Whit - Paper

graphs/possible_bipartition.py

@@ -5,8 +5,31 @@ 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+e)
+        Space Complexity: O(n)
     """
-    pass
+    if len(dislikes) < 2:
+        return True
 
+    queue = deque([1])
+
+    groups = {}
+    groups[1] = 'X'
+    seen = set([1])
+
+    while len(queue) > 0:
+        current = queue.popleft()
+        group = groups[current]
+
+        for dislike in dislikes[current]:
+            if dislike in groups:
+                if groups[dislike] == group:
+                    return False
+            else:
+                groups[dislike] = 'X' if group == 'O' else 'O'
+
+            if dislike not in seen:
+                queue.append(dislike)
+                seen.add(dislike)
+
+    return True