(**************************************************************************)
(*                                                                        *)
(*  Ocamlgraph: a generic graph library for OCaml                         *)
(*  Copyright (C) 2004-2007                                               *)
(*  Sylvain Conchon, Jean-Christophe Filliatre and Julien Signoles        *)
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
(*  modify it under the terms of the GNU Library General Public           *)
(*  License version 2, with the special exception on linking              *)
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

(* Ocamlgraph demo program: solving the Sudoku puzzle using graph coloring *)

open Format
open Graph

(* We use undirected graphs with nodes containing a pair of integers
   (the cell coordinates in 0..8 x 0..8).
   The integer marks of the nodes will store the colors. *)
module G = Imperative.Graph.Abstract(struct type t = int * int end)

(* The Sudoku grid = a graph with 9x9 nodes *)
let g = G.create ()

(* We create the 9x9 nodes, add them to the graph and keep them in a matrix 
   for later access *)
let nodes = 
  let new_node i j = let v = G.V.create (i, j) in G.add_vertex g v; v in
  Array.init 9 (fun i -> Array.init 9 (new_node i))

let node i j = nodes.(i).(j) (* shortcut for easier access *)

(* We add the edges: 
   two nodes are connected whenever they can't have the same value,
   i.e. they belong to the same line, the same column or the same 3x3 group *)
let () =
  for i = 0 to 8 do for j = 0 to 8 do
    for k = 0 to 8 do
      if k <> i then G.add_edge g (node i j) (node k j);
      if k <> j then G.add_edge g (node i j) (node i k);
    done;
    let gi = 3 * (i / 3) and gj = 3 * (j / 3) in
    for di = 0 to 2 do for dj = 0 to 2 do
      let i' = gi + di and j' = gj + dj in
      if i' <> i || j' <> j then G.add_edge g (node i j) (node i' j')
    done done
  done done

(* Displaying the current state of the graph *)
let display () =
  for i = 0 to 8 do
    for j = 0 to 8 do printf "%d" (G.Mark.get (node i j)) done;
    printf "\n";
  done;
  printf "@?"

(* We read the initial constraints from standard input and we display g *)
let () =
  for i = 0 to 8 do
    let s = read_line () in
    for j = 0 to 8 do match s.[j] with
      | '1'..'9' as ch -> G.Mark.set (node i j) (Char.code ch - Char.code '0')
      | _ -> ()
    done
  done;
  display ();
  printf "---------@."

(* We solve the Sudoku by 9-coloring the graph g and we display the solution *)
module C = Coloring.Mark(G)

let () =
  C.coloring g 9; display ()
