Ruby Forum Ruby > Hexagonal Grid Game Board (#190)

Summary of quiz #189 coming in a day or two.

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## Hexagonal Grid Game Board

This week's quiz is to create the distance computation methods for a
hexagonal game board. In addition to implementing the simple
unobstructed distance you will also implement an obstructed_distance
method: the distance between two positions where you must go around
obstructions. I've provided a couple of classes to help you get
started. The print method on HexBoard prints out a board where each
hex displays it's distance from position [4,4].

Partial solutions are welcome! Team solutions are welcome! I want to
see everyone on ruby-talk give this one a shot!

class Hex
  def obstructed?
    false
  end
end

class HexBoard
  def initialize(rows=9, cols=9)
    @rows, @cols = rows, cols
    @board = Array.new(@rows) do |row|
      Array.new(@cols) do |col|
        Hex.new
      end
    end
  end

  def distance(position1, position2)
    # Distance between two hexes on the board
  end

  def obstructed_distance(position1, position2, &block)
    # Distance between two hexes on the board having to navigate 
obstructions
    # Obstructions are detected by passing the hex in question into the 
block
    # block will return true if the yielded hex should be counted as 
obstructed
    # EX: dist = obstructed_distance(a, b) { |hex| hex.obstructed? }
  end

  # This will print the board out to the console to let you
  # know if you're on the right track
  def draw
    @rows.times do |row|
      line = ''
      line << "#{row}:"
      (@cols - row).times {line << ' '}

      @cols.times do |col|
        line << (distance([4,4], [row,col]) || 'X').to_s
        line << ' '
      end

      puts line
    end
  end

  def [](row)
    @board[row]
  end
end

board = HexBoard.new
board.draw

- - - - - - - - - - - - - - - - - - - - - - - -
Example Output of print:
0:         4 4 4 4 4 5 6 7 8
1:        4 3 3 3 3 4 5 6 7
2:       4 3 2 2 2 3 4 5 6
3:      4 3 2 1 1 2 3 4 5
4:     4 3 2 1 0 1 2 3 4
5:    5 4 3 2 1 1 2 3 4
6:   6 5 4 3 2 2 2 3 4
7:  7 6 5 4 3 3 3 3 4
8: 8 7 6 5 4 4 4 4 4

On Jan 30, 2009, at 11:06 AM, Daniel Moore wrote:

> ## Hexagonal Grid Game Board

Ooo, I like this problem.  Nice one Daniel!  :)

James Edward Gray II

On Fri, Jan 30, 2009 at 6:15 PM, James Gray <james@grayproductions.net> 
wrote:
> On Jan 30, 2009, at 11:06 AM, Daniel Moore wrote:
>
>> ## Hexagonal Grid Game Board
>
> Ooo, I like this problem.  Nice one Daniel!  :)

Me too, crossing my fingers to have some time to make a try...

Jesus.

Here is my solution.
Pastie: http://pastie.org/377536
The pastie still has the comment on the distances function as
returning the distance between two hexes, but I changed this to return
an array of all distances from some position, since the breadth-first
search was already calculating this anyway.


class Hex
 attr_accessor :neighbours,:distance
 def initialize(row,col,rows,cols)
  @neighbours =
[[-1,-1],[-1,0],[0,-1],[0,1],[1,0],[1,1]].map{|r,c|[row+r,col+c]}.select{|r,c|
r>=0 && c>=0 && r<rows && c<cols}
  @obstructed = col==3 && row!=rows-1  ||  col==6 && row!=0 # double 
barrier
 end
 def obstructed?; @obstructed ;end
end

class HexBoard < Array
 def initialize(rows=9, cols=9)
   super(rows) {|row| Array.new(cols) {|col| Hex.new(row,col, rows,cols) 
}}
 end
 # Distance from position to each hex
 def distances(position,&block)
   each{|row| row.each{|hex| hex.distance = nil } }
   bfs_distance([position],0, &block);
   map{|row| row.map &:distance }
 end
 # Breadth-first search distance
 def bfs_distance(hexes,dist, &block)
   q = []
   hexes.map{|r,c| self[r][c] }.each{|hex|
     next if hex.distance || block_given? && yield(hex)
     hex.distance = dist
     q += hex.neighbours
   }
   bfs_distance(q.uniq,dist+1, &block) unless hexes.empty?
 end
 # Draw solution
 def draw(from=[4,4],&block)
   distances(from,&block).each_with_index{|dists,row| puts "#{row}:#{'
'*(size - row)}#{dists.map{|x|x||'#'}.join ' '}\n" }
 end
end

board = HexBoard.new
board.draw
board.draw([0,0],&:obstructed?)

Here's my solution. The request for the unobstructed distance and then
the obstructed distance immediately suggested the A* algorithm (since
the unobstructed distance is clearly an admissible heuristic.) Though
I knew an algorithm to use, I had to look up the algorithm itself.


---[main.rb]
require 'hex_board'

# board = HexBoard.new(9, 9)
# board = HexBoard.new(9, 9) { |row,col| ((4-row).abs <= 1) && (col == 
5) }
# board = HexBoard.new(9, 9) { |row,col| [row,col]==[4,4] ? true : 
rand(6)==0 }
board = HexBoard.new(9, 9) { |row,col| [row,col]==[4,4] ? false : 
rand(6)==0 }
board.draw
board.draw_map
board.draw_obstructed

---[hex_board.rb]
require 'set'
require 'hex'

class HexBoard
  def initialize(rows=9, cols=9)
    @rows, @cols = rows, cols
    @board = Array.new(@rows) do |row|
      Array.new(@cols) do |col|
        Hex.new(:obstructed => (block_given? && yield(row,col)))
      end
    end
  end

  def distance(start, goal)
    if ((start[0]-goal[0]) < 0) == ((start[1]-goal[1]) < 0)
      [(start[0]-goal[0]).abs, (start[1]-goal[1]).abs].max
    else
      (start[0]-goal[0]).abs+(start[1]-goal[1]).abs
    end
  end

  def neighbors(position)
    [
      [position[0], position[1]-1],
      [position[0]-1, position[1]-1],
      [position[0]-1, position[1]],
      [position[0], position[1]+1],
      [position[0]+1, position[1]+1],
      [position[0]+1, position[1]]
    ].delete_if {|x,y| x<0 || y <0 || x>@rows || y>@cols}
  end

  # Distance between two hexes on the board having to navigate 
obstructions
  # Obstructions are detected by passing the hex in question into the 
block
  # block will return true if the yielded hex should be counted as 
obstructed
  # EX: dist = obstructed_distance(a, b) { |hex| hex.obstructed? }
  def obstructed_distance(start, goal)
    return nil if (yield(@board[goal[0]][goal[1]]) ||
yield(@board[start[0]][start[1]]))
    closed_set = Set.new
    @board.size.times {|row|
      row.size.times {|col|
        if yield @board[row][col]
          closed_set << [row,col]
        end
      }
    }
    open_set = [start]
    actual_distance_to = {start=>0}
    estimated_distance_from = {start=>distance(start,goal)}
    estimated_distance_through = {start=>estimated_distance_from[start]}

    while !(open_set.empty?)
      node = open_set.first
      return actual_distance_to[node] if node == goal
      open_set.delete node
      closed_set << node
      neighbors(node).each { |neighbor|
        next if closed_set.include? neighbor
        distance_this_route = actual_distance_to[node] + 1
        this_route_good = false
        if !open_set.include?(neighbor)
          open_set << neighbor
          estimated_distance_from[neighbor] = distance(neighbor,goal)
          this_route_good = true
        elsif distance_this_route < actual_distance_to[neighbor]
          this_route_good = true
        end
        if this_route_good
          actual_distance_to[neighbor] = distance_this_route
          estimated_distance_through[neighbor] = distance_this_route +
estimated_distance_from[neighbor]
          open_set.sort! {|x,y|
estimated_distance_through[x]<=>estimated_distance_through[y]}
        end
      }
    end
    return nil
  end

  # This will print the board out to the console to let you
  # know if you're on the right track
  def draw
    @rows.times do |row|
      line = ''
      line << "#{row}:"
      (@cols - row).times {line << ' '}

      @cols.times do |col|
        line << (distance([4,4], [row,col]) || 'X').to_s
        line << ' '
      end

      puts line
    end
  end

  def draw_map
    @rows.times do |row|
      line = ''
      line << "#{row}:"
      (@cols - row).times {line << ' '}

      @cols.times do |col|
        line << (@board[row][col].obstructed? ? 'X' : 'O')
        line << ' '
      end

      puts line
    end
  end

  def draw_obstructed
    @rows.times do |row|
      line = ''
      line << "#{row}:"
      (@cols - row).times {line << ' '}

      @cols.times do |col|
        line << (obstructed_distance([4,4], [row,col]) {|hex|
hex.obstructed?} || 'X').to_s
        line << ' '
      end

      puts line
    end
  end

  def [](row)
    @board[row]
  end
end

---[hex.rb]
class Hex
  def initialize(opts={})
    @obstructed = !!opts[:obstructed]
  end

  def obstructed?
    @obstructed
  end
end

There were two solutions to this weeks quiz. One by Sander Land using
[breadth-first search][1], and another by Christopher Dicely using the
[A* search algorithm][2].

Both of the solutions added a similar concept of neighboring hexes.
Let's examine Sander's code in the `initialize` method of the `Hex`
class (I've modified the formatting slightly):

    @neighbors =
      [[-1,-1],[-1,0],[0,-1],[0,1],[1,0],[1,1]].map do |r, c|
        [row+r, col+c]
      end

Here we take an array of the six positions around this hex and map it
to world coordinates by adding the the deltas (differences in
position) to row and column values to get the position of the
neighboring hex.

      .select do |r, c|
        r >= 0 && c >= 0 && r < rows && c < cols
      end

In order to prevent having neighbors that are off the board or out of
range we select the ones that are valid positions.

Christopher's method is very similar, except instead of computing the
neighbors at the creation of each hex they are computed as needed via
a method of the `HexBoard` class.

For the simple distance Christopher uses the following formula:

    def distance(start, goal)
      if ((start[0]-goal[0]) < 0) == ((start[1]-goal[1]) < 0)
        [(start[0]-goal[0]).abs, (start[1]-goal[1]).abs].max
      else
        (start[0]-goal[0]).abs+(start[1]-goal[1]).abs
      end
    end

Here is an equivalent distance formula that found (though I can't
remember where) and converted to Ruby:

    def distance(pos1, pos2)
      dx = pos2[0] - pos1[0]
      dy = pos2[1] - pos1[1]
      return (dx.abs + dy.abs + (dx - dy).abs) / 2
    end

The deeper meaning behind these distance methods is still somewhat of
a mystery to me. I see that they work, but I'm not fully sure of the
why. I also don't see how to alter them to change the orientation of
the grid (maybe a future quiz?).

For the obstructed distance Christopher uses the [A* search
algorithm][2]. The essence of the A* algorithm is that it searches the
most promising paths first. In order to know which nodes are most
promising a heuristic function is used, in this case the simple
distance. We maintain a list (priority queue) of the nodes available
to explore. As we remove the best node from the list we examine it's
neighbors and insert them into the list, most promising first. If we
find the goal node we return the distance to it and are done. There is
much more that can be said about A* than I can say here, so check it
out.

In fact, breadth-first search is a special case of A* where the
heuristic function always returns 0 and the priority queue is replaced
with a regular (FIFO) queue. Sander's solution uses recursion instead
of a queue. It sets the distance to each hex based to the distance at
the current level, skipping hexes that have already had their distance
set or are obstructed, and adding the neighbors to a list to compute
the distance on the next recursive call. Once the list of remaining
nodes is empty it returns, having set the distance for all reachable
nodes.

Let's look at the results:

Sander creates a board that has two long walls with just one gap each:

    0:         0 1 2 # 17 18 19 20 21
    1:        1 1 2 # 16 17 # 20 21
    2:       2 2 2 # 15 16 # 21 21
    3:      3 3 3 # 14 15 # 22 22
    4:     4 4 4 # 13 14 # 23 23
    5:    5 5 5 # 12 13 # 24 24
    6:   6 6 6 # 11 12 # 25 25
    7:  7 7 7 # 10 11 # 26 26
    8: 8 8 8 8 9 10 # 27 27


Christopher generates random obstructions and provides a map view
which shows what is open and what is blocked:

    0:         O X O X O O O O O
    1:        O X O X O O O X O
    2:       O O O O O O O X O
    3:      O O O O O O O O O
    4:     O X O O O O X O O
    5:    O O X O O O X O X
    6:   O O O O O O O O O
    7:  O O O O O O O O O
    8: O O X X O O O X O

    0:         5 X 4 X 4 5 6 7 8
    1:        4 X 3 X 3 4 5 X 7
    2:       4 3 2 2 2 3 4 X 6
    3:      4 3 2 1 1 2 3 4 5
    4:     5 X 2 1 0 1 X 3 4
    5:    6 5 X 2 1 1 X 3 X
    6:   6 5 4 3 2 2 2 3 4
    7:  7 6 5 4 3 3 3 3 4
    8: 8 7 X X 4 4 4 X 4

Both solutions to this week's quiz provide interesting ways to solve
distance computations on a hexagonal game board. I hope they come in
handy when you build your next hex based board game!

[1]: http://en.wikipedia.org/wiki/Breadth-first_search
[2]: http://en.wikipedia.org/wiki/A*_search_algorithm

There were two solutions to this weeks quiz. One by Sander Land using
[breadth-first search][1], and another by Christopher Dicely using the
[A* search algorithm][2].

Both of the solutions added a similar concept of neighboring hexes.
Let's examine Sander's code in the `initialize` method of the `Hex`
class (I've modified the formatting slightly):

    @neighbors =
      [[-1,-1],[-1,0],[0,-1],[0,1],[1,0],[1,1]].map do |r, c|
        [row+r, col+c]
      end

Here we take an array of the six positions around this hex and map it
to world coordinates by adding the the deltas (differences in
position) to row and column values to get the position of the
neighboring hex.

      .select do |r, c|
        r >= 0 && c >= 0 && r < rows && c < cols
      end

In order to prevent having neighbors that are off the board or out of
range we select the ones that are valid positions.

Christopher's method is very similar, except instead of computing the
neighbors at the creation of each hex they are computed as needed via
a method of the `HexBoard` class.

For the simple distance Christopher uses the following formula:

    def distance(start, goal)
      if ((start[0]-goal[0]) < 0) == ((start[1]-goal[1]) < 0)
        [(start[0]-goal[0]).abs, (start[1]-goal[1]).abs].max
      else
        (start[0]-goal[0]).abs+(start[1]-goal[1]).abs
      end
    end

Here is an equivalent distance formula that found (though I can't
remember where) and converted to Ruby:

    def distance(pos1, pos2)
      dx = pos2[0] - pos1[0]
      dy = pos2[1] - pos1[1]
      return (dx.abs + dy.abs + (dx - dy).abs) / 2
    end

The deeper meaning behind these distance methods is still somewhat of
a mystery to me. I see that they work, but I'm not fully sure of the
why. I also don't see how to alter them to change the orientation of
the grid (maybe a future quiz?).

For the obstructed distance Christopher uses the [A* search
algorithm][2]. The essence of the A* algorithm is that it searches the
most promising paths first. In order to know which nodes are most
promising a heuristic function is used, in this case the simple
distance. We maintain a list (priority queue) of the nodes available
to explore. As we remove the best node from the list we examine it's
neighbors and insert them into the list, most promising first. If we
find the goal node we return the distance to it and are done. There is
much more that can be said about A* than I can say here, so check it
out.

In fact, breadth-first search is a special case of A* where the
heuristic function always returns 0 and the priority queue is replaced
with a regular (FIFO) queue. Sander's solution uses recursion instead
of a queue. It sets the distance to each hex based to the distance at
the current level, skipping hexes that have already had their distance
set or are obstructed, and adding the neighbors to a list to compute
the distance on the next recursive call. Once the list of remaining
nodes is empty it returns, having set the distance for all reachable
nodes.

Let's look at the results:

Sander creates a board that has two long walls with just one gap each:

    0:         0 1 2 # 17 18 19 20 21
    1:        1 1 2 # 16 17 # 20 21
    2:       2 2 2 # 15 16 # 21 21
    3:      3 3 3 # 14 15 # 22 22
    4:     4 4 4 # 13 14 # 23 23
    5:    5 5 5 # 12 13 # 24 24
    6:   6 6 6 # 11 12 # 25 25
    7:  7 7 7 # 10 11 # 26 26
    8: 8 8 8 8 9 10 # 27 27


Christopher generates random obstructions and provides a map view
which shows what is open and what is blocked:

    0:         O X O X O O O O O
    1:        O X O X O O O X O
    2:       O O O O O O O X O
    3:      O O O O O O O O O
    4:     O X O O O O X O O
    5:    O O X O O O X O X
    6:   O O O O O O O O O
    7:  O O O O O O O O O
    8: O O X X O O O X O

    0:         5 X 4 X 4 5 6 7 8
    1:        4 X 3 X 3 4 5 X 7
    2:       4 3 2 2 2 3 4 X 6
    3:      4 3 2 1 1 2 3 4 5
    4:     5 X 2 1 0 1 X 3 4
    5:    6 5 X 2 1 1 X 3 X
    6:   6 5 4 3 2 2 2 3 4
    7:  7 6 5 4 3 3 3 3 4
    8: 8 7 X X 4 4 4 X 4

Both solutions to this week's quiz provide interesting ways to solve
distance computations on a hexagonal game board. I hope they come in
handy when you build your next hex based board game!

[1]: http://en.wikipedia.org/wiki/Breadth-first_search
[2]: http://en.wikipedia.org/wiki/A*_search_algorithm