Warshall-Floyd algorithm
(Mylib/Graph/ShortestPath/warshall_floyd.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Depends on

• Basic graph (Mylib/Graph/Template/graph.cpp)

Verified with

• test/aoj/GRL_1_C/main.test.cpp

Code

#pragma once
#include <optional>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  namespace warshall_floyd_impl {
    template <typename T>
    struct result {
      std::vector<std::vector<std::optional<T>>> dist;
      bool has_negative_cycle;
      const auto &operator[](int i) const { return dist[i]; }
    };
  }  // namespace warshall_floyd_impl

  template <typename T>
  auto warshall_floyd(const graph<T> &g) {
    const int n = g.size();
    auto dist   = std::vector(n, std::vector<std::optional<T>>(n));

    for (int i = 0; i < n; ++i) dist[i][i] = 0;

    for (int i = 0; i < n; ++i) {
      for (auto &e : g[i]) {
        dist[e.from][e.to] = e.cost;
      }
    }

    for (int k = 0; k < n; ++k) {
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          if (dist[i][k] and dist[k][j]) {
            if (not dist[i][j]) {
              dist[i][j] = *dist[i][k] + *dist[k][j];
            } else {
              dist[i][j] = std::min(*dist[i][j], *dist[i][k] + *dist[k][j]);
            }
          }
        }
      }
    }

    bool has_negative_cycle = false;
    for (int i = 0; i < n; ++i)
      if (*dist[i][i] < 0) has_negative_cycle = true;

    return warshall_floyd_impl::result<T>{dist, has_negative_cycle};
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/ShortestPath/warshall_floyd.cpp"
#include <optional>
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 5 "Mylib/Graph/ShortestPath/warshall_floyd.cpp"

namespace haar_lib {
  namespace warshall_floyd_impl {
    template <typename T>
    struct result {
      std::vector<std::vector<std::optional<T>>> dist;
      bool has_negative_cycle;
      const auto &operator[](int i) const { return dist[i]; }
    };
  }  // namespace warshall_floyd_impl

  template <typename T>
  auto warshall_floyd(const graph<T> &g) {
    const int n = g.size();
    auto dist   = std::vector(n, std::vector<std::optional<T>>(n));

    for (int i = 0; i < n; ++i) dist[i][i] = 0;

    for (int i = 0; i < n; ++i) {
      for (auto &e : g[i]) {
        dist[e.from][e.to] = e.cost;
      }
    }

    for (int k = 0; k < n; ++k) {
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          if (dist[i][k] and dist[k][j]) {
            if (not dist[i][j]) {
              dist[i][j] = *dist[i][k] + *dist[k][j];
            } else {
              dist[i][j] = std::min(*dist[i][j], *dist[i][k] + *dist[k][j]);
            }
          }
        }
      }
    }

    bool has_negative_cycle = false;
    for (int i = 0; i < n; ++i)
      if (*dist[i][i] < 0) has_negative_cycle = true;

    return warshall_floyd_impl::result<T>{dist, has_negative_cycle};
  }
}  // namespace haar_lib

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