Ruby Forum Ruby > Plot the Shape (#211)

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

The three rules of Ruby Quiz:

1.  Please do not post any solutions or spoiler discussion for this
quiz until 48 hours have elapsed from the time this message was
sent.

2.  Support Ruby Quiz by submitting ideas and responses
as often as you can!
Visit: http://rubyquiz.strd6.com/suggestions

3.  Enjoy!

Suggestion:  A [QUIZ] in the subject of emails about the problem
helps everyone on Ruby Talk follow the discussion.  Please reply to
the original quiz message, if you can.

RSS Feed: http://rubyquiz.strd6.com/quizzes.rss

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

## Plot the Shape (#211)

 Kvetha Rubyists,

This week's quiz was submitted by Alan at 
http://rubyquiz.strd6.com/suggestions

Somewhere on a 10x20 grid is a 10 block shape. The shape parts are all
adjacent, either horizontally, vertically or diagonally.

Write a simple algorithm that will list the co-ordinates of the 10
parts of the shape. Try to minimize lookups to the grid.

Here is an example shape to get started (you may need to copy into a
monospaced font):

 0123456789ABCDEFGHIJ
0....................
1....................
2.........@@.........
3........@...........
4........@@@@@.......
5.............@......
6............@.......
7....................
8....................
9....................


Have Fun!

--
-Daniel
http://rubyquiz.strd6.com

P.S. Submitting quiz ideas is fun and easy. Visit
http://rubyquiz.strd6.com/suggestions to find out more!

Hello,
Here's my solution, it works also with grid with different sizes but it 
does
not
check the adjacency of the shape parts.

http://github.com/sandropaganotti/Ruby-Quiz-Repository/blob/222c931fcca22e1b89ae764efaa463b376b90eb9/211_plot_the_shape.rb

Sandro

> ## Plot the Shape (#211)
>
> Somewhere on a 10x20 grid is a 10 block shape. The shape parts are all
> adjacent, either horizontally, vertically or diagonally.
>
> Write a simple algorithm that will list the co-ordinates of the 10
> parts of the shape. Try to minimize lookups to the grid.

Six little methods.  The first two started with some simplifying 
assumptions:
  * The grid is stored in a "convenient" data-structure
  * The grid only contains one shape
  * The shape doesn't violate any of the rules
The third dispenses with the convenient structure and simply
brute-force scans the whole grid.  The last three build on each other
until the sixth iteration attempts to follow the part adjacency rules
and minimize lookups (and is super-super-ugly-code :-).

#!/usr/bin/env ruby

$input = <<-EO
....................
....................
.........@@.........
........@...........
........@@@@@.......
.............@......
............@.......
....................
....................
....................
EO

def foo1
  # assuming the grid is stored hash-like, keyed on coordinate
  grid = {}
  $input.split.each_with_index{|line, y|
    line.split(//).each_with_index{|char, x|
      grid[[x,y]] = char
    }
  }

  # reject by value and return the keys
  grid.reject{|k,v| v != "@"}.keys
end

def foo2
  # assuming the grid is stored hash-like, keyed on value
  grid = {}
  $input.split.each_with_index{|line, y|
    line.split(//).each_with_index{|char, x|
      (grid[char] ||= []) << [x,y]
    }
  }

  # return the value
  grid['@']
end

def foo3
  # grid is stored nested-array-liked, indexed by row then column
  grid = $input.split

  rows, cols, parts = grid.size, grid[0].size, []

  # :-( my 'clever' duck is defeated by 1.8's String#[]
  rows.times{|r| cols.times{|c| parts << [c,r] if grid[r][c] == 64 }}
  parts
end

def foo4
  # grid is stored nested-array-liked, indexed by row then column
  grid = $input.split

  rows, cols, parts, checked = grid.size, grid[0].size, [], {}

  until (parts.size == 10)
    # pick a random spot
    r, c = rand(rows), rand(cols)
    next if checked[[r,c]]       # skip if we've already checked this 
one
    checked[[r,c]] = true
    next unless grid[r][c] == 64 # skip if this one isn't a part
    parts << [c,r]               # store if it is a part
  end

  parts
end

def foo5
  # grid is stored nested-array-liked, indexed by row then column
  grid = $input.split

  rows, cols, parts, checked = grid.size, grid[0].size, [], {}

  until (parts.size == 10)
    # pick a random spot
    r, c = rand(rows), rand(cols)
    next if checked[[r,c]]       # skip if we've already checked this 
one
    checked[[r,c]] = true
    next unless grid[r][c] == 64 # skip if this one isn't a part
    parts << [c,r]               # store if it is a part

    # check the current parts neighbors
    (-1..1).each do |dc|
      (-1..1).each do |dr|
        cprime = (c + dc).abs
        rprime = (r + dr).abs
        next if checked[[rprime,cprime]]       # skip if we've already
checked this one
        checked[[rprime,cprime]] = true
        next unless grid[rprime][cprime] == 64 # skip if this one isn't 
a part
        parts << [cprime,rprime]               # store if it is a part
      end
    end
  end

  parts
end

def foo6
  # grid is stored nested-array-liked, indexed by row then column
  grid = $input.split

  rows, cols, parts, checked = grid.size, grid[0].size, [], {}

  l = lambda {|r, c, parts, checked|
    # check the current parts neighbors
    (-1..1).each do |dc|
      (-1..1).each do |dr|
        cprime = (c + dc).abs
        rprime = (r + dr).abs
        next if checked[[rprime,cprime]]       # skip if we've already
checked this one
        checked[[rprime,cprime]] = true
        next unless grid[rprime][cprime] == 64 # skip if this one isn't 
a part
        parts << [cprime,rprime]               # store if it is a part
        l.call(rprime, cprime, parts, checked) # recurse to check more 
neighbors
      end
    end
  }

  loop do
    # pick a random starting spot
    r, c = rand(rows), rand(cols)
    next if checked[[r,c]]       # skip if we've already checked this 
one
    checked[[r,c]] = true
    next unless grid[r][c] == 64 # skip if this one isn't a part
    parts << [c,r]               # store if it is a part
    l.call(r, c, parts, checked)
    break
  end

  parts
end

p foo1.sort
p foo2.sort
p foo3.sort
p foo4.sort
p foo5.sort
p foo6.sort

#(ruby 1.8.6)=>
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]
[[8, 3], [8, 4], [9, 2], [9, 4], [10, 2], [10, 4], [11, 4], [12, 4],
[12, 6], [13, 5]]

Here's the first solution that came to my mind. Nothing tricky or
efficient really. Just gets the job done. It uses recursion to search
adjacent squares so as to meet the requirement/suggestion to avoid
merely doing a linear search of the whole game board (at least, that's
what I read into it).

This supports boards of arbitrary size and can be configured via
constants to support a different maximum number of characters to
search for (and specific character to search for).

It assumes the board, if provided, is rectangular.

http://snipt.org/kmnm

(Just noticed I left in a hard-coded regex using the '@' character;
otherwise this supports searching for a different character)

My solution is in two parts:
  -divide and conquerer until a '@' is found
  -use a recursive backtracker starting from the seed coord. found in 
step 1.

I am not positive about my worst-case analysis on lookups.

-C

$map = File.new(ARGV[0]).inject([]){|a,line| a << line.split("")}
#vertical line
m = lambda {|x| (1..10).detect{|y| $map[y][x] == '@'}}
#horizontal line
n = lambda {|y| (1..20).detect{|x| $map[y][x] == '@'}}
#find a coordinate with an '@'; worst case 118 lookups
seed = 
[[n.call(5),5],[n.call(6),6],[10,m.call(10)],[6,m.call(6)],[3,m.call(3)],[8,m.call(8)],\
        [16,m.call(16)],[13,m.call(13)],[18,m.call(18)]].detect{|a| a[1] 
!= nil and a[0] != nil}
#recursive maze solver; worst case 80 lookups
$visits = {}
def m_solver(a,found)
        x,y = a[0],a[1]
        return if found >= 10
        if $visits["#{y},#{x}"] == nil
                puts "#{x-1 > 9 ? (x-1+55).chr : (x-1)},#{y-1}"
                found += 1;$visits["#{y},#{x}"] = true
        end
        #vertical or horizontal
        m_solver([x,y-1],found) if y-1 >= 1  and $map[y-1][x] == '@' and 
$visits["#{y-1},#{x}"] == nil
        m_solver([x,y+1],found) if y+1 <= 10 and $map[y+1][x] == '@' and 
$visits["#{y+1},#{x}"] == nil
        m_solver([x-1,y],found) if x-1 >= 1  and $map[y][x-1] == '@' and 
$visits["#{y},#{x-1}"] == nil
        m_solver([x+1,y],found) if x+1 <= 20 and $map[y][x+1] == '@' and 
$visits["#{y},#{x+1}"] == nil
        #diagonal
        m_solver([x-1,y-1],found) if y-1 >= 1  and x-1 >= 1  and 
$map[y-1][x-1] == '@' and $visits["#{y-1},#{x-1}"] == nil
        m_solver([x-1,y+1],found) if y+1 <= 10 and x-1 >= 1  and 
$map[y+1][x-1] == '@' and $visits["#{y+1},#{x-1}"] == nil
        m_solver([x+1,y-1],found) if x+1 <= 20 and y-1 >= 1  and 
$map[y-1][x+1] == '@' and $visits["#{y-1},#{x+1}"] == nil
        m_solver([x+1,y+1],found) if x+1 <= 20 and y+1 <= 10 and 
$map[y+1][x+1] == '@' and $visits["#{y+1},#{x+1}"] == nil
end
#worst case 198 lookups
m_solver(seed,0)

Here is my solution. On average, for a 10x10 grid with a 10 sized shape, 
it
will plot the shape in about 31.7 guesses. If you change the neighbors
definition to exclude diagonals, it does it in around 24 guesses.  Worst
case scenario is of course the size of the grid.

I spent a fair amount of effort trying to collect statistical 
information
about the shapes I am generating, but experiments have shown that even
though there is a certain amount of non-uniformity in the distribution
across the board, it is not enough to gain a significant advantage in 
the
total number of guesses (probably less than a half a guess.)

--Chris

# The Shape class accomplishes a couple of things.
# First, it randomly generates shapes and provides some
# accounting, keeping track of how many lookups one does.

# Next, it acts as a kind of geometry manager for the board.
# (each, each_neighbors, get_neighbors. Changing the definition
# of each_neighbors can change the rules for what it means for
# squares to be adjacent.

# Finally, it keeps track of occupancy statistics for the board
# over successive regenerations of the shape.
class Shape
 attr_reader :h,:w,:l,:count
 def initialize(hh = 10, ww = 10, ll = 10)
  @h,@w,@l=hh,ww,ll #height,width, shape size
  @regens = @count = 0 #number of times shape generated, times 
dereferenced

  @stats = [] #used to count frequency of occupancy

  # seed the stats array with all 1s.
  h.times { |y| @stats[y] = [ 1 ] * w }
  @regens = h*w/(1.0 * l)
  rebuild
 end

 def each_neighbors(xxx,yyy=nil)
  if xxx.kind_of?( Array ) then
   x,y = xxx[0],xxx[1]
  else
   x,y = xxx,yyy
  end
  lowx,hix = [x-1,0].max, [x+1,w-1].min
  lowy,hiy = [y-1,0].max, [y+1,h-1].min
  (lowy..hiy).each do |yy|
   (lowx..hix).each do |xx|
    yield([xx,yy]) unless x==xx and y==yy
   end
  end
 end

 def get_neighbors(x,y=nil)
  result = []
  each_neighbors(x,y) do |coords|
   result.push(coords)
  end
  return result
 end

 def each
  h.times { |y| w.times { |x| yield [x,y] } }
 end

 def rebuild()
  @regens += 1 #increment the build count
  @count = 0 #clear the deref count

 #initialize board to contain only spaces
  @board=[]
  h.times { |y| @board[y] = [" "] * w  }

  neighbors = []
  shape = []

  l.times do
   if neighbors.length == 0 then
    # first piece - place it anywhere
    x,y = [w,h].map {|z| (rand*z).to_i}
   else
    # subsequent pieces - pick a random neighbor
    x,y = neighbors[ (rand * neighbors.length).to_i ]
   end
   @board[y][x] = "@" #mark occupancy
   @stats[y][x] += 1  #track occupancy

   shape |= [ [x,y] ] # add choice to list of shape coords

   # update neigbors
   neighbors -= [[x,y]]
   neighbors |= get_neighbors(x,y) - shape
  end
  return self
 end

 def to_s
  return @board.map { |x| x.join "" }.join("\n") + "\nTotal Lookups:
#{@count}\n"
 end

 def [](xx,yy=nil)
  if xx.kind_of?(Array) then
   x,y = xx[0],xx[1]
  else
   x,y = xx,yy
  end
  @count += 1
  return @board[y][x]
 end

 def stats
  norm_stats = []
  h.times do |y|
   norm_stats[y] = []
   w.times do |x|
    # correct stats for rotation and reflection symmetry
    norm_stats[y][x] = (@stats[y][x] + @stats[-y-1][x] + 
@stats[-y-1][-x-1]
+ @stats[y][-x-1] + @stats[x][y] + @stats[-x-1][y] + @stats[-x-1][-y-1] 
+
@stats[x][-y-1])/(8.0*@regens)
   end
  end
  return norm_stats
 end

 def statstring
  return stats.map { |y| y.map { |x| "%0.3f" % x}.join(" ") }.join("\n")
 end
end

class ShapePlot
 def initialize(r = Shape.new, c=0)
  @shape = r
  c.times {@shape.rebuild}
  @stats = @shape.stats
  @plays = 0
  @count = 0
  reset
 end

 def reset
  @guesses = []
  @members = []
  @neighbors = []
  @choices = []
  @shape.each { |coords| @choices << coords }
 end

 def to_s
  board = []
  @shape.each { |x,y| @shape.h.times { |y| board[y] = [ " " ] * @shape.w 
}}
  @neighbors.each { |x,y| board[y][x] = "." }
  @guesses.each { |x,y| board[y][x] = "x" }
  @members.each { |x,y| board[y][x] = "@" }
  header = "+" + ("-"*(@shape.w*2-1)) + "+\n"
  return header + "|" + board.map{|x| x.join(" ")}.join("|\n|") + "|\n" 
+
header
 end

 def choose_random(p_list)
   sum = 0
   #choose from among the choices, probibilistiacally, weighted by
   #the occupation probabilities
   p_list.each { |p,c| sum += p }
   r = rand * sum
   p_list.each do |p,c|
     r -= p
     return c if r <= 0
   end

   # shouldnt ever be here, but return the last one anyway
   puts "BAAAAD"
   puts p_list
   puts @shape
   return p_list[-1][1]
 end

 def build_weighted(list)
  return list.map {|x| [ @stats[x[1]][x[0]], x ]}
 end

 def guess_none_known
  return choose_random( build_weighted( @choices ) )
 end

 def guess_some_known
  choices = @neighbors - @guesses
  return choose_random( build_weighted( choices ) )
 end

 def found_a_hit(coords)
  # update the members of the shape
  @members += [ coords ]
  x,y=coords
  # calculate the neigbors of the new piece
  @neighbors += @shape.get_neighbors(x,y)
  # the intersection of @members and @neighbors should be empty, but
  # we are subtracting out @guesses, which includes all @members when
  # we go to pick a choice list anyway...
 end

 def guess
  #choose a square to look at
  # if we know some part of the shape is known, restrict guesses
  # to neighbors of the stuff we know
  #if we dont know any of them yet, choose from the whole board
  x,y = coords = (@members.length > 0 ? guess_some_known : 
guess_none_known)
  @guesses += [coords]
  @choices -= [coords]
  if @shape[x,y]=="@" then
   found_a_hit(coords)
  end
 end

 def play( draw = false)
  reset

  # upldate statistics before we update the shape
  @stats = @shape.stats
  @shape.rebuild
  while @members.length < @shape.l
   guess
   puts self if draw
  end

  @plays +=1
  @count += @shape.count
  return @shape.count
 end

 def report
  mean = @count / (1.0 * @plays)
  puts "After #{@plays} plays, the mean score is: #{mean}"
 end
end

q = ShapePlot.new
q.play(true)
999.times { q.play }
q.report

There were many good solutions to this week's quiz, but Chris Howe's
solution stands out as the best.

Chris's solution consists of two parts: a `Shape` class that handles
creating the shape and tracking lookups to the grid and a `ShapePlot`
class that handles the guesses.

Chris also provides a mode that draws the board as it is searched. The
'@' characters represent the parts of the shape that have been
discovered so far, the 'x' characters represent misses, and the '.'
characters represent neighbors to the discovered shapes: the places
that the program will search next.

<pre>
    +-------------------+
    |            x      |
    |                   |
    |                   |
    |                   |
    |    . x x .        |
    |x x x @ @ .        |
    |x @ @ @ x .        |
    |x x @ x x          |
    |  . x .       x    |
    |    x              |
    +-------------------+
</pre>

As you can see the two 'x's off to the side are random choices that
missed. The program continues to guess randomly a location with part
of the shape is found. A piece of the shape was then discovered near
the bottom left and the program began searching the neighbors of the
already discovered pieces to find the rest of it.

The default output of the program is to display one game in drawing
mode, and then run 999 more games to generate the statistics for the
average number of lookups. After 1000 plays the average number of
lookups is around 31.7.

Thank you Brabuhr, Chris Cacciatore, Chris Howe, Kendal Gifford, and
Sandro Paganotti for your solutions this week!