Paper: Graph Exercise

graphs/possible_bipartition.py

@@ -5,8 +5,37 @@ 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 not dislikes:
+        return True
 
+    frontier = [0]
+    visited = {}
+    group1 = set()
+    group2 = set()
+
+    while frontier:
+        current = frontier.pop(0)
+
+        if not dislikes[current]:
+            if (current+1) not in visited:
+                visited[current+1] = True
+                frontier.append(current+1)
+
+        for neigbor in dislikes[current]:
+            if neigbor not in visited:
+                visited[neigbor] = True
+                frontier.append(neigbor)
+
+            if current not in group1:
+                if neigbor in group2:
+                    return False
+                group1.add(neigbor)
+            else:
+                if neigbor in group1:
+                    return False
+                group2.add(neigbor)
+
+    return True