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--
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-- Floyd-Warshall algorithm.
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--
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-- See https://en.wikipedia.org/w/index.php?title=Floyd%E2%80%93Warshall_algorithm&oldid=1082310013
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--
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with Ada.Containers.Vectors;
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with Ada.Text_IO; use Ada.Text_IO;
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with Interfaces; use Interfaces;
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with Ada.Numerics.Generic_Elementary_Functions;
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procedure floyd_warshall_task
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is
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Floyd_Warshall_Exception : exception;
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-- The floating point type we shall use is one that has infinities.
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subtype FloatPt is IEEE_Float_32;
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package FloatPt_Elementary_Functions is new Ada.Numerics
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.Generic_Elementary_Functions
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(FloatPt);
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use FloatPt_Elementary_Functions;
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-- The following should overflow and give us an IEEE infinity. But I
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-- have kept the code so you could use some non-IEEE floating point
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-- format and set ENORMOUS_FloatPt to some value that is finite but
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-- much larger than actual graph traversal distances.
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ENORMOUS_FloatPt : constant FloatPt :=
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(FloatPt (1.0) / FloatPt (1.0e-37))**1.0e37;
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--
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-- Input is a Vector of records representing the edges of a graph.
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--
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-- Vertices are identified by integers from 1 .. n.
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--
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type edge is record
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u : Positive;
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weight : FloatPt;
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v : Positive;
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end record;
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package Edge_Vectors is new Ada.Containers.Vectors
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(Index_Type => Positive, Element_Type => edge);
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use Edge_Vectors;
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subtype edge_vector is Edge_Vectors.Vector;
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--
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-- Floyd-Warshall.
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--
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type distance_array is
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array (Positive range <>, Positive range <>) of FloatPt;
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type next_vertex_array is
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array (Positive range <>, Positive range <>) of Natural;
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Nil_Vertex : constant Natural := 0;
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function find_max_vertex -- Find the maximum vertex number.
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(edges : in edge_vector)
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return Positive
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is
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max_vertex : Positive;
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begin
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if Is_Empty (edges) then
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raise Floyd_Warshall_Exception with "no edges";
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end if;
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max_vertex := 1;
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for i in edges.First_Index .. edges.Last_Index loop
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max_vertex := Positive'Max (max_vertex, edges.Element (i).u);
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max_vertex := Positive'Max (max_vertex, edges.Element (i).v);
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end loop;
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return max_vertex;
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end find_max_vertex;
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procedure floyd_warshall -- Perform Floyd-Warshall.
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(edges : in edge_vector;
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max_vertex : in Positive;
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distance : out distance_array;
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next_vertex : out next_vertex_array)
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is
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u, v : Positive;
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dist_ikj : FloatPt;
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begin
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-- Initialize.
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for i in 1 .. max_vertex loop
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for j in 1 .. max_vertex loop
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distance (i, j) := ENORMOUS_FloatPt;
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next_vertex (i, j) := Nil_Vertex;
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end loop;
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end loop;
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for i in edges.First_Index .. edges.Last_Index loop
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u := edges.Element (i).u;
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v := edges.Element (i).v;
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distance (u, v) := edges.Element (i).weight;
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next_vertex (u, v) := v;
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end loop;
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for i in 1 .. max_vertex loop
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distance (i, i) :=
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FloatPt (0.0); -- Distance from a vertex to itself.
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next_vertex (i, i) := i;
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end loop;
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-- Perform the algorithm.
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for k in 1 .. max_vertex loop
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for i in 1 .. max_vertex loop
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for j in 1 .. max_vertex loop
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dist_ikj := distance (i, k) + distance (k, j);
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if dist_ikj < distance (i, j) then
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distance (i, j) := dist_ikj;
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next_vertex (i, j) := next_vertex (i, k);
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end if;
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end loop;
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end loop;
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end loop;
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end floyd_warshall;
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--
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-- Path reconstruction.
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--
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procedure put_path
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(next_vertex : in next_vertex_array;
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u, v : in Positive)
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is
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i : Positive;
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begin
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if next_vertex (u, v) /= Nil_Vertex then
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i := u;
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Put (Positive'Image (i));
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while i /= v loop
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Put (" ->");
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i := next_vertex (i, v);
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Put (Positive'Image (i));
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end loop;
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end if;
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end put_path;
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example_graph : edge_vector;
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max_vertex : Positive;
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begin
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Append (example_graph, (u => 1, weight => FloatPt (-2.0), v => 3));
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Append (example_graph, (u => 3, weight => FloatPt (+2.0), v => 4));
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Append (example_graph, (u => 4, weight => FloatPt (-1.0), v => 2));
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Append (example_graph, (u => 2, weight => FloatPt (+4.0), v => 1));
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Append (example_graph, (u => 2, weight => FloatPt (+3.0), v => 3));
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max_vertex := find_max_vertex (example_graph);
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declare
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distance : distance_array (1 .. max_vertex, 1 .. max_vertex);
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next_vertex : next_vertex_array
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(1 .. max_vertex, 1 .. max_vertex);
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begin
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floyd_warshall (example_graph, max_vertex, distance, next_vertex);
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Put_Line (" pair distance path");
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Put_Line ("---------------------------------------------");
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for u in 1 .. max_vertex loop
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for v in 1 .. max_vertex loop
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if u /= v then
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Put (Positive'Image (u));
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Put (" ->");
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Put (Positive'Image (v));
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Put (" ");
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Put (FloatPt'Image (distance (u, v)));
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Put (" ");
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put_path (next_vertex, u, v);
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Put_Line ("");
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end if;
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end loop;
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end loop;
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end;
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end floyd_warshall_task;
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@ -1,5 +1,4 @@
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require "table2"
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require "math2"
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class floydWarshall
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static function do_calcs(weights, nvertices)
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