Grace Park C17 Whales

graphs/possible_bipartition.py

@@ -5,8 +5,30 @@ def possible_bipartition(dislikes):
     """ Will return True or False if the given graph
         can be bipartitioned without neighboring nodes put
         into the same partition.
-        Time Complexity: ?
-        Space Complexity: ?
+        Time Complexity: O(n+m) where is the number of dogs and n is the number of dislikes
+        Space Complexity: O(n) where n is the number of dogs 
     """
-    pass
+    def can_partition_dog(current_dog):
+        dog_group = { current_dog: True }
+        to_visit = [current_dog]
+        visited = set()
 
+        while len(to_visit) > 0:
+            dog = to_visit.pop()
+            if dog in visited: continue
+            visited.add(dog)
+
+            for other_dog in dislikes[dog]:
+                if other_dog in dog_group and dog_group[dog] == dog_group[other_dog]:
+                    return False
+
+                dog_group[other_dog] = not dog_group[dog]
+                to_visit.append(other_dog)
+
+        return True
+
+    for dog in dislikes.keys():
+        if not can_partition_dog(dog):
+            return False
+
+    return True