Water - Beatrice

lib/possible_bipartition.rb

@@ -1,4 +1,40 @@
-
+# Time complexity: O(N + E) for BFS * O(N) for each node - O(N^2)?
+# Space complexity: O(N) for dog_groups and queue
 def possible_bipartition(dislikes)
-  raise NotImplementedError, "possible_bipartition isn't implemented yet"
+  # The goal is to find out if it is possible to put the dogs into two groups
+  # We are going to denote these as 1 & -1, with 0 as "unvisited"
+  # We are going to do BFS starting from each vertices
+
+  size = dislikes.length
+  dog_groups = Hash.new(0) # hash of dog groups
+  queue = Queue.new
+  size.times do |node|
+    # If we haven't put this dog in a group yet
+    if dog_groups[node].zero?
+      dog_groups[node] = 1 # Start with group 1
+      queue << node # Put the node into the BFS queue
+
+      # Process the queue
+      until queue.empty?
+        neighbor = queue.pop
+        this_group = dog_groups[neighbor] # Group that the parent belongs to
+
+        dislikes[neighbor].each do |node| # Traverse all the children
+          # Visit each connected node and assign to opposite group
+          if dog_groups[node].zero? # Node has not been visited
+            dog_groups[node] = this_group * -1 # Assign opposite group and add to queue
+            queue << node
+          elsif dog_groups[node] == this_group
+            return false # We have an existing connection in the same group - bipartition not possible
+          end
+        end
+
+      end
+
+    end
+  end
+
+  # If we're here - we have sorted the dogs into two groups!
+  return true
+
 end