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=begin | |
The solution is contained in 2 files | |
1. maze.rb - the Maze class (this file. It in turn relies heavily on 2. | |
2. RPCFN3_classes.rb - Contains all class definitions for the node network | |
RPCFN3_classes were written in my doomed attempt to solve RPCFN3. | |
I failed that one, but only by a (stupid) hairs breadth. | |
So here, i use the same framework. A maze is just another network or map, | |
a collection of nodes/points connected by links/paths/edges. | |
I did intend at the time of RPCFN3 to develop some reusable code. | |
This challenge has given me a use case to demostrate reuse. | |
= SYNOPSIS ======================================================= | |
A point/node is added to the map for each space character on the | |
input maze. These are all the locations to which we can navigate. | |
The (#) maze wall/brick nodes are just discarded. | |
Each space node can have up to 4 links/edges that lead to an adjacent | |
space node positioned either to the immediate left or right, or | |
immediately above or below it. | |
By using the RPCFN3 classes, the challenge is limited to priming | |
the network or map with the input maze. | |
a) Load all the space nodes from the input file. They are identified | |
by their line and character numbers, starting at 0_0 and ending | |
at 12_36. At this point the nodes are orphans, no links. | |
b) Visit each node and add links (i call them paths) to all | |
adjacent nodes. | |
All of a) and b) is done when a maze is instantiated. | |
The rest of it is in RPCFN3_classes built previously. | |
c) Get all possible routes that link the given start to end nodes. | |
d) If the array of routes is empty, then there is no solution. | |
e) Each path / link /edge traversed is assigned a cost of 1. That way | |
the total cost of any route is equal to the number of steps required | |
to get from start to end. | |
=end | |
require 'RPCFN3_classes' | |
class Maze | |
attr_reader :from, :to, :map | |
def initialize(maze) | |
@map = Network.new | |
add_map_nodes(maze) # load all navigable locations/points into the map | |
build_links # create links / paths / edges that link adjacent points | |
map.get_routes(from, to) # create the list of routes that link the start and end points | |
end | |
def solvable? | |
map.route_count > 0 ? true : false | |
end | |
def steps | |
route_count > 0 ? map.min_cost_routes.first.cost : 0 | |
end | |
def route_count | |
map.routes.count | |
end | |
private | |
def add_map_nodes(maze) | |
# Load nodes that correspond to maze coordinates which | |
# can be traversed. (i.e. spaces, not bricks) | |
# Also record start end end points. | |
r = c = 0 | |
maze.chars.to_a.each do |ch| | |
node_id = r.to_s + '_' + c.to_s | |
case ch | |
when ' ' | |
map.add_node(Node.new(node_id)) | |
when '#' #dump the bricks | |
when 'A' | |
map.add_node(Node.new(node_id)) | |
@from = node_id | |
when 'B' | |
map.add_node(Node.new(node_id)) | |
@to = node_id | |
else #reached end of row | |
r += 1 | |
c = -1 | |
end | |
c += 1 | |
end | |
end | |
def build_links | |
map.nodes.each_pair do |id, node| | |
# construct names of potential neighbors | |
# if it exists create the link | |
loc = id.split('_') #node location: row and column | |
nxt = "#{loc[0]}_#{(loc[1].to_i + 1).to_s}" | |
prv = "#{loc[0]}_#{(loc[1].to_i - 1).to_s}" | |
up = "#{(loc[0].to_i - 1).to_s}_#{loc[1]}" | |
dwn = "#{(loc[0].to_i + 1).to_s}_#{loc[1]}" | |
[nxt, prv, up, dwn].each {|n| node.add_path(Path.new('', id, n, 1)) if map.has_node?(n)} | |
end | |
end | |
end |
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=begin | |
Network - outer container, a collection of node objects | |
Node - a point in the network that can be reached via at least one pathway. | |
includes a collection of paths that point to neighboring nodes. | |
Path - a link or association between 2 nodes. A path between 2 nodes implies | |
that they are neighbors. | |
Each path has a cost attribute, a generalization of things such as | |
resistance, distance, weight, difficulty, traffic density, | |
the toll or outlay or price incurred when following the path from | |
one end to the other. | |
Route - A pathway that connects 2 nodes defined as start and destination nodes. | |
There can be many different routes between 2 chosen nodes. | |
There can be one or more routes that have the same cost | |
=end | |
########################################### | |
class Network ############################ | |
########################################### | |
# | |
# The outer container. | |
# A collection of Node objects, hashed for easy location of specific nodes | |
# Synonyms: Map, CircuitBoard, ... | |
# | |
# Its behaviour includes the ability to find all the possible routes | |
# between any 2 nodes (the start and end nodes). see get_routes | |
# | |
attr_reader :name, # a unique identifier | |
:nodes, # hash of nodes where the key is the node name | |
:routes, # array of routes populated when start and end nodes are provided | |
# see method get_routes | |
:max_cost, # max cost incurred following a specified route | |
:max_cost_routes, # list of routes that share max cost | |
:min_cost, # min cost incurred following a specified route | |
:min_cost_routes, # list of routes that share min cost | |
:avg_cost # average cost incurred across all routes | |
def initialize(name = 'myMap', nodes = []) | |
@name = name | |
@nodes = {} | |
@routes = [] | |
nodes.each {|n| @nodes.store(n.name, n)} | |
init_stats | |
end | |
def import(paths) # import RPCFN3 format map data | |
paths.each do |p_in| | |
p_to = Path.new('', p_in[0],p_in[1],p_in[2]) | |
p_reverse = p_to.reverse | |
[p_to, p_reverse].each do |p| | |
if has_node?(p.from) | |
node(p.from).add_path p | |
else | |
add_node Node.new(p.from, p) | |
end | |
end | |
end | |
end | |
def export # export to RPCFN3 format TODO | |
end | |
def has_node?(node) # some overloading | |
if node.kind_of? String | |
@nodes.has_key?(node) | |
elsif node.kind_of? Node | |
@nodes.has_key?(node.name) | |
else | |
false | |
end | |
end | |
def is_empty? | |
@nodes.length == 0 | |
end | |
def node(node) | |
if node.kind_of? String | |
@nodes[node] | |
elsif node.kind_of? Node | |
@nodes[node.name] | |
else | |
false | |
end | |
end | |
def add_node(node) # single Node assumed if not array of nodes | |
node = [node] unless node.kind_of? Array | |
node.each {|n| @nodes.store(n.name, n)} | |
end | |
def node_count | |
@nodes.length | |
end | |
def neighbors(node) #neighboring nodes | |
node = node(node) if node.kind_of? String | |
node.paths.keys.collect {|pk| node(pk)} | |
end | |
def path_count | |
nodes.values.inject(0) {|cnt, n| cnt+= n.path_count} | |
end | |
def path(path_name) | |
# TODO: | |
# Making shaky assumptions wrt path name format, as follows: | |
# 1. Format is <from_nodename>_<to_nodename> | |
# 2. nodenames may not contain underscores | |
# It works for RPCFN3 but certainly requires some | |
# attention for use beyond that. | |
node(path_name.split('_').first).path(path_name.split('_').last) | |
end | |
def path_list # array of all paths in the network | |
nodes.values.collect {|n| n.paths.values}.flatten | |
end | |
def route_count | |
routes.length | |
end | |
def get_routes(from, to) | |
# | |
# The stack is processed as a LIFO queue | |
# Each entry includes a node identifier (name) and a tail of breadcrumbs | |
# that include the nodes we have traversed to get to this entry's node. | |
# | |
# The traverse_node method processes the top stack entry (index=0) | |
# 1. Identify all possible next steps from here | |
# 2. Filter out possible destinations that we have already visited | |
# 3. Remove the top stack entry, been there, done that. | |
# 4. If we have not yet reached the end node, then | |
# put valid next steps onto the stack, each with breadcrumbs attached | |
# otherwise | |
# create a route from the bradcrumbs and save it | |
# | |
@from = from | |
@to = to | |
@stack = [[from, []]] | |
@routes = [] | |
traverse_node until @stack.empty? | |
calc_stats | |
end | |
private | |
def traverse_node # This is the heart of the challenge | |
here = @stack.first[0] | |
crumbs = @stack.first[1] + [here] # list of node names that show where we came from | |
nb = neighbors(here).collect {|n| n.name} # all possible nodes we can reach from here | |
next_steps = nb - crumbs # remove nodes we have already been to | |
@stack.delete_at(0) # remove the top stack entry | |
if here != @to # Not there yet.. | |
# pile next step nodes with breadcrumbs on top of stack | |
next_steps.each { |nn| @stack.insert(0, [nn, crumbs])} | |
else # We have reached the destination node. | |
# The nodes traversed are in crumbs. | |
# Create a list of nodes traversed and hook on each the actual path followed | |
# Use that list to create a new route object an add it to the list of routes | |
rnodes = [] | |
crumbs.each_index do |i| | |
rn = Node.new(crumbs[i]) | |
rn.add_path(node(crumbs[i]).path(crumbs[i + 1])) unless i == (crumbs.length - 1) | |
rnodes << rn | |
end | |
routes << Route.new("#{@from}_#{@to}_#{routes.length + 1}", node(@from), node(@to), rnodes) | |
end | |
end | |
def calc_stats | |
init_stats | |
costs = routes.collect {|r| r.cost} | |
costs.each {|d| @max_cost = d if d > @max_cost} | |
@min_cost += @max_cost | |
costs.each do |d| | |
@min_cost = d if d < @min_cost | |
@avg_cost += d | |
end | |
@avg_cost /= (routes.count > 0 ? routes.count : 1) | |
#finally save a list of routes that share min / max values | |
#format key is the cost, value is an array of matching routes | |
routes.each do |r| | |
@min_cost_routes << r if r.cost == @min_cost | |
@max_cost_routes << r if r.cost == @max_cost | |
end | |
end | |
def init_stats | |
# max and min stats are implemented as hash to cater | |
# for more than one route with min or max values | |
@max_cost = @min_cost = @avg_cost = 0 | |
@max_cost_routes = [] | |
@min_cost_routes = [] | |
end | |
end | |
########################################### | |
class Node ################################## | |
########################################### | |
attr_reader :name, # a unique identifier | |
:paths # a list of Path objects that lead us to adjacent nodes | |
# *Note* as implemented here (hash where key is | |
# the destination node identifier) we can only have | |
# one path that connects any 2 nodes. | |
# TODO: Allow more than one path between 2 nodes, ensuring | |
# that there is a cost (distance/weight/resistance) | |
# difference between them - (otherwise it makes no sense?) | |
def initialize(name, paths = []) | |
@name = name | |
# paths.kind_of?(Path) ? @paths = [paths] : @paths = paths | |
@paths = {} | |
paths.kind_of?(Path) ? @paths.store(paths.to, paths) : paths.each {|p| @paths.store(p.to, p)} | |
end | |
def is_orphaned? | |
paths.length == 0 | |
end | |
def add_path(path) #String assumed if not array of paths | |
path.kind_of?(Path) ? @paths.store(path.to, path) : path.each {|p| @paths.store(p.to, p)} | |
end | |
def path(path) | |
if path.kind_of? String | |
@paths[path] | |
elsif path.kind_of? Path | |
@paths[path.to] | |
else | |
false | |
end | |
end | |
def cost(node) | |
@paths[node.kind_of?(Node) ? node.name : node].cost | |
end | |
def clear_paths | |
@paths = [] | |
end | |
def path_count | |
@paths.length | |
end | |
end | |
########################################### | |
class Path ################################## | |
########################################### | |
attr_reader :name, # a unique identifier | |
:from, :to, # connecting node names. "from" is redundant, "to" is the destination node | |
:cost # alias distance, resistance, weight ... | |
def initialize(name, from, to, cost) | |
@name = name == '' ? "#{from}_#{to}" : name | |
@from = from | |
@to = to | |
@cost = cost | |
end | |
def reverse | |
Path.new(@name == "#{@from}_#{@to}" ? '' : @name, @to, @from, @cost) | |
end | |
def to_a #build output format for ROCFN3 | |
[@from, @to, @cost] | |
end | |
end | |
########################################### | |
class Route ############################## | |
########################################### | |
attr_reader :name, # a unique identifier | |
:origin, :destination, # the start and end nodes | |
:nodes, # list of nodes traversed en route | |
:cost #incurred following this route | |
def initialize(name, origin, destination, nodes = []) | |
@name = name == '' ? "#{origin.name}_#{destination.name}" : name | |
@origin = origin | |
@destination = destination | |
@nodes = nodes | |
@cost = calculate_cost | |
end | |
def add_node(node) # single Node assumed if not array of nodes | |
node = [node] unless node.kind_of? Array | |
node.each {|n| @nodes.store(n.name, n)} | |
end | |
def path_list # array of all paths in the route | |
nodes.collect {|n| n.paths.values}.flatten | |
end | |
def reverse # the return route | |
rev = nodes.reverse | |
i = 0 | |
begin | |
rev[i].add_path(rev[i+1].paths.values.first.reverse) | |
rev[i+1].clear_paths | |
i += 1 | |
end until i = (rev.length - 2) | |
Route.new(name == "#{origin.name}_#{destination.name}" ? '' : "Reverse of #{name}", destination, origin, rev) | |
end | |
private | |
def calculate_cost | |
nodes.inject(0) {|dist, n| dist += (n.paths.count == 1 ? n.paths.values.first.cost : 0)} | |
end | |
end | |
########################################### | |
class String # Playing around with bits of DSL ############## | |
########################################### | |
def is_a_node_on(theMap) # the string here is the name of a node | |
theMap.has_node?(self) | |
end | |
end |
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