, M; cin >> N >> M;
    auto graph = nachia::Graph(N, true, M);
    vector<i64> W(M);
    rep(i,M){
        cin >> graph[i].from >> graph[i].to >> W[i];
        W[i] = -W[i];
    }
    for(auto& [u,v] : graph){ u--; v--; } 
    auto mst = nachia::MinimumSpanningForest(graph, W);
    i64 ans = 0;
    rep(i,mst.size()) ans -= W[mst[i]];
    ans *= 2;
    cout << ans << "\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    rep(t,1) testcase();
    return 0;
}
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