グラフ/巡回セールスマン問題
(test/graph/traveling_salesman_problem.test.cpp)

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• Last update: 2023-02-25 01:48:23+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A

Depends on

• 辺 (include/emthrm/graph/edge.hpp)
• 巡回セールスマン問題 (traveling salesman problem) (include/emthrm/graph/traveling_salesman_problem.hpp)

Code

/*
 * @title グラフ/巡回セールスマン問題
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A
 */

#include <iostream>
#include <limits>
#include <vector>

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

int main() {
  constexpr int INF = std::numeric_limits<int>::max();
  int v, e;
  std::cin >> v >> e;
  std::vector<std::vector<emthrm::Edge<int>>> g(v);
  while (e--) {
    int s, t, d;
    std::cin >> s >> t >> d;
    g[s].emplace_back(s, t, d);
  }
  const int ans = emthrm::traveling_salesman_problem(g, INF);
  std::cout << (ans == INF ? -1 : ans) << '\n';
  return 0;
}

#line 1 "test/graph/traveling_salesman_problem.test.cpp"
/*
 * @title グラフ/巡回セールスマン問題
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_2_A
 */

#include <iostream>
#include <limits>
#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/traveling_salesman_problem.hpp"



#include <algorithm>
#line 6 "include/emthrm/graph/traveling_salesman_problem.hpp"
#include <numeric>
#line 8 "include/emthrm/graph/traveling_salesman_problem.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 10 "include/emthrm/graph/traveling_salesman_problem.hpp"

namespace emthrm {

template <typename CostType>
CostType traveling_salesman_problem(
    const std::vector<std::vector<Edge<CostType>>>& graph,
    const CostType inf = std::numeric_limits<CostType>::max()) {
  const int n = graph.size();
  if (n == 1) [[unlikely]] return 0;
  std::vector<std::vector<CostType>> dp(1 << n, std::vector<CostType>(n, inf));
  dp[1][0] = 0;
  for (int i = 1; i < (1 << n); ++i) {
    for (int j = 0; j < n; ++j) {
      if (dp[i][j] == inf) continue;
      for (const Edge<CostType>& e : graph[j]) {
        if (i >> e.dst & 1) continue;
        dp[i | (1 << e.dst)][e.dst] =
            std::min(dp[i | (1 << e.dst)][e.dst], dp[i][j] + e.cost);
      }
    }
  }
  CostType res = inf;
  for (int j = 1; j < n; ++j) {
    if (dp.back()[j] == inf) continue;
    for (const Edge<CostType>& e : graph[j]) {
      if (e.dst == 0) res = std::min(res, dp.back()[j] + e.cost);
    }
  }
  return res;
}

}  // namespace emthrm


#line 13 "test/graph/traveling_salesman_problem.test.cpp"

int main() {
  constexpr int INF = std::numeric_limits<int>::max();
  int v, e;
  std::cin >> v >> e;
  std::vector<std::vector<emthrm::Edge<int>>> g(v);
  while (e--) {
    int s, t, d;
    std::cin >> s >> t >> d;
    g[s].emplace_back(s, t, d);
  }
  const int ans = emthrm::traveling_salesman_problem(g, INF);
  std::cout << (ans == INF ? -1 : ans) << '\n';
  return 0;
}

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