From fb3ce530859562aa922931696d48d3861880873d Mon Sep 17 00:00:00 2001
From: Michael Thelander <michael.thelander@rentrakmail.com>
Date: Fri, 13 Apr 2012 09:23:42 -0700
Subject: [PATCH] RubyQuiz #7: Countdown

---
 countdown/countdown.rb      | 111 ++++++++++++++++++++++++++++++++++++
 countdown/countdown_spec.rb |  51 +++++++++++++++++
 2 files changed, 162 insertions(+)
 create mode 100644 countdown/countdown.rb
 create mode 100644 countdown/countdown_spec.rb

diff --git a/countdown/countdown.rb b/countdown/countdown.rb
new file mode 100644
index 0000000..83f95f1
--- /dev/null
+++ b/countdown/countdown.rb
@@ -0,0 +1,111 @@
+module RubyQuiz
+  class Countdown
+    attr_reader :tree
+
+    def initialize(target, source)
+      @target, @source, = target.to_f, source.map(&:to_f)
+
+      @tree = Node.new(0, :+)
+      @source.product([:+]).each do |n|
+        next unless should_continue?(n)
+        @tree << build(Node.new(*n), @source)
+      end
+    end
+
+    def operators
+      @operators ||= [:+, :-, :*, :/]
+    end
+
+    def build(node, possibilities, depth = 1)
+      node.tap do |node|
+        sub_possibilities = possibilities.reject { |n| n == node.value }
+        return node if sub_possibilities.empty?
+        sub_possibilities.product(operators()) do |p|
+          next unless should_continue?(p)
+          node <<  build(Node.new(p.first, p.last), sub_possibilities, depth + 1)
+        end
+      end
+    end
+
+    def should_continue?(p)
+      return false if p.empty?
+      case p.first
+        when 1 then ![:*, :/].include?(p.last)
+        when 0 then ![:-, :+].include?(p.last)
+        else true
+      end
+    end
+
+    def evaluate(solution, depth = 0)
+      while (i = solution.rindex(?())
+        j = solution[i..solution.size-1].index(?))
+        solution[i..j] = _eval(solution[i+1..j-1])
+      end
+      _eval(reduce(solution))
+    end
+
+    def _eval(solution)
+      solution = reduce(solution)
+      op = :+
+      solution.reduce(0) do |result, term|
+        case term
+          when Fixnum then result = result.send(op, term)
+          when Symbol then op = term; result
+        end
+      end
+    end
+
+    def reduce(terms)
+      0.upto(terms.size) do |i|
+        a, op, b = terms[i..i+2]
+        if [:*, :/].include?(op)
+          terms[i..i+2] = a.send(op, b)
+        end
+      end
+
+      terms
+    end
+
+    def solve
+      find_solution(@tree, '')
+    end
+
+    def find_solution(node, solution, depth = 0)
+      solution.chop! if solution =~ /.*[-+*\/]$/
+      return solution if valid_solution?(solution)
+
+      node.children.each do |child|
+        parenthesized = solution.empty? ? '' : "(#{solution})"
+        s = find_solution(child, child.term + parenthesized, depth + 1)
+        return s if valid_solution?(s)
+      end
+
+      solution
+    end
+
+    def valid_solution?(expression)
+      eval(expression) == @target
+    end
+  end
+
+  class Node
+    attr_accessor :children, :visited
+    attr_reader :value, :op
+
+    def initialize(value, op, children = [])
+      @value, @op, @children = value, op, children
+    end
+
+    def <<(node)
+      @children << node
+    end
+
+    def to_s
+      "#@op #@value [ #@children ]"
+    end
+
+    def term
+      "#@value#@op"
+    end
+  end
+end
diff --git a/countdown/countdown_spec.rb b/countdown/countdown_spec.rb
new file mode 100644
index 0000000..88b6267
--- /dev/null
+++ b/countdown/countdown_spec.rb
@@ -0,0 +1,51 @@
+require '~/work/rubyquiz/countdown/countdown.rb'
+require 'benchmark'
+include RubyQuiz
+
+describe Countdown do
+  describe '#build' do
+    it 'should build a tree' do
+      countdown = Countdown.new(3, [1, 2])
+      countdown.tree.should.to_s == Node.new(0, :+, [
+        [ 1.0, :+, [ Node.new(2.0, :+), Node.new(2.0, :-), Node.new(2.0, :*), Node.new(2.0, :/) ] ],
+        [ 2.0, :+, [ Node.new(1.0, :+), Node.new(1.0, :-), Node.new(1.0, :*), Node.new(1.0, :/) ] ],
+      ]).to_s
+    end
+  end
+
+  describe '#solve' do
+    it 'should calculate a solution' do
+      target = 522
+      countdown = Countdown.new(target, [100, 5, 5, 2, 6, 8])
+      solution = countdown.solve
+      p solution
+      solution.should_not be_nil
+      eval(solution).should == target
+    end
+  end
+
+  describe '#evaluate' do
+    it 'should evaluate an expression faster than eval' do
+      countdown = Countdown.new(3, [1, 3])
+      countdown.evaluate([3, :+, 9]).should == 12
+      countdown._eval([3, :+, 9]).should == 12
+      countdown.evaluate([?(, 3, :+, 9, ?), :*, 12]).should == 144
+      time = Benchmark.realtime do
+        1000.times { countdown.evaluate([?(, 3, :+, 9, ?), :*, 12]) }
+      end
+      puts "Countdown#evaluate time: #{time}ms"
+
+      time = Benchmark.realtime do
+        1000.times { eval "(3+9)*12" }
+      end
+      puts "eval time: #{time}ms"
+    end
+  end
+
+  describe '#reduce' do
+    it 'should eliminate multiplication and division' do
+      countdown = Countdown.new(3, [1, 3])
+      countdown.reduce([3, :+, 8, :*, 9, :+, 2, :/, 2]).should == [3, :+, 72, :+, 1]
+    end
+  end
+end