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#!/usr/bin/env ruby -Ku
# encoding: utf-8
=begin
Benoit Daloze
RPCFN5 : Mazes
I extended the test suite, with small but harder examples.
I think the tests should have provided more mazes(bigger), to get an idea about the speed
Point represent a palce in the maze, by @x and @y.
It is just a coordinate system to ease the process.
I got kind of an issue, as I create 2-3 instances of every Point,
while one is far enough(even for multiple mazes).
Keeping them in an Array is too expensive in time,
but my which was to rewrite Point.new to return an existing Point if there is.
I used 2 kind of methods to solve this challenge
1) The tree and get_all_paths, get_paths_to_arrival and get_path_to_arrival
I build paths using a simple Tree structure and then
I just look if a parent node doesn't include already the Point, to not make circular paths
The first method, get_all_paths, is quite slow when there are many possible paths
(which is not the case in the test suite given)
The two others are taking only the interesting part of the Tree.
The last is quite good compared to dijkstra
2) Dijkstra's algorithm with dijkstra, dijkstra_to_arrival and dijkstra_optimized
There is the dijkstra algorithm for this case (with adjacent cells)
=end
# tree.rb
module Tree
class Node
attr_accessor :args, :parent, :children
def initialize(*args)
@args = args
@parent = nil
@children = []
end
def name
@args.first
end
def == o
(o.is_a?(Node) and @args == o.args) or
@args.include?(o)
end
def << child
case child
when Node
@children << child
child.parent = self
child
when Array
child.each { |c| self << c }
self
else
self << Node.new(child)
end
end
def root
root? ? self : @parent.root
end
# Boolean
def root?
@parent.nil?
end
def parent?(p)
ascendants.include?(p)
end
def leaf?
@children.empty?
end
# selectors
def all
root.descendants
end
def ascendants # [self, parent, ..., root] array of ancestors in reverse order, includes self
root? ? [self] : [self] + parent.ascendants
end
def descendants # [self, child1, ...] includes self
@children.inject([self]) { |desc, c| desc + c.descendants } rescue []
end
def leafs
descendants.select { |n| n.leaf? }
end
def single_tree # return a tree containing only this node and his parents
ascendants.reverse[1..-1].inject(Tree.new(*root.args)) { |t, n|
t.leafs[0] << Node.new(*n.args)
}
end
def linearize
descendants.select { |n| n.leaf? }.map { |n| n.ascendants.reverse }
end
end
def new(*args)
Node.new(*args)
end
module_function :new
end
################################
# maze.rb
include Tree
module Kernel
def ∈(set)
set.include?(self)
end
end
class Point
attr_reader :x, :y
def initialize(x, y)
@x, @y = x, y
end
def + c
Point.new(@x + c.x, @y + c.y)
end
def == o
# Should also include o.is_a?(Point), but it's very slower
@x == o.x and @y == o.y
end
# Hash stuff
alias :eql? :==
def hash
@x ^ @y
end
def to_s
"(#{@x},#{@y})"
end
end
class Maze
WALL = '#'
GROUND = ' '
DEPARTURE = 'A'
ARRIVAL = 'B'
DIRECTIONS = [
Point.new( 0, -1), # north
Point.new( 1, 0), # east
Point.new( 0, 1), # south
Point.new(-1, 0) # west
]
Infinity = +1.0/0.0
def initialize(maze)
@maze = maze.sub(/\A\n(.+)\Z/, '\1').lines.with_index.map { |l, y|
l.chomp.chars.with_index.map { |c, x|
case c
when WALL then :wall
when GROUND then :ground
when DEPARTURE
@d = Point.new(x,y)
:departure
when ARRIVAL
@a = Point.new(x,y)
:arrival
else
raise "Unknown character in maze's string: #{c}"
end
}
}
@reachable = {}
end
def to_s
@maze.map { |l|
l.map { |c|
case c
when :wall then WALL
when :ground then GROUND
when :departure then DEPARTURE
when :arrival then ARRIVAL
end
}.join
}.join("\n")
end
def [](c)
return :wall unless c.y.∈(0...@maze.length) and c.x.∈(0...@maze[c.y].length)
@maze[c.y][c.x]
end
def solvable?
@a.∈ all_reachable
end
# Return (example) {(1,0)=>:wall, (0,1)=>:ground, (-1,0)=>:wall, (0,-1)=>:ground}
# {Point => Symbol} of neighbours of c with their states
def neighbors(c)
DIRECTIONS.inject({}) { |h, d|
h.merge({d => self[c + d]})
}
end
# [Point] that can be reached from c
def reachable(c)
@reachable[c] ||= DIRECTIONS.inject([]) { |r, d|
next(r) if self[p = c + d] == :wall
r << p
}.freeze
end
def all_reachable
@all_reachable ||= begin
to_look = [@d]
looked = [@d]
while c = to_look.pop
to_look += reachable(c).reject { |r| r.∈ looked }
looked << c
end
looked
end
end
def get_all_paths
t = Tree.new(@d)
# A leaf is a node without parent in a Tree
# here it is a Point without reachebale Point next to it (or who has not been looked yet)
until t.leafs.all? { |leaf|
# We don't want to go at the same Point we passed
leaf << reachable(leaf.name).reject { |c| leaf.parent?(c) }
leaf.leaf? # Did we found any Point reacheable ?
}
end
t
end
def get_paths_to_arrival
t = Tree.new(@d)
until t.leafs.all? { |leaf|
unless leaf == @a
leaf << reachable(leaf.name).reject { |c| leaf.parent?(c) }
end
leaf.leaf?
}
end
t
end
def get_path_to_arrival # Notice the singular
t = Tree.new(@d)
loop do
t.leafs.each { |leaf|
# We can be sure this is the shortest, as we advance step by step for each path
return leaf.single_tree if leaf == @a
leaf << reachable(leaf.name).reject { |c| leaf.parent?(c) }
leaf.leaf?
}
end
end
def select_shortest_path(paths)
paths.linearize.
select { |path| @a.∈ path }.
map { |p|
p[0...p.index(@a)] # let's take the part to the arrival, we won't go further
}.map(&:length).min # And get the length of shortest one
end
def steps(method = :do)
return 0 if not solvable?
case method
when :dijkstra, :d
dijkstra[@a]
when :dijkstra_to_arrival, :da
dijkstra_to_arrival[@a]
when :dijkstra_optimized, :do
dijkstra_optimized
else
select_shortest_path(send(method))
end
end
def dijkstra
dist = Hash.new(Infinity) # Unknown distance function from source to v
prev = {} # Previous node in optimal path from source
dist[@d] = 0 # Distance from source to source
q = all_reachable.dup # All nodes in the graph are unoptimized - thus are in Q
until q.empty?
u = q.min_by { |v| dist[v] } # vertex in Q with smallest dist
break if dist[u] == Infinity # all remaining vertices are inaccessible from source
q.delete(u)
reachable(u).each do |v| # where v has not yet been removed from Q
alt = dist[u] + 1 # dist_between(u, v) = 1 because they are neighbors
if alt < dist[v] # Relax (u,v,a)
dist[v] = alt
prev[v] = u
end
end
end
dist
end
def dijkstra_to_arrival # return when we reach arrival
dist = Hash.new(Infinity)
prev = {}
dist[@d] = 0
q = all_reachable.dup
until q.empty?
u = q.min_by { |v| dist[v] }
return dist if u == @a
break if dist[u] == Infinity
q.delete(u)
reachable(u).each do |v|
alt = dist[u] + 1
if alt < dist[v]
dist[v] = alt
prev[v] = u
end
end
end
end
def dijkstra_optimized # Without prev {}
dist = Hash.new(Infinity)
dist[@d] = 0
q = all_reachable.dup
until q.empty?
u = q.min_by { |v| dist[v] }
return dist[@a] if u == @a
q.delete(u)
reachable(u).each do |v|
alt = dist[u] + 1
dist[v] = alt if alt < dist[v]
end
end
end
end
################################
# test_maze.rb
require 'test/unit'
MAZE1 = %{
#####################################
# # # #A # # #
# # # # # # ####### # ### # ####### #
# # # # # # # # #
# ##### # ################# # #######
# # # # # # # # #
##### ##### ### ### # ### # # # # # #
# # # # # # B# # # # # #
# # ##### ##### # # ### # # ####### #
# # # # # # # # # # # #
# ### ### # # # # ##### # # # ##### #
# # # # # # #
#####################################}
# Maze 1 should SUCCEED
MAZE2 = %{
#####################################
# # # # # #
# ### ### # ########### ### # ##### #
# # # # # # # # # #
# # ###A##### # # # # ### ###########
# # # # # # # # #
####### # ### ####### # ### ####### #
# # # # # # # #
# ####### # # # ####### # ##### # # #
# # # # # # # # # # #
# ##### # # ##### ######### # ### # #
# # # # #B#
#####################################}
# Maze 2 should SUCCEED
MAZE3 = %{
#####################################
# # # # #
# ### # ####### # # # ############# #
# # # # # # # # # #
### ##### ### ####### # ##### ### # #
# # # # A # # # # #
# ######### ##### # ####### ### ### #
# ### # # # # #
# ### ### ####### ####### # # # # ###
# # # # # #B# # # # # # #
# # # ##### ### # # # # ### # ##### #
# # # # # #
#####################################}
# Maze 3 should FAIL
### Perso
MAZE4 = '
########
#A #
###### #
# B# #
# #### #
# #
########
' # 19
MAZE5 = '
############
# #####
# ## #
# B#### #
#### #### #
#A #
############
' # 25
MAZE6 = '
#############
#A B#
###### #####
#############
' # 10
MAZE7 = '
#######
# #
#A B #
# #
#######
' # 2
MAZE8 = '
#
A # B
' # 8
MAZE9 = '
#
#A#
# #
#B#
#
' # 2
MAZE10 = '
A
B
' # 10
class MazeTest < Test::Unit::TestCase
def test_good_mazes
assert_equal true, Maze.new(MAZE1).solvable?
assert_equal true, Maze.new(MAZE2).solvable?
end
def test_bad_mazes
assert_equal false, Maze.new(MAZE3).solvable?
end
def test_maze_steps
assert_equal 44, Maze.new(MAZE1).steps
assert_equal 75, Maze.new(MAZE2).steps
assert_equal 0, Maze.new(MAZE3).steps
end
def test_perso
assert_equal 19, Maze.new(MAZE4).steps
assert_equal 25, Maze.new(MAZE5).steps
assert_equal 10, Maze.new(MAZE6).steps
assert_equal 2, Maze.new(MAZE7).steps
end
def test_without_ext_walls
assert_equal 8, Maze.new(MAZE8).steps
end
def test_not_rectangular
assert_equal 2, Maze.new(MAZE9).steps
end
def test_open
assert_equal 10, Maze.new(MAZE10).steps
end
end
# Time on my laptop for each method (ruby 1.9.2)
# 0.105 dijkstra_optimized
# 0.107 dijkstra_to_arrival
# 0.119 dijkstra
# 0.166 get_path_to_arrival
# 2.154 get_paths_to_arrival
# 6.533 get_all_paths: 7.51
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