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require 'tree' | |
class Maze | |
WALL_CHAR = '#' | |
START_CHAR = 'A' | |
GOAL_CHAR = 'B' | |
def initialize(maze) | |
@maze = maze.lines.map { |l| l.chomp.split '' } | |
determine_start | |
@tree = build_path_tree | |
end | |
def solvable? | |
@tree.contains? true | |
end | |
def steps | |
if ! self.solvable? then | |
0 | |
else | |
@tree.minimal_pathlength_to true | |
end | |
end | |
def at(x, y) | |
@maze[y][x] | |
end | |
def wall_at?(x, y) | |
@maze[y][x] == WALL_CHAR | |
end | |
def possible_directions_at(x, y, came_from = nil) | |
directions = [] | |
raise ArgumentError 'y too big' if y >= @maze.size | |
raise ArgumentError 'x too big' if x >= @maze[0].size | |
raise ArgumentError "there is a wall at #{x},#{y}!" if wall_at?(x, y) | |
directions = Direction.all.select do |d| | |
# all directions where there is no wall and were we did not come from | |
(! wall_at?(*Direction.goto(x, y, d))) && (d != came_from) | |
end | |
end | |
private | |
def determine_start | |
@maze.each_with_index do |line, y| | |
line.each_with_index do |char, x| | |
if char == START_CHAR then | |
@start = [x, y] | |
end | |
end | |
end | |
end | |
# Builds a tree with all paths through the maze. | |
# | |
# The 'name' of the tree elements is a boolean variable that | |
# determines whether we have reached the goal ('B'). This way, | |
# we can later just test whether the tree contains 'true' to | |
# see if the maze is solvable | |
def build_path_tree(x = @start[0], y = @start[1], came_from = nil) | |
name = (at(x, y) == GOAL_CHAR) | |
t = Tree.new(name) | |
possible_directions_at(x, y, came_from).each do |d| | |
new_x, new_y = Direction.goto(x, y, d) | |
t.add_child(build_path_tree new_x, new_y, Direction.opposite(d)) | |
end | |
t | |
end | |
end | |
class Direction | |
NORTH = [0, -1] | |
SOUTH = [0, +1] | |
WEST = [-1, 0] | |
EAST = [+1, 0] | |
def self.all | |
self.constants.map { |d| self.const_get(d) } | |
end | |
def self.opposite(dir) | |
dir.map { |d| -1 * d } | |
end | |
def self.goto(x, y, dir) | |
[x + dir[0], y + dir[1]] | |
end | |
end |
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class Tree | |
attr_reader :children, :object | |
def initialize(object) | |
@object = object | |
@children = [] | |
end | |
def add_child(child) | |
if child.is_a? Tree then | |
@children.push child | |
else | |
@children.push Tree.new(child) | |
end | |
end | |
def contains?(object) | |
# is the root itself the object we're looking for? | |
contained = (@object == object) | |
# iterate over the tree to look for the object | |
children.each do |c| | |
contained ||= c.contains? object | |
end | |
contained | |
end | |
def pp(level = 0) | |
result = (" " * level) + "#{object}\n" | |
@children.each do |c| | |
result += c.pp(level + 1) | |
end | |
result | |
end | |
def depth(depth = 0, curr_max_depth = 0) | |
if (depth > curr_max_depth) | |
curr_max_depth = depth | |
end | |
@children.each do |c| | |
curr_max_depth = c.depth(depth + 1, curr_max_depth) | |
end | |
curr_max_depth | |
end | |
# the minimal length of a path to a certain object | |
def minimal_pathlength_to(object, length = 0, curr_min_length = self.depth) | |
if (@object == object) && (length < curr_min_length) then | |
curr_min_length = length | |
end | |
@children.each do |c| | |
curr_min_length = c.minimal_pathlength_to(object, length + 1, | |
curr_min_length) | |
end | |
curr_min_length | |
end | |
end |
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