Add a pretty printer for the solution.

This lets us validate the solution more easily, and gives us what we
actually want which is a pretty picture of the layout.

bin/main.ml

@@ -1,4 +1,4 @@
-let debugf = Format.ifprintf Format.std_formatter
+(*let debugf = Format.ifprintf Format.std_formatter*)
 
 let pp_card out ((x, y), n) = Format.fprintf out "((%d, %d), %d)" x y n
 
@@ -36,31 +36,31 @@ let next_pos size (x, y) cards =
   in
   impl (x + 1) y
 
-let pp_pos out (x, y) = Format.fprintf out "(@[%d,@ %d@])" x y
+(*let pp_pos out (x, y) = Format.fprintf out "(@[%d,@ %d@])" x y*)
 
-let rec find_solutions_impl cards size n idx current_alloc current_pos = begin
-	debugf "find_solutions_impl:@ @[<hov>%a@ %d@ %d@ %d@ %a@ %a@]@;@?"
+let rec find_solutions_impl cards size n idx current_alloc current_pos =
+  begin
+    (*debugf "find_solutions_impl:@ @[<hov>%a@ %d@ %d@ %d@ %a@ %a@]@;@?"
 	(Format.pp_print_array Format.pp_print_int) cards
 	size n idx
 	(Format.pp_print_list pp_card) current_alloc
-	pp_pos current_pos;
-
-  if current_pos = (0, size) then current_alloc
-  else if idx = 0 then []
-  else if cards.(idx) = 0 then
-    find_solutions_impl cards size n (idx - 1) current_alloc current_pos
-  else if card_fits size idx current_alloc current_pos then begin
-    Array.set cards idx (cards.(idx) - 1);
-    let new_alloc = (current_pos, idx) :: current_alloc in
-    let new_pos = next_pos size current_pos new_alloc in
-    let alloc = find_solutions_impl cards size n n new_alloc new_pos in
-    Array.set cards idx (cards.(idx) + 1);
-    if List.is_empty alloc then
-    find_solutions_impl cards size n (idx - 1) current_alloc current_pos
-    else alloc
+	pp_pos current_pos;*)
+    if current_pos = (0, size) then current_alloc
+    else if idx = 0 then []
+    else if cards.(idx) = 0 then
+      find_solutions_impl cards size n (idx - 1) current_alloc current_pos
+    else if card_fits size idx current_alloc current_pos then begin
+      Array.set cards idx (cards.(idx) - 1);
+      let new_alloc = (current_pos, idx) :: current_alloc in
+      let new_pos = next_pos size current_pos new_alloc in
+      let alloc = find_solutions_impl cards size n n new_alloc new_pos in
+      Array.set cards idx (cards.(idx) + 1);
+      if List.is_empty alloc then
+        find_solutions_impl cards size n (idx - 1) current_alloc current_pos
+      else alloc
+    end
+    else find_solutions_impl cards size n (idx - 1) current_alloc current_pos
   end
-  else find_solutions_impl cards size n (idx - 1) current_alloc current_pos
-end
 
 let find_solutions cards size =
   find_solutions_impl cards size
@@ -68,6 +68,59 @@ let find_solutions cards size =
     (Array.length cards - 1)
     [] (0, 0)
 
+exception Overlapping_value
+
+let print_solution size cards =
+  let array = Array.make (size * size) '.' in
+  let set_pos x y c =
+    if array.(x + (y * size)) <> '.' then raise Overlapping_value
+    else Array.set array (x + (y * size)) c
+  in
+  let rec write_size x y n =
+    if n = 0 then ()
+    else begin
+      Array.set array (x + (y * size)) (Char.chr (48 + (n mod 10)));
+      write_size (x - 1) y (n / 10)
+    end
+  in
+  let rec impl cards =
+    match cards with
+    | [] -> ()
+    | ((x, y), n) :: t -> begin
+        if n = 1 then set_pos x y '*'
+        else if n = 2 then begin
+          set_pos x y '+';
+          set_pos (x + 1) y '+';
+          set_pos x (y + 1) '+';
+          set_pos (x + 1) (y + 1) '+'
+        end
+        else begin
+          set_pos x y '+';
+          set_pos (x + n - 1) y '+';
+          set_pos x (y + n - 1) '+';
+          set_pos (x + n - 1) (y + n - 1) '+';
+          for a = 1 to n - 2 do
+            set_pos (x + a) y '-';
+            set_pos (x + a) (y + n - 1) '-';
+            for b = 1 to n - 2 do
+              set_pos (x + a) (y + b) ' '
+            done;
+            set_pos x (y + a) '|';
+            set_pos (x + n - 1) (y + a) '|'
+          done;
+          write_size (x + n - 2) (y + 1) n
+        end;
+        impl t
+      end
+  in
+  impl cards;
+  for y = 0 to size - 1 do
+    for x = 0 to size - 1 do
+      Format.printf "%c" array.(x + (y * size))
+    done;
+    Format.printf "\n"
+  done
+
 let n = 8
 let tri_n = (n + 1) * n / 2
 
@@ -79,3 +132,4 @@ let cards = Array.init (n + 1) Fun.id
 let soln = find_solutions cards tri_n
 let () = Format.printf "@[<hov>Base number: %d,@;side length: %d@;" n tri_n
 let () = Format.printf "Solution: %a@]@\n" (Format.pp_print_list pp_card) soln
+let () = print_solution tri_n soln