C15 - Christian Spencer

graphs/possible_bipartition.py

@@ -1,12 +1,59 @@
 # Can be used for BFS
 from collections import deque 
 
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 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(Nodes + Edges) 
+          - Every edge for a dog starting with the first dog and exploring all edges. Edges are only expored once and all nodes must be
+          colored.
+        Space Complexity: O(Nodes + Edges)
+         - The adjacency list has O + E space complexity. Each node and edge requires an array or list space, but it is
+         not squre when stored in 2 dimensions.
     """
-    pass
+
+    if not dislikes:
+        return True  
+
+    color = {}
+    for i in range(len(dislikes)):
+
+        if i not in color:
+            # Implement a stack for the marked path
+            color[i] = 0
+            stack = [(i, 0)]
+            while stack:
+                node, paint = stack.pop() # Remove from stack, "marked" for coloring.  
+                dog = dislikes[node]
+                for enemy in dog:
+                    if enemy in color:
+                        if color[enemy] != (paint+1)%2:
+                            return False
+                    else:
+                        stack.append((enemy, (paint+1)%2))
+                        color[enemy] = (paint+1)%2                   
+    return True
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