class PYRAMID
   --
   -- Solving the problem of the Pyramid for small pyramid only.
   --
   -- This program uses the back-tracking method.
   -- Its goal is to try to fill a pyramid by making a subtraction
   -- between two successive columns and to take its absolute value.
   -- The result is put on the next line.
   -- Example:
   --  6   14   15   3   13
   --    8    1   12  10
   --       7   11   2
   --         4    9
   --            5
   --
   -- See also pyramid2, which run faster than this first solution.

insert
   ARGUMENTS
      redefine out_in_tagged_out_memory
      end

create {ANY}
   make

feature {ANY}
   size: INTEGER

   make
      do
         if argument_count = 0 then
            std_output.put_string("Want to compute a small pyramid ?%N%
                                  %Enter a small number (> 1): ")
            std_output.flush
            std_input.read_integer
            size := std_input.last_integer
         else
            size := argument(1).to_integer
         end
         if size <= 1 then
            std_output.put_string("You feel sick ?%N")
         elseif size > biggest_one then
            std_output.put_string("Value too big for this method.%N")
         else
            create elem.make(1, max)
            if fill_up(1) then
               std_output.put_string("Full pyramid:%N")
               print_on(std_output)
            else
               std_output.put_string("Unable to fill_up such one.%N")
            end
         end
      end

   max: INTEGER
      do
         Result := size * (size + 1) // 2
      end

   out_in_tagged_out_memory
      local
         lig, col, nb: INTEGER
      do
         from
            lig := 1
            col := 1
            nb := 0
         until
            nb = max
         loop
            if col = 1 then
               tagged_out_memory.extend('%N')
            end
            elem.item(indice(lig, col)).append_in(tagged_out_memory)
            tagged_out_memory.append(" ")
            if col = size - lig + 1 then
               col := 1
               lig := lig + 1
            else
               col := col + 1
            end

            nb := nb + 1
         end
         tagged_out_memory.extend('%N')
      end

   belongs_to (nb: INTEGER): BOOLEAN
      require
         too_small: nb >= 1
         too_large: nb <= max
      local
         i: INTEGER; found: BOOLEAN
      do
         from
            i := 1
         until
            i > max or found
         loop
            found := nb = elem.item(i)
            i := i + 1
         end
         Result := found
      end

   propagate (col, val_column_1: INTEGER): BOOLEAN
      require
         val_column_1.in_range(1, max)
         col.in_range(1, size)
      local
         stop: BOOLEAN; lig: INTEGER; val: INTEGER
      do
         if belongs_to(val_column_1) then
            Result := False
         else
            from
               elem.put(val_column_1, indice(1, col))
               lig := 1
               val := val_column_1
               stop := False
               Result := True
            until
               stop
            loop
               lig := lig + 1
               if lig > col then
                  stop := True
               else
                  val := val - elem.item(indice(lig - 1, col - lig + 1))
                  val := val.abs
                  if belongs_to(val) then
                     clear_column(col)
                     stop := True
                     Result := False
                  else
                     elem.put(val, indice(lig, col - lig + 1))
                  end
               end
            end
         end
      end

   fill_up (col: INTEGER): BOOLEAN
      require
         col >= 1
      local
         stop: BOOLEAN; nb: INTEGER
      do
         if col > size then
            Result := True
         else
            from
               stop := False
               nb := max
            until
               stop
            loop
               if belongs_to(nb) then
                  nb := nb - 1
                  stop := nb = 0
               elseif propagate(col, nb) then
                  if fill_up(col + 1) then
                     stop := True
                  else
                     clear_column(col)
                     nb := nb - 1
                     stop := nb = 0
                  end
               else
                  nb := nb - 1
                  stop := nb = 0
               end
            end
            Result := nb > 0
         end
      end

feature {}
   elem: ARRAY[INTEGER]

   case_vide: INTEGER 0

   biggest_one: INTEGER 10

   indice (lig, col: INTEGER): INTEGER
      require
         lig_trop_petit: lig >= 1
         lig_trop_grand: lig <= size
         col_trop_petit: col >= 1
         col_trop_grand: col <= size
      local
         l: INTEGER
      do
         l := size - lig + 1
         Result := max - l * (l + 1) // 2 + col
      ensure
         Result >= 1
         Result <= max
      end

   clear_column (col: INTEGER)
      require
         col >= 1
         col <= size
      local
         lig: INTEGER
      do
         from
            lig := 1
         until
            lig > col
         loop
            elem.put(case_vide, indice(lig, col - lig + 1))
            lig := lig + 1
         end
      end

end -- class PYRAMID