Task: Floyd-Warshall algorithm



C#: using System;

namespace FloydWarshallAlgorithm {
    class Program {
        static void FloydWarshall(int[,] weights, int numVerticies) {
            double[,] dist = new double[numVerticies, numVerticies];
            for (int i = 0; i < numVerticies; i++) {
                for (int j = 0; j < numVerticies; j++) {
                    dist[i, j] = double.PositiveInfinity;
                }
            }

            for (int i = 0; i < weights.GetLength(0); i++) {
                dist[weights[i, 0] - 1, weights[i, 1] - 1] = weights[i, 2];
            }

            int[,] next = new int[numVerticies, numVerticies];
            for (int i = 0; i < numVerticies; i++) {
                for (int j = 0; j < numVerticies; j++) {
                    if (i != j) {
                        next[i, j] = j + 1;
                    }
                }
            }

            for (int k = 0; k < numVerticies; k++) {
                for (int i = 0; i < numVerticies; i++) {
                    for (int j = 0; j < numVerticies; j++) {
                        if (dist[i, k] + dist[k, j] < dist[i, j]) {
                            dist[i, j] = dist[i, k] + dist[k, j];
                            next[i, j] = next[i, k];
                        }
                    }
                }
            }

            PrintResult(dist, next);
        }

        static void PrintResult(double[,] dist, int[,] next) {
            Console.WriteLine("pair     dist    path");
            for (int i = 0; i < next.GetLength(0); i++) {
                for (int j = 0; j < next.GetLength(1); j++) {
                    if (i != j) {
                        int u = i + 1;
                        int v = j + 1;
                        string path = string.Format("{0} -> {1}    {2,2:G}     {3}", u, v, dist[i, j], u);
                        do {
                            u = next[u - 1, v - 1];
                            path += " -> " + u;
                        } while (u != v);
                        Console.WriteLine(path);
                    }
                }
            }
        }

        static void Main(string[] args) {
            int[,] weights = { { 1, 3, -2 }, { 2, 1, 4 }, { 2, 3, 3 }, { 3, 4, 2 }, { 4, 2, -1 } };
            int numVerticies = 4;

            FloydWarshall(weights, numVerticies);
        }
    }
}








Fortran: module floyd_warshall_algorithm

  use, intrinsic :: ieee_arithmetic

  implicit none

  integer, parameter :: floating_point_kind = &
       & ieee_selected_real_kind (6, 37)
  integer, parameter :: fpk = floating_point_kind

  integer, parameter :: nil_vertex = 0

  type :: edge
     integer :: u
     real(kind = fpk) :: weight
     integer :: v
  end type edge

  type :: edge_list
     type(edge), allocatable :: element(:)
  end type edge_list

contains

  subroutine make_example_graph (edges)
    type(edge_list), intent(out) :: edges

    allocate (edges%element(1:5))
    edges%element(1) = edge (1, -2.0, 3)
    edges%element(2) = edge (3, +2.0, 4)
    edges%element(3) = edge (4, -1.0, 2)
    edges%element(4) = edge (2, +4.0, 1)
    edges%element(5) = edge (2, +3.0, 3)
  end subroutine make_example_graph

  function find_max_vertex (edges) result (n)
    type(edge_list), intent(in) :: edges
    integer n

    integer i

    n = 1
    do i = lbound (edges%element, 1), ubound (edges%element, 1)
       n = max (n, edges%element(i)%u)
       n = max (n, edges%element(i)%v)
    end do
  end function find_max_vertex

  subroutine floyd_warshall (edges, max_vertex, distance, next_vertex)

    type(edge_list), intent(in) :: edges
    integer, intent(out) :: max_vertex
    real(kind = fpk), allocatable, intent(out) :: distance(:,:)
    integer, allocatable, intent(out) :: next_vertex(:,:)

    integer :: n
    integer :: i, j, k
    integer :: u, v
    real(kind = fpk) :: dist_ikj
    real(kind = fpk) :: infinity

    n = find_max_vertex (edges)
    max_vertex = n

    allocate (distance(1:n, 1:n))
    allocate (next_vertex(1:n, 1:n))

    infinity = ieee_value (1.0_fpk,  ieee_positive_inf)

    

    do i = 1, n
       do j = 1, n
          distance(i, j) = infinity
          next_vertex (i, j) = nil_vertex
       end do
    end do
    do i = lbound (edges%element, 1), ubound (edges%element, 1)
       u = edges%element(i)%u
       v = edges%element(i)%v
       distance(u, v) = edges%element(i)%weight
       next_vertex(u, v) = v
    end do
    do i = 1, n
       distance(i, i) = 0.0_fpk 
       next_vertex(i, i) = i
    end do

    

    do k = 1, n
       do i = 1, n
          do j = 1, n
             dist_ikj = distance(i, k) + distance(k, j)
             if (dist_ikj < distance(i, j)) then
                distance(i, j) = dist_ikj
                next_vertex(i, j) = next_vertex(i, k)
             end if
          end do
       end do
    end do

  end subroutine floyd_warshall

  subroutine print_path (next_vertex, u, v)
    integer, intent(in) :: next_vertex(:,:)
    integer, intent(in) :: u, v

    integer i

    if (next_vertex(u, v) /= nil_vertex) then
       i = u
       write (*, '(I0)', advance = 'no') i
       do while (i /= v)
          i = next_vertex(i, v)
          write (*, '('' -> '', I0)', advance = 'no') i
       end do
    end if
  end subroutine print_path

end module floyd_warshall_algorithm

program floyd_warshall_task

  use, non_intrinsic :: floyd_warshall_algorithm

  implicit none

  type(edge_list) :: example_graph
  integer :: max_vertex
  real(kind = fpk), allocatable :: distance(:,:)
  integer, allocatable :: next_vertex(:,:)
  integer :: u, v

  call make_example_graph (example_graph)
  call floyd_warshall (example_graph, max_vertex, distance, &
       &               next_vertex)

1000 format (1X, I0, ' -> ', I0, 5X, F4.1, 6X)

  write (*, '(''  pair     distance    path'')')
  write (*, '(''---------------------------------------'')')
  do u = 1, max_vertex
     do v = 1, max_vertex
        if (u /= v) then
           write (*, 1000, advance = 'no') u, v, distance(u, v)
           call print_path (next_vertex, u, v)
           write (*, '()', advance = 'yes')
        end if
     end do
  end do

end program floyd_warshall_task