From: rubytraining@...
Date: 2006-12-11T11:40:09+09:00
Subject: Re: [QUIZ] Tournament Matchups (#105) -- Solution

Below you'll find my solution.  The code to create the binary tree is
pretty small.  The code to produce the text version of the tournament
tree is not so small, however.  Oh well...

Eric


SAMPLE OTUPUT

$ ruby tournament.rb 5
 R1  R2  R3
============
  1
---+
   +---+
---+   |
bye    |
       +---+
  4    |   |
---+   |   |
   +---+   |
---+       |
  5        |
           +---
  2        |
---+       |
   +---+   |
---+   |   |
bye    |   |
       +---+
  3    |
---+   |
   +---+
---+
bye



SOLUTION

# Solution for Ruby Quiz #105
# Author: Eric I.
# December 10, 2006
# www.learnruby.com

class Numeric
  # A monkey-patched convenience method to compute the maximum of two
  # numbers.
  def max(other)
    if self >= other : self
    else other
    end
  end
end


class Integer
  # A monkey-patched method to compute the gray code of an integer.
The
  # gray code has properties that make it helpful to the tournament
problem.
  def gray_code
    self ^ (self >> 1)
  end
end


# A tournament is really a node in a binary tree.  The value in each
# node contains the ranking of the best ranking team contained in the
# tournament tree below.
class Tournament
  attr_reader :ranking

  def initialize(ranking)
    @ranking = ranking
  end

  # Creates a tournament with the given number of teams.
  def self.create(teams)
    # create the initial node
    head_node = Tournament.new(1)

    # insert additional nodes for each further team
    for ranking in 2..teams
      head_node.add_team(ranking)
    end

    head_node
  end

  # Adds a team with the given ranking to the tournament.  It turns out
  # that the gray code of the ranking-1 has a bit pattern that
conveniently
  # helps us descend the binary tree to the appropriate place at which
to
  # put the team.
  def add_team(ranking)
    add_team_help(ranking, (ranking - 1).gray_code)
  end

  # Returns the number of rounds in the tournament.  This is determined
by
  # taking the max of the depths of the two sub-trees and adding one.
  def rounds
    unless @left : 0
    else 1 + (@left.rounds.max(@right.rounds))
    end
  end

  # Returns the pairs playing at a given round.  A round number of 1 is
  # the first round played and therefore the bottom-most layer of the
tree.
  def round(level)
    round_help(rounds - level)
  end

  # Converts the tournament tree into a String representation.
  def to_s
    lines = []  # store the result as an array of lines initially

    # create the lowest layer of the tree representing the first round
    round(1).each do |game|
      lines << game[0].to_s.rjust(3)
      lines << "---"
      lines << "   "
      lines << "---"
      lines << game[1].to_s.rjust(3)
      lines << "   "
    end
    lines.pop # last line, which just contains blanks, is not needed

    # the rest of the text tree is made through textual operations
    # by connecting teams playing with veritcal lines, then branching
    # horizontally to the next level, and then extending those branches
    begin
      count = to_s_connect(lines)
      to_s_branch(lines)
      3.times { to_s_extend(lines) }
    end until count == 1

    header_string + lines.join("\n")
  end


  protected

  # Recursively descends the tree to place a team with a new ranking.
  # Ultimately it will create two new nodes and insert them into the
  # tree representing itself and the team to be played.  When
  # descending the three, the bits in the gray code of the ranking
  # from least-significant to most-significant indicate which branch
  # to take.
  def add_team_help(ranking, gray_code)
    if @left == nil
      # bottomed out; create two new nodes
      @left = Tournament.new(@ranking)
      @right = Tournament.new(ranking)
    elsif gray_code % 2 == 0
      # bit in gray code indicates the left branch
      @left.add_team_help(ranking, gray_code >> 1)
    else
      # bit in gray code indicates the right branch
      @right.add_team_help(ranking, gray_code >> 1)
    end
  end

  # Returns the teams playing at the given round level.  The parameter
  # is actually the desired round subtracted from the number of
  # rounds.  That way we know we're at the right level when it reaches
  # zero.  It can be the case where a given branch does not have
  # enough levels; that indicates a "bye" for a good-ranking team.
  def round_help(reverse_level)
    if @left == nil : [[@ranking, "bye"]]
    elsif reverse_level == 0 : [[@left.ranking, @right.ranking]]
    else @left.round_help(reverse_level - 1) +
        @right.round_help(reverse_level - 1)
    end
  end

  # Creates a simple pair of lines showing the round numbers; this
helps
  # in the interpretation of the text-tree below.
  def header_string
    result = (1..rounds).to_a.inject("") do |collect, round|
      collect + "R#{round}".center(4)
    end
    result + "\n" + "=" * result.length + "\n"
  end

  # Creates vertical lines used to indicate a game and that connect
  # the horizontal lines that refer to teams.  The teams referred to
  # are either from the first round or that have won the previous
  # round.
  def to_s_connect(lines)
    count = 0
    connect = false
    lines.each do |line|
      if line[-1, 1] == "-"
        line << "+"
        connect = !connect
        count += 1 if connect
      elsif connect
        line << "|"
      else
        line << " "
      end
    end
    count
  end

  # From the vertical lines used to represent a game, this places a
  # horizontal line in the *middle* of it which indicates the winning
  # team.  Except for the final round, these horizontal lines will be
  # used to create a game at the next round.
  def to_s_branch(lines)
    range_began = false
    lines.each_index do |i|
      if lines[i][-1, 1] == "|"
        range_began = i unless range_began
      elsif range_began
        lines[(i + range_began - 1)/2][-1] = "+"
        range_began = false
      end
      #lines[i] << " "
    end
  end

  # Extends the horizontal lines by one character.
  def to_s_extend(lines)
    lines.each do |line|
      if line =~ /(-| \+)$/
        line << "-"
      else
        line << " "
      end
    end
  end
end


if ARGV.length != 1
  $stderr.puts "Usage: #{$0} team-count"
  exit 1
end

tournament = Tournament.create(ARGV[0].to_i)

puts tournament