グラフ/lowlink（橋）
(test/graph/lowlink.1.test.cpp)

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• Last update: 2023-02-27 16:57:22+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_B

Depends on

• 辺 (include/emthrm/graph/edge.hpp)
• lowlink (include/emthrm/graph/lowlink.hpp)

Code

/*
 * @title グラフ/lowlink（橋）
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_B
 */

#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>

#include "emthrm/graph/edge.hpp"
#include "emthrm/graph/lowlink.hpp"

int main() {
  int v, e;
  std::cin >> v >> e;
  std::vector<std::vector<emthrm::Edge<bool>>> graph(v);
  while (e--) {
    int s, t;
    std::cin >> s >> t;
    graph[s].emplace_back(s, t);
    graph[t].emplace_back(t, s);
  }
  emthrm::Lowlink<bool> l(graph);
  std::ranges::sort(l.bridges.begin(), l.bridges.end(), {},
                    [](const emthrm::Edge<bool>& e) -> std::pair<int, int> {
                      return std::make_pair(e.src, e.dst);
                    });
  for (const emthrm::Edge<bool>& bridge : l.bridges) {
    std::cout << bridge.src << ' ' << bridge.dst << '\n';
  }
  return 0;
}

#line 1 "test/graph/lowlink.1.test.cpp"
/*
 * @title グラフ/lowlink（橋）
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_B
 */

#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 1 "include/emthrm/graph/lowlink.hpp"



#line 6 "include/emthrm/graph/lowlink.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 8 "include/emthrm/graph/lowlink.hpp"

namespace emthrm {

template <typename CostType>
struct Lowlink {
  std::vector<int> order, lowlink, articulation_points;
  std::vector<Edge<CostType>> bridges;
  const std::vector<std::vector<Edge<CostType>>> graph;

  explicit Lowlink(const std::vector<std::vector<Edge<CostType>>>& graph)
      : graph(graph) {
    const int n = graph.size();
    order.assign(n, -1);
    lowlink.resize(n);
    int t = 0;
    for (int i = 0; i < n; ++i) {
      if (order[i] == -1) dfs(-1, i, &t);
    }
  }

 private:
  void dfs(const int par, const int ver, int* t) {
    order[ver] = lowlink[ver] = (*t)++;
    int num = 0;
    bool is_articulation_point = false;
    for (const Edge<CostType>& e : graph[ver]) {
      if (order[e.dst] == -1) {
        ++num;
        dfs(ver, e.dst, t);
        lowlink[ver] = std::min(lowlink[ver], lowlink[e.dst]);
        if (order[ver] <= lowlink[e.dst]) {
          is_articulation_point = true;
          if (order[ver] < lowlink[e.dst]) {
            bridges.emplace_back(std::min(ver, e.dst), std::max(ver, e.dst),
                                 e.cost);
          }
        }
      } else if (e.dst != par) {
        lowlink[ver] = std::min(lowlink[ver], order[e.dst]);
      }
    }
    if ((par == -1 && num >= 2) || (par != -1 && is_articulation_point)) {
      articulation_points.emplace_back(ver);
    }
  }
};

}  // namespace emthrm


#line 14 "test/graph/lowlink.1.test.cpp"

int main() {
  int v, e;
  std::cin >> v >> e;
  std::vector<std::vector<emthrm::Edge<bool>>> graph(v);
  while (e--) {
    int s, t;
    std::cin >> s >> t;
    graph[s].emplace_back(s, t);
    graph[t].emplace_back(t, s);
  }
  emthrm::Lowlink<bool> l(graph);
  std::ranges::sort(l.bridges.begin(), l.bridges.end(), {},
                    [](const emthrm::Edge<bool>& e) -> std::pair<int, int> {
                      return std::make_pair(e.src, e.dst);
                    });
  for (const emthrm::Edge<bool>& bridge : l.bridges) {
    std::cout << bridge.src << ' ' << bridge.dst << '\n';
  }
  return 0;
}

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