зеркало из https://github.com/github/ruby.git
290 строки
7.8 KiB
Ruby
290 строки
7.8 KiB
Ruby
#!/usr/bin/env ruby
|
|
#--
|
|
# tsort.rb - provides a module for topological sorting and strongly connected components.
|
|
#++
|
|
#
|
|
|
|
#
|
|
# TSort implements topological sorting using Tarjan's algorithm for
|
|
# strongly connected components.
|
|
#
|
|
# TSort is designed to be able to be used with any object which can be interpreted
|
|
# as a directed graph.
|
|
# TSort requires two methods to interpret an object as a graph:
|
|
# tsort_each_node and tsort_each_child:
|
|
#
|
|
# * tsort_each_node is used to iterate for all nodes over a graph.
|
|
# * tsort_each_child is used to iterate for child nodes of a given node.
|
|
#
|
|
# The equality of nodes are defined by eql? and hash since
|
|
# TSort uses Hash internally.
|
|
#
|
|
# == A Simple Example
|
|
#
|
|
# The following example demonstrates how to mix the TSort module into an
|
|
# existing class (in this case, Hash). Here, we're treating each key in
|
|
# the hash as a node in the graph, and so we simply alias the required
|
|
# #tsort_each_node method to Hash's #each_key method. For each key in the
|
|
# hash, the associated value is an array of the node's child nodes. This
|
|
# choice in turn leads to our implementation of the required #tsort_each_child
|
|
# method, which fetches the array of child nodes and then iterates over that
|
|
# array using the user-supplied block.
|
|
#
|
|
# require 'tsort'
|
|
#
|
|
# class Hash
|
|
# include TSort
|
|
# alias tsort_each_node each_key
|
|
# def tsort_each_child(node, &block)
|
|
# fetch(node).each(&block)
|
|
# end
|
|
# end
|
|
#
|
|
# {1=>[2, 3], 2=>[3], 3=>[], 4=>[]}.tsort
|
|
# #=> [3, 2, 1, 4]
|
|
#
|
|
# {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}.strongly_connected_components
|
|
# #=> [[4], [2, 3], [1]]
|
|
#
|
|
# == A More Realistic Example
|
|
#
|
|
# A very simple `make' like tool can be implemented as follows:
|
|
#
|
|
# require 'tsort'
|
|
#
|
|
# class Make
|
|
# def initialize
|
|
# @dep = {}
|
|
# @dep.default = []
|
|
# end
|
|
#
|
|
# def rule(outputs, inputs=[], &block)
|
|
# triple = [outputs, inputs, block]
|
|
# outputs.each {|f| @dep[f] = [triple]}
|
|
# @dep[triple] = inputs
|
|
# end
|
|
#
|
|
# def build(target)
|
|
# each_strongly_connected_component_from(target) {|ns|
|
|
# if ns.length != 1
|
|
# fs = ns.delete_if {|n| Array === n}
|
|
# raise TSort::Cyclic.new("cyclic dependencies: #{fs.join ', '}")
|
|
# end
|
|
# n = ns.first
|
|
# if Array === n
|
|
# outputs, inputs, block = n
|
|
# inputs_time = inputs.map {|f| File.mtime f}.max
|
|
# begin
|
|
# outputs_time = outputs.map {|f| File.mtime f}.min
|
|
# rescue Errno::ENOENT
|
|
# outputs_time = nil
|
|
# end
|
|
# if outputs_time == nil ||
|
|
# inputs_time != nil && outputs_time <= inputs_time
|
|
# sleep 1 if inputs_time != nil && inputs_time.to_i == Time.now.to_i
|
|
# block.call
|
|
# end
|
|
# end
|
|
# }
|
|
# end
|
|
#
|
|
# def tsort_each_child(node, &block)
|
|
# @dep[node].each(&block)
|
|
# end
|
|
# include TSort
|
|
# end
|
|
#
|
|
# def command(arg)
|
|
# print arg, "\n"
|
|
# system arg
|
|
# end
|
|
#
|
|
# m = Make.new
|
|
# m.rule(%w[t1]) { command 'date > t1' }
|
|
# m.rule(%w[t2]) { command 'date > t2' }
|
|
# m.rule(%w[t3]) { command 'date > t3' }
|
|
# m.rule(%w[t4], %w[t1 t3]) { command 'cat t1 t3 > t4' }
|
|
# m.rule(%w[t5], %w[t4 t2]) { command 'cat t4 t2 > t5' }
|
|
# m.build('t5')
|
|
#
|
|
# == Bugs
|
|
#
|
|
# * 'tsort.rb' is wrong name because this library uses
|
|
# Tarjan's algorithm for strongly connected components.
|
|
# Although 'strongly_connected_components.rb' is correct but too long.
|
|
#
|
|
# == References
|
|
#
|
|
# R. E. Tarjan, "Depth First Search and Linear Graph Algorithms",
|
|
# <em>SIAM Journal on Computing</em>, Vol. 1, No. 2, pp. 146-160, June 1972.
|
|
#
|
|
|
|
module TSort
|
|
class Cyclic < StandardError
|
|
end
|
|
|
|
#
|
|
# Returns a topologically sorted array of nodes.
|
|
# The array is sorted from children to parents, i.e.
|
|
# the first element has no child and the last node has no parent.
|
|
#
|
|
# If there is a cycle, TSort::Cyclic is raised.
|
|
#
|
|
def tsort
|
|
result = []
|
|
tsort_each {|element| result << element}
|
|
result
|
|
end
|
|
|
|
#
|
|
# The iterator version of the #tsort method.
|
|
# <tt><em>obj</em>.tsort_each</tt> is similar to <tt><em>obj</em>.tsort.each</tt>, but
|
|
# modification of _obj_ during the iteration may lead to unexpected results.
|
|
#
|
|
# #tsort_each returns +nil+.
|
|
# If there is a cycle, TSort::Cyclic is raised.
|
|
#
|
|
def tsort_each # :yields: node
|
|
each_strongly_connected_component {|component|
|
|
if component.size == 1
|
|
yield component.first
|
|
else
|
|
raise Cyclic.new("topological sort failed: #{component.inspect}")
|
|
end
|
|
}
|
|
end
|
|
|
|
#
|
|
# Returns strongly connected components as an array of arrays of nodes.
|
|
# The array is sorted from children to parents.
|
|
# Each elements of the array represents a strongly connected component.
|
|
#
|
|
def strongly_connected_components
|
|
result = []
|
|
each_strongly_connected_component {|component| result << component}
|
|
result
|
|
end
|
|
|
|
#
|
|
# The iterator version of the #strongly_connected_components method.
|
|
# <tt><em>obj</em>.each_strongly_connected_component</tt> is similar to
|
|
# <tt><em>obj</em>.strongly_connected_components.each</tt>, but
|
|
# modification of _obj_ during the iteration may lead to unexpected results.
|
|
#
|
|
#
|
|
# #each_strongly_connected_component returns +nil+.
|
|
#
|
|
def each_strongly_connected_component # :yields: nodes
|
|
id_map = {}
|
|
stack = []
|
|
tsort_each_node {|node|
|
|
unless id_map.include? node
|
|
each_strongly_connected_component_from(node, id_map, stack) {|c|
|
|
yield c
|
|
}
|
|
end
|
|
}
|
|
nil
|
|
end
|
|
|
|
#
|
|
# Iterates over strongly connected component in the subgraph reachable from
|
|
# _node_.
|
|
#
|
|
# Return value is unspecified.
|
|
#
|
|
# #each_strongly_connected_component_from doesn't call #tsort_each_node.
|
|
#
|
|
def each_strongly_connected_component_from(node, id_map={}, stack=[]) # :yields: nodes
|
|
minimum_id = node_id = id_map[node] = id_map.size
|
|
stack_length = stack.length
|
|
stack << node
|
|
|
|
tsort_each_child(node) {|child|
|
|
if id_map.include? child
|
|
child_id = id_map[child]
|
|
minimum_id = child_id if child_id && child_id < minimum_id
|
|
else
|
|
sub_minimum_id =
|
|
each_strongly_connected_component_from(child, id_map, stack) {|c|
|
|
yield c
|
|
}
|
|
minimum_id = sub_minimum_id if sub_minimum_id < minimum_id
|
|
end
|
|
}
|
|
|
|
if node_id == minimum_id
|
|
component = stack.slice!(stack_length .. -1)
|
|
component.each {|n| id_map[n] = nil}
|
|
yield component
|
|
end
|
|
|
|
minimum_id
|
|
end
|
|
|
|
#
|
|
# Should be implemented by a extended class.
|
|
#
|
|
# #tsort_each_node is used to iterate for all nodes over a graph.
|
|
#
|
|
def tsort_each_node # :yields: node
|
|
raise NotImplementedError.new
|
|
end
|
|
|
|
#
|
|
# Should be implemented by a extended class.
|
|
#
|
|
# #tsort_each_child is used to iterate for child nodes of _node_.
|
|
#
|
|
def tsort_each_child(node) # :yields: child
|
|
raise NotImplementedError.new
|
|
end
|
|
end
|
|
|
|
if __FILE__ == $0
|
|
require 'test/unit'
|
|
|
|
class Hash # :nodoc:
|
|
include TSort
|
|
alias tsort_each_node each_key
|
|
def tsort_each_child(node, &block)
|
|
fetch(node).each(&block)
|
|
end
|
|
end
|
|
|
|
class Array # :nodoc:
|
|
include TSort
|
|
alias tsort_each_node each_index
|
|
def tsort_each_child(node, &block)
|
|
fetch(node).each(&block)
|
|
end
|
|
end
|
|
|
|
class TSortTest < Test::Unit::TestCase # :nodoc:
|
|
def test_dag
|
|
h = {1=>[2, 3], 2=>[3], 3=>[]}
|
|
assert_equal([3, 2, 1], h.tsort)
|
|
assert_equal([[3], [2], [1]], h.strongly_connected_components)
|
|
end
|
|
|
|
def test_cycle
|
|
h = {1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}
|
|
assert_equal([[4], [2, 3], [1]],
|
|
h.strongly_connected_components.map {|nodes| nodes.sort})
|
|
assert_raises(TSort::Cyclic) { h.tsort }
|
|
end
|
|
|
|
def test_array
|
|
a = [[1], [0], [0], [2]]
|
|
assert_equal([[0, 1], [2], [3]],
|
|
a.strongly_connected_components.map {|nodes| nodes.sort})
|
|
|
|
a = [[], [0]]
|
|
assert_equal([[0], [1]],
|
|
a.strongly_connected_components.map {|nodes| nodes.sort})
|
|
end
|
|
end
|
|
|
|
end
|
|
|