Warshall-Floyd algorithm (For adjacency matrix graph)
(Mylib/Graph/ShortestPath/warshall_floyd_for_matrix_graph.cpp)

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

Operations

Requirements

Notes

Problems

References

Verified with

• test/aoj/2171/main.test.cpp

Code

#pragma once
#include <optional>
#include <vector>

namespace haar_lib {
  namespace warshall_floyd_for_matrix_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_for_matrix_impl

  template <typename T, T INVALID>
  auto warshall_floyd_for_matrix(const std::vector<std::vector<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 (int j = 0; j < n; ++j) {
        if (g[i][j] != INVALID) {
          dist[i][j] = g[i][j];
        }
      }
    }

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

#line 2 "Mylib/Graph/ShortestPath/warshall_floyd_for_matrix_graph.cpp"
#include <optional>
#include <vector>

namespace haar_lib {
  namespace warshall_floyd_for_matrix_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_for_matrix_impl

  template <typename T, T INVALID>
  auto warshall_floyd_for_matrix(const std::vector<std::vector<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 (int j = 0; j < n; ++j) {
        if (g[i][j] != INVALID) {
          dist[i][j] = g[i][j];
        }
      }
    }

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

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