#567220 (C++17) No.1254 補強への架け橋

• 問題: No.1254 補強への架け橋
• ユーザー: hitonanode
• 提出日時: 2020-10-16 20:17:05
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 66 ms / 2,000 ms
• コード長: 8,095 bytes
• コンパイル時間: 2,082 ms
• コンパイル使用メモリ: 205,216 KB
• 最終ジャッジ日時: 2025-01-15 07:54:45
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 123

ソースコード

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x) {}
#endif

struct UndirectedGraph
{
    int V; // # of vertices
    int E; // # of edges
    int k;
    std::vector<std::vector<std::pair<int, int>>> to;
    std::vector<std::pair<int, int>> edges;
    std::vector<int> root_ids; // DFS forestの構築で根になった頂点

    std::vector<int> is_bridge; // Whether edge i is bridge or not, size = E
    std::vector<int> is_articulation; // whether vertex i is articulation point or not, size = V

    // lowlink
    std::vector<int> order;   // visiting order of DFS tree, size = V
    std::vector<int> lowlink; // size = V
    std::vector<int> is_dfstree_edge; // size = E

    int tecc_num; // 二重辺連結成分数
    std::vector<int> tecc_id; // 各頂点が何個目の二重辺連結成分か

    int tvcc_num; // 二重頂点連結成分数
    std::vector<int> tvcc_id; // 各辺が何個目の二重頂点連結成分か

    UndirectedGraph(int V) : V(V), E(0), k(0), to(V), is_articulation(V, 0), order(V, -1), lowlink(V, -1), tecc_num(0), tvcc_num(0) {}

    void add_edge(int v1, int v2)
    {
        assert(v1 >= 0 and v1 < V);
        assert(v2 >= 0 and v2 < V);
        to[v1].emplace_back(v2, E);
        to[v2].emplace_back(v1, E);
        edges.emplace_back(v1, v2);
        is_bridge.push_back(0);
        is_dfstree_edge.push_back(0);
        tvcc_id.push_back(-1);
        E++;
    }

    std::vector<int> _edge_stack;
    int _root_now;

    // Build DFS tree
    // Complexity: O(V + E)
    void dfs_lowlink(int now, int prv_eid = -1)
    {
        if (prv_eid < 0) _root_now = k;
        if (prv_eid == -1) root_ids.push_back(now);
        order[now] = lowlink[now] = k++;
        for (const auto &nxt : to[now]) if (nxt.second != prv_eid)
        {
            if (order[nxt.first] < order[now]) _edge_stack.push_back(nxt.second);
            if (order[nxt.first] >= 0)
            {
                lowlink[now] = std::min(lowlink[now], order[nxt.first]);
            }
            else
            {
                is_dfstree_edge[nxt.second] = 1;
                dfs_lowlink(nxt.first, nxt.second);
                lowlink[now] = std::min(lowlink[now], lowlink[nxt.first]);

                if ((order[now] == _root_now and order[nxt.first] != _root_now + 1) or (order[now] != _root_now and lowlink[nxt.first] >= order[now])) {
                    is_articulation[now] = 1;
                }
                if (lowlink[nxt.first] >= order[now]) {
                    while (true) {
                        int e = _edge_stack.back();
                        tvcc_id[e] = tvcc_num;
                        _edge_stack.pop_back();
                        if (std::minmax(edges[e].first, edges[e].second) == std::minmax(now, nxt.first)) {
                            break;
                        }
                    }
                    tvcc_num++;
                }
            }
        }
    }

    // Find all bridges
    // Complexity: O(V + E)
    void detectBridge()
    {
        for (int i = 0; i < E; i++)
        {
            int v1 = edges[i].first, v2 = edges[i].second;
            if (order[v1] < 0) dfs_lowlink(v1);
            if (order[v1] > order[v2]) std::swap(v1, v2);
            if (order[v1] < lowlink[v2]) is_bridge[i] = 1;
        }
    }

    // Find two-edge-connected components and classify all vertices
    // Complexity:  O(V + E)
    void two_edge_connected_components()
    {
        tecc_num = 0;
        tecc_id.assign(V, -1);

        for (int i = 0; i < V; i++) if (tecc_id[i] == -1)
        {
            tecc_id[i] = tecc_num;
            std::queue<int> que;
            que.push(i);
            while (!que.empty())
            {
                int now = que.front();
                que.pop();
                for (const auto &edge : to[now])
                {
                    int nxt = edge.first;
                    if (tecc_id[nxt] >= 0 or is_bridge[edge.second]) continue;
                    tecc_id[nxt] = tecc_num;
                    que.push(nxt);
                }
            }
            tecc_num++;
        }
    }
};

int main()
{
    int N;
    cin >> N;
    UndirectedGraph graph(N);
    REP(i, N) {
        int a, b;
        cin >> a >> b;
        graph.add_edge(a - 1, b - 1);
    }
    graph.detectBridge();
    vector<int> ret;
    REP(i, N) if (!graph.is_bridge[i]) ret.emplace_back(i + 1);
    cout << ret.size() << '\n';
    for (auto x : ret) cout << x << ' ';
    cout << '\n';
}