グラフ/最短路問題/Dijkstra 法
(test/graph/shortest_path/dijkstra.test.cpp)

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• Last update: 2023-02-25 16:35:06+09:00
• Problem: https://judge.yosupo.jp/problem/shortest_path

Depends on

• 辺 (include/emthrm/graph/edge.hpp)
• Dijkstra 法 (include/emthrm/graph/shortest_path/dijkstra.hpp)

Code

/*
 * @title グラフ/最短路問題/Dijkstra 法
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/shortest_path
 */

#include <iostream>
#include <vector>

#include "emthrm/graph/edge.hpp"
#include "emthrm/graph/shortest_path/dijkstra.hpp"

int main() {
  int n, m, s, t;
  std::cin >> n >> m >> s >> t;
  std::vector<std::vector<emthrm::Edge<long long>>> graph(n);
  while (m--) {
    int a, b, c;
    std::cin >> a >> b >> c;
    graph[a].emplace_back(a, b, c);
  }
  emthrm::Dijkstra<long long> dijkstra(graph);
  const long long x = dijkstra.build(s)[t];
  if (x == dijkstra.inf) {
    std::cout << "-1\n";
    return 0;
  }
  const std::vector<int> path = dijkstra.build_path(t);
  const int y = path.size() - 1;
  std::cout << x << ' ' << y << '\n';
  for (int i = 0; i < y; ++i) {
    std::cout << path[i] << ' ' << path[i + 1] << '\n';
  }
  return 0;
}

#line 1 "test/graph/shortest_path/dijkstra.test.cpp"
/*
 * @title グラフ/最短路問題/Dijkstra 法
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/shortest_path
 */

#include <iostream>
#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/shortest_path/dijkstra.hpp"



#include <algorithm>
#include <cassert>
#include <functional>
#include <limits>
#include <queue>
#include <utility>
#line 11 "include/emthrm/graph/shortest_path/dijkstra.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 13 "include/emthrm/graph/shortest_path/dijkstra.hpp"

namespace emthrm {

template <typename CostType>
struct Dijkstra {
  const CostType inf;

  Dijkstra(const std::vector<std::vector<Edge<CostType>>>& graph,
           const CostType inf = std::numeric_limits<CostType>::max())
      : inf(inf), is_built(false), graph(graph) {}

  std::vector<CostType> build(const int s) {
    is_built = true;
    const int n = graph.size();
    std::vector<CostType> dist(n, inf);
    dist[s] = 0;
    prev.assign(n, -1);
    std::priority_queue<std::pair<CostType, int>,
                        std::vector<std::pair<CostType, int>>,
                        std::greater<std::pair<CostType, int>>> que;
    que.emplace(0, s);
    while (!que.empty()) {
      const auto [d, ver] = que.top();
      que.pop();
      if (d > dist[ver]) continue;
      for (const Edge<CostType>& e : graph[ver]) {
        if (dist[ver] + e.cost < dist[e.dst]) {
          dist[e.dst] = dist[ver] + e.cost;
          prev[e.dst] = ver;
          que.emplace(dist[e.dst], e.dst);
        }
      }
    }
    return dist;
  }

  std::vector<int> build_path(int t) const {
    assert(is_built);
    std::vector<int> res;
    for (; t != -1; t = prev[t]) {
      res.emplace_back(t);
    }
    std::reverse(res.begin(), res.end());
    return res;
  }

 private:
  bool is_built;
  std::vector<int> prev;
  std::vector<std::vector<Edge<CostType>>> graph;
};

}  // namespace emthrm


#line 12 "test/graph/shortest_path/dijkstra.test.cpp"

int main() {
  int n, m, s, t;
  std::cin >> n >> m >> s >> t;
  std::vector<std::vector<emthrm::Edge<long long>>> graph(n);
  while (m--) {
    int a, b, c;
    std::cin >> a >> b >> c;
    graph[a].emplace_back(a, b, c);
  }
  emthrm::Dijkstra<long long> dijkstra(graph);
  const long long x = dijkstra.build(s)[t];
  if (x == dijkstra.inf) {
    std::cout << "-1\n";
    return 0;
  }
  const std::vector<int> path = dijkstra.build_path(t);
  const int y = path.size() - 1;
  std::cout << x << ' ' << y << '\n';
  for (int i = 0; i < y; ++i) {
    std::cout << path[i] << ' ' << path[i + 1] << '\n';
  }
  return 0;
}

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