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Diffstat (limited to 'ruby_1_8_6/lib/tsort.rb')
| -rw-r--r-- | ruby_1_8_6/lib/tsort.rb | 290 |
1 files changed, 290 insertions, 0 deletions
diff --git a/ruby_1_8_6/lib/tsort.rb b/ruby_1_8_6/lib/tsort.rb new file mode 100644 index 0000000000..a014e7f6c2 --- /dev/null +++ b/ruby_1_8_6/lib/tsort.rb @@ -0,0 +1,290 @@ +#!/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 TSortHash < Hash # :nodoc: + include TSort + alias tsort_each_node each_key + def tsort_each_child(node, &block) + fetch(node).each(&block) + end + end + + class TSortArray < 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 = TSortHash[{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 = TSortHash[{1=>[2], 2=>[3, 4], 3=>[2], 4=>[]}] + assert_equal([[4], [2, 3], [1]], + h.strongly_connected_components.map {|nodes| nodes.sort}) + assert_raise(TSort::Cyclic) { h.tsort } + end + + def test_array + a = TSortArray[[1], [0], [0], [2]] + assert_equal([[0, 1], [2], [3]], + a.strongly_connected_components.map {|nodes| nodes.sort}) + + a = TSortArray[[], [0]] + assert_equal([[0], [1]], + a.strongly_connected_components.map {|nodes| nodes.sort}) + end + end + +end + |