#!/usr/local/bin/ruby

class Game
  attr :vertices
  attr :edges

  def initialize(vertices = 0, edges = Hash.new {|h, k| h[k] = Hash.new {0} })
    @vertices = vertices
    @edges = edges
  end

  def grow(a, b)
    c = @vertices
    @vertices += 1

    @edges[a][c] += 1
    @edges[c][b] += 1

    if a != b
      @edges[c][a] += 1
      @edges[b][c] += 1
    end
  end

  def legal_tie?(a, b)

  end

  def progress
    0.upto(@vertices - 1)
      .select {|v| @edges[v].values.reduce(:+) < 3 }
      .combination(2).select{|a, b| legal_tie?(a, b) }
      .map {|a, b| grow(a, b) }
  end

  def winnable?
    progress.any? {|games| games.all?(:winnable?) }
  end
end