グラフ/オイラー路 有向グラフ版
(test/graph/eulerian_trail_in_directed_graph.test.cpp)

• View this file on GitHub
• Last update: 2023-02-25 16:35:06+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0225

Depends on

• 辺 (include/emthrm/graph/edge.hpp)
• オイラー路 (Eulerian trail) 有向グラフ版 (include/emthrm/graph/eulerian_trail_in_directed_graph.hpp)

Code

/*
 * @title グラフ/オイラー路 有向グラフ版
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0225
 */

#include <iostream>
#include <string>
#include <vector>

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

int main() {
  constexpr int SIGMA = 26;
  while (true) {
    int n;
    std::cin >> n;
    if (n == 0) [[unlikely]] break;
    std::vector<std::vector<emthrm::Edge<bool>>> graph(SIGMA);
    while (n--) {
      std::string word;
      std::cin >> word;
      graph[word.front() - 'a'].emplace_back(word.front() - 'a',
                                             word.back() - 'a');
    }
    const std::vector<emthrm::Edge<bool>> trail =
        emthrm::eulerian_trail_in_directed_graph(graph);
    std::cout << (!trail.empty() && trail.front().src == trail.back().dst ?
                  "OK\n" : "NG\n");
  }
  return 0;
}

#line 1 "test/graph/eulerian_trail_in_directed_graph.test.cpp"
/*
 * @title グラフ/オイラー路 有向グラフ版
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0225
 */

#include <iostream>
#include <string>
#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/eulerian_trail_in_directed_graph.hpp"



#include <algorithm>
#include <iterator>
#include <ranges>
#include <utility>
#line 9 "include/emthrm/graph/eulerian_trail_in_directed_graph.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 11 "include/emthrm/graph/eulerian_trail_in_directed_graph.hpp"

namespace emthrm {

template <typename CostType>
std::vector<Edge<CostType>> eulerian_trail_in_directed_graph(
    std::vector<std::vector<Edge<CostType>>> graph, int s = -1) {
  const int n = graph.size();
  int edge_num = 0;
  std::vector<int> deg(n, 0);
  for (int i = 0; i < n; ++i) {
    edge_num += graph[i].size();
    deg[i] += graph[i].size();
    for (const int e : graph[i] | std::views::transform(&Edge<CostType>::dst)) {
      --deg[e];
    }
  }
  if (edge_num == 0) [[unlikely]] return {};
  const int not0 = n - std::count(deg.begin(), deg.end(), 0);
  if (not0 == 0) {
    if (s == -1) {
      s = std::distance(
          graph.begin(),
          std::find_if_not(
              graph.begin(), graph.end(),
              [](const std::vector<Edge<CostType>>& edges) -> bool {
                return edges.empty();
              }));
    }
  } else if (not0 == 2) {
    bool t_exists = false;
    for (int i = 0; i < n; ++i) {
      if (deg[i] == 0) continue;
      if (deg[i] == 1) {
        if (s == -1) s = i;
        if (s != i) return {};
      } else if (deg[i] == -1) {
        if (t_exists) return {};
        t_exists = true;
      } else {
        return {};
      }
    }
  } else {
    return {};
  }
  std::vector<Edge<CostType>> res;
  const auto dfs = [&graph, &res](auto dfs, const int ver) -> void {
    while (!graph[ver].empty()) {
      const Edge<CostType> e = graph[ver].back();
      graph[ver].pop_back();
      dfs(dfs, e.dst);
      res.emplace_back(e);
    }
  };
  dfs(dfs, s);
  if (std::cmp_equal(res.size(), edge_num)) {
    std::reverse(res.begin(), res.end());
    return res;
  }
  return {};
}

}  // namespace emthrm


#line 14 "test/graph/eulerian_trail_in_directed_graph.test.cpp"

int main() {
  constexpr int SIGMA = 26;
  while (true) {
    int n;
    std::cin >> n;
    if (n == 0) [[unlikely]] break;
    std::vector<std::vector<emthrm::Edge<bool>>> graph(SIGMA);
    while (n--) {
      std::string word;
      std::cin >> word;
      graph[word.front() - 'a'].emplace_back(word.front() - 'a',
                                             word.back() - 'a');
    }
    const std::vector<emthrm::Edge<bool>> trail =
        emthrm::eulerian_trail_in_directed_graph(graph);
    std::cout << (!trail.empty() && trail.front().src == trail.back().dst ?
                  "OK\n" : "NG\n");
  }
  return 0;
}

Back to top page