#987190 (C++17) No.2780 The Bottle Imp

提出ソース

結果

問題	No.2780 The Bottle Imp
ユーザー	👑 Nachia
提出日時	2024-06-07 23:42:36
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	30 ms / 2,000 ms
コード長	8,291 bytes
コンパイル時間	1,300 ms
コンパイル使用メモリ	111,296 KB
実行使用メモリ	7,820 KB
最終ジャッジ日時	2024-06-08 10:39:33
合計ジャッジ時間	3,367 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	19 ms 6,272 KB
testcase_08	AC	19 ms 6,184 KB
testcase_09	AC	20 ms 6,188 KB
testcase_10	AC	19 ms 6,312 KB
testcase_11	AC	18 ms 6,188 KB
testcase_12	AC	29 ms 7,816 KB
testcase_13	AC	30 ms 7,820 KB
testcase_14	AC	17 ms 6,760 KB
testcase_15	AC	17 ms 6,872 KB
testcase_16	AC	17 ms 6,884 KB
testcase_17	AC	17 ms 6,756 KB
testcase_18	AC	17 ms 6,884 KB
testcase_19	AC	17 ms 6,752 KB
testcase_20	AC	17 ms 6,756 KB
testcase_21	AC	17 ms 6,760 KB
testcase_22	AC	10 ms 5,376 KB
testcase_23	AC	15 ms 5,732 KB
testcase_24	AC	17 ms 5,620 KB
testcase_25	AC	26 ms 7,044 KB
testcase_26	AC	17 ms 5,992 KB
testcase_27	AC	15 ms 6,248 KB
testcase_28	AC	15 ms 6,248 KB
testcase_29	AC	13 ms 5,608 KB
testcase_30	AC	11 ms 5,376 KB
testcase_31	AC	22 ms 7,008 KB
testcase_32	AC	13 ms 6,244 KB
testcase_33	AC	24 ms 7,440 KB
testcase_34	AC	24 ms 7,816 KB
testcase_35	AC	10 ms 5,376 KB
testcase_36	AC	1 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB
testcase_38	AC	11 ms 5,472 KB
testcase_39	AC	21 ms 7,316 KB
testcase_40	AC	22 ms 7,188 KB
testcase_41	AC	21 ms 7,312 KB
testcase_42	AC	2 ms 5,376 KB
testcase_43	AC	2 ms 5,376 KB

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ソースコード

raw source code

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#define rep(i,n) for(int i=0; i<int(n); i++)
#define repr(i,n) for(int i=int(n)-1; i>=0; i--)
const char* yn(bool x){ return x ? "Yes" : "No"; }
#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(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 StronglyConnectedComponents{
private:
    int m_n;
    CsrArray<int> induce;
    int componentNum;
public:

    StronglyConnectedComponents() : m_n(0), induce(), componentNum(0) {}
    StronglyConnectedComponents(Graph E) {
        int n = E.numVertices();
        m_n = n;
        std::vector<int> O(n);
        {
            auto adj = E.getAdjacencyArray();
            int Oi = n;
            std::vector<int> P(n, -1), EI(n, 0);
            for(int s=0; s<n; s++) if(P[s] == -1){
                P[s] = -2;
                int p = s;
                while(p >= 0){
                    if(EI[p] == adj[p].size()){ O[--Oi] = p; p = P[p]; continue; }
                    int q = adj[p][EI[p]++];
                    if(P[q] == -1){ P[q] = p; p = q; }
                }
            }
        }
        E.reverseEdges();
        auto adj = E.getAdjacencyArray();
        std::vector<int> sep = {0}, csr(n), vis(n,0);
        int p1 = 0, p2 = 0;
        for(int s : O) if(!vis[s]){
            csr[p2++] = s; vis[s] = 1;
            for(; p1<p2; p1++){
                int v = csr[p1];
                for(auto e : adj[v]) if(!vis[e]){ vis[e] = 1; csr[p2++] = e; }
            }
            sep.push_back(p2);
        }
        induce = CsrArray<int>::FromRaw(std::move(csr), std::move(sep));
        componentNum = induce.size();
    }

    int numComponents() const noexcept { return componentNum; }
    const CsrArray<int>& getCsr() const noexcept { return induce; }
    std::vector<int> getMapping() const {
        std::vector<int> res(m_n);
        for(int i=0; i<numComponents(); i++) for(int v : induce[i]) res[v] = i;
        return res;
    }
};

} // namespace nachia
using namespace std;

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N; cin >> N;
    auto graph = nachia::Graph(N, false);
    rep(i,N){
        int a; cin >> a;
        rep(t,a){ int b; cin >> b; graph.addEdge(i,b-1); }
    }
    auto scc = nachia::StronglyConnectedComponents(graph);
    graph.contract(scc.numComponents(), scc.getMapping());
    auto adj = graph.getAdjacencyArray();
    bool ans = scc.getMapping()[0] == 0;
    rep(i,adj.size()-1){
        bool ok = false;
        for(int j : adj[i]) if(j == i+1) ok = true;
        if(!ok) ans = false;
    }
    cout << yn(ans) << endl;
    return 0;
}

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結果

テストケース

ソースコード