Implementing topological sorting for DAGs

data_structures/graphs/topological_sort.rb

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+require 'set'
+
+##
+# This class aims to provide topological sorting capabilities for directed acyclic graphs.
+#
+# Topological sorting runs in O(|V|), where |V| is the number of graph nodes.
+
+class TopologicalSorter
+  attr_reader :graph
+
+  def initialize(graph)
+    raise ArgumentError, "Topological sort is only applicable to directed graphs!" unless graph.directed
+    @graph = graph
+  end
+
+  def topological_sort
+    @sorted_nodes = []
+    @seen = Set[]
+    @visited = Set[]
+    for node in graph.nodes
+      dfs_visit(node)
+    end
+    @sorted_nodes
+  end
+
+  private
+  def dfs_visit(node)
+    return if @visited.include?(node)
+    raise ArgumentError, "Cycle in graph detected on node #{node}!" if @seen.include?(node)
+    @seen.add(node)
+    for neighbor in graph.neighbors(node)
+      dfs_visit(neighbor)
+    end
+    @visited.add(node)
+    @sorted_nodes.unshift(node)
+  end
+end

data_structures/graphs/topological_sort_test.rb

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+require 'minitest/autorun'
+require_relative 'topological_sort'
+require_relative 'unweighted_graph'
+
+class TestTopologicalSort < Minitest::Test
+  def test_topological_sort_returns_valid_order_for_acyclic_graph
+    wardrobe_items = [:underwear, :trousers, :belt, :shirt, :tie, :jacket, :socks, :shoes, :watch]
+    wardrobe_graph = UnweightedGraph.new(nodes: wardrobe_items, directed: true)
+    wardrobe_graph.add_edge(:underwear, :trousers)
+    wardrobe_graph.add_edge(:underwear, :shoes)
+    wardrobe_graph.add_edge(:socks, :shoes)
+    wardrobe_graph.add_edge(:trousers, :shoes)
+    wardrobe_graph.add_edge(:trousers, :belt)
+    wardrobe_graph.add_edge(:shirt, :belt)
+    wardrobe_graph.add_edge(:belt, :jacket)
+    wardrobe_graph.add_edge(:shirt, :tie)
+    wardrobe_graph.add_edge(:tie, :jacket)
+
+    sorted_items = TopologicalSorter.new(wardrobe_graph).topological_sort
+
+    assert sorted_items.index(:underwear) < sorted_items.index(:trousers)
+    assert sorted_items.index(:underwear) < sorted_items.index(:shoes)
+    assert sorted_items.index(:socks) < sorted_items.index(:shoes)
+    assert sorted_items.index(:trousers) < sorted_items.index(:shoes)
+    assert sorted_items.index(:trousers) < sorted_items.index(:belt)
+    assert sorted_items.index(:shirt) < sorted_items.index(:belt)
+    assert sorted_items.index(:belt) < sorted_items.index(:jacket)
+    assert sorted_items.index(:shirt) < sorted_items.index(:tie)
+    assert sorted_items.index(:tie) < sorted_items.index(:jacket)
+  end
+
+  def test_topological_sort_raises_exception_for_undirected_graph
+    nodes = [:u, :v]
+    graph = UnweightedGraph.new(nodes: nodes, directed: false)
+    graph.add_edge(:u, :v)
+
+    assert_raises ArgumentError do
+      TopologicalSorter.new(graph).topological_sort
+    end
+  end
+
+  def test_topological_sort_raises_exception_for_cyclic_graph
+    nodes = [:u, :v]
+    graph = UnweightedGraph.new(nodes: nodes, directed: true)
+    graph.add_edge(:u, :v)
+    graph.add_edge(:v, :u)
+
+    assert_raises ArgumentError do
+      TopologicalSorter.new(graph).topological_sort
+    end
+  end
+end