From 360cba9a6114c6082ecf23d188759a8c8b6c946d Mon Sep 17 00:00:00 2001
From: Amos Paribocci <aparibocci@gmail.com>
Date: Tue, 23 May 2023 08:37:39 +0200
Subject: [PATCH] Implementing unweighted graph BFS

---
 data_structures/graphs/bfs.rb      | 56 +++++++++++++++++++++++++
 data_structures/graphs/bfs_test.rb | 67 ++++++++++++++++++++++++++++++
 2 files changed, 123 insertions(+)
 create mode 100644 data_structures/graphs/bfs.rb
 create mode 100644 data_structures/graphs/bfs_test.rb

diff --git a/data_structures/graphs/bfs.rb b/data_structures/graphs/bfs.rb
new file mode 100644
index 0000000..fcb1b33
--- /dev/null
+++ b/data_structures/graphs/bfs.rb
@@ -0,0 +1,56 @@
+require 'set'
+
+##
+# This class represents the result of a breadth-first search performed on an unweighted graph.
+#
+# It exposes:
+# - the set of visited nodes
+# - a hash of distances by node from the search root node
+#   (only for visited nodes, 0 for the search root node);
+# - a hash of parent nodes by node
+#   (only for visited nodes, nil for the search root node).
+
+class GraphBfsResult
+  attr_reader :visited
+  attr_reader :parents
+  attr_reader :distances
+
+  def initialize(visited, parents, distances)
+    @visited = visited
+    @parents = parents
+    @distances = distances
+  end
+end
+
+##
+# Performs a breadth-first search for the provided graph, starting at the given node.
+# Returns the search result (see GraphBfsResult).
+#
+# The algorithm has a time complexity of O(|V| + |E|), where:
+# - |V| is the number of nodes in the graph;
+# - |E| is the number of edges in the graph.
+
+def bfs(graph, start_node)
+  seen = Set[]
+  visited = Set[]
+  parents = { start_node => nil }
+  distances = { start_node => 0 }
+
+  seen.add(start_node)
+  q = Queue.new
+  q.push(start_node)
+  until q.empty?
+    node = q.pop
+    for neighbor in graph.neighbors(node)
+      unless seen.include?(neighbor)
+        seen.add(neighbor)
+        distances[neighbor] = distances[node] + 1
+        parents[neighbor] = node
+        q.push(neighbor)
+      end
+    end
+    visited.add(node)
+  end
+
+  GraphBfsResult.new(visited, parents, distances)
+end
diff --git a/data_structures/graphs/bfs_test.rb b/data_structures/graphs/bfs_test.rb
new file mode 100644
index 0000000..933adab
--- /dev/null
+++ b/data_structures/graphs/bfs_test.rb
@@ -0,0 +1,67 @@
+require 'minitest/autorun'
+require_relative 'bfs'
+require_relative 'unweighted_graph'
+
+class TestBfs < Minitest::Test
+  def test_bfs_visits_single_graph_node
+    graph = UnweightedGraph.new(nodes: [:u, :v, :w], directed: false)
+    graph.add_edge(:u, :v)
+
+    bfs_result = bfs(graph, :w)
+
+    assert bfs_result.visited.to_set == [:w].to_set
+    assert bfs_result.parents == {
+        :w => nil
+    }
+    assert bfs_result.distances == {
+        :w => 0
+    }
+  end
+
+  def test_bfs_visits_undirected_graph_fully
+    graph = UnweightedGraph.new(nodes: [:u, :v, :w, :x], directed: false)
+    graph.add_edge(:u, :v)
+    graph.add_edge(:u, :w)
+    graph.add_edge(:w, :x)
+
+    bfs_result = bfs(graph, :u)
+
+    assert bfs_result.visited.to_set == [:u, :v, :w, :x].to_set
+    assert bfs_result.parents == {
+        :u => nil,
+        :v => :u,
+        :w => :u,
+        :x => :w
+    }
+    assert bfs_result.distances == {
+        :u => 0,
+        :v => 1,
+        :w => 1,
+        :x => 2
+    }
+  end
+
+  def test_bfs_visits_undirected_graph_partially
+    graph = UnweightedGraph.new(nodes: [:u, :v, :w, :x, :y, :z], directed: false)
+    graph.add_edge(:u, :v)
+    graph.add_edge(:w, :x)
+    graph.add_edge(:x, :y)
+    graph.add_edge(:y, :z)
+
+    bfs_result = bfs(graph, :x)
+
+    assert bfs_result.visited.to_set == [:w, :x, :y, :z].to_set
+    assert bfs_result.parents == {
+        :w => :x,
+        :x => nil,
+        :y => :x,
+        :z => :y
+    }
+    assert bfs_result.distances == {
+      :w => 1,
+      :x => 0,
+      :y => 1,
+      :z => 2
+    }
+  end
+end