Rock-Leilani

graphs/possible_bipartition.py

@@ -1,12 +1,38 @@
+
 # Can be used for BFS
-from collections import deque 
+from collections import deque
+# Check whether Graph is Bipartite or Not using DFS
+
+# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
+# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
+# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
+# or u belongs to V and v to U. We can also say that there is no edge that connects
+# vertices of same set.
 
 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^2)
+        Space Complexity: O(n)
     """
-    pass
+    visited = [False] * len(dislikes)
+    color = [-1] * len(dislikes)
+
+    def dfs(v, c):
+        visited[v] = True
+        color[v] = c
+        for u in dislikes[v]:
+            if not visited[u]:
+                dfs(u, 1 - c)
+
+    for i in range(len(dislikes)):
+        if not visited[i]:
+            dfs(i, 0)
+
+    for i in range(len(dislikes)):
+        for j in dislikes[i]:
+            if color[i] == color[j]:
+                return False
 
+    return True