- Inheritance
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
- E. Tarjan, "Depth First Search and Linear Graph Algorithms",
SIAM Journal on Computing, Vol. 1, No. 2, pp. 146-160, June 1972.
Classes & Modules
Methods
Instance
| Visibility | Signature |
|---|---|
| public | each_strongly_connected_component ( {|nodes| ...} |
| public | each_strongly_connected_component_from (node, id_map={}, stack=[]) {|nodes| ...} |
| public | strongly_connected_components () |
| public | tsort () |
| public | tsort_each ( {|node| ...} |
| public | tsort_each_child (node) {|child| ...} |
| public | tsort_each_node ( {|node| ...} |
Instance Method Detail
each_strongly_connected_component( {|nodes| ...}
The iterator version of the strongly_connected_components method. obj.each_strongly_connected_component is similar to obj.strongly_connected_components.each, but modification of obj during the iteration may lead to unexpected results.
each_strongly_connected_component returns nil.
each_strongly_connected_component_from(node, id_map={}, stack=[]) {|nodes| ...}
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.
strongly_connected_components()
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.
tsort()
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.
tsort_each( {|node| ...}
The iterator version of the tsort method. obj.tsort_each is similar to obj.tsort.each, 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.
tsort_each_child(node) {|child| ...}
Should be implemented by a extended class.
tsort_each_child is used to iterate for child nodes of node.
tsort_each_node( {|node| ...}
Should be implemented by a extended class.
tsort_each_node is used to iterate for all nodes over a graph.