From 3e1cfd732eed355a6aeaaf7ef65e59319be904d2 Mon Sep 17 00:00:00 2001
From: ggrossvi <hello.gloria@gmail.com>
Date: Fri, 14 Jan 2022 01:23:59 -0800
Subject: [PATCH] added space and time complexity

---
 graphs/possible_bipartition.py | 63 +++++++++++++++++++++++++++++++---
 1 file changed, 59 insertions(+), 4 deletions(-)

diff --git a/graphs/possible_bipartition.py b/graphs/possible_bipartition.py
index ca55677..06800b4 100644
--- a/graphs/possible_bipartition.py
+++ b/graphs/possible_bipartition.py
@@ -1,12 +1,67 @@
 # Can be used for BFS
 from collections import deque 
 
+# does breadth first search(BFS)
+def partition_helper(visited, dislikes, starting_dog):
+    """ Will return True or False if the given graph
+        can be bipartitioned without neighboring nodes put
+        into the same partition.
+        Time Complexity: O(N + E)
+            Since you will visit each node once, and loop through each of the edges in each node the Big-O of this algorithm is O(N + E) where N is the number of nodes in the graph and E is the number of edges since each node and each edge will be explored.
+        Space Complexity: O(n)
+            In the worst-case you will need to add each node to the Queue, so the space complexity is O(N) where N is the number of nodes in the graph.
+    """  
+    queue = deque()
+    queue.append(starting_dog)
+    # visited holds all the nodes.  It is set to false at beginning indicating it has not been visited 
+    visited[starting_dog] = "group_1"
+    if not dislikes[starting_dog]:
+        return True
+    while queue:
+        
+        current_dog = queue.popleft()
+        # dislikes[current_dog] has value of dogs that the current dog doesn't like 
+        for enemy_dog in dislikes[current_dog]:
+            # don't want to compare current dog to itself
+            #assign other dogs to other group if not assigned 
+            # if not assigned/visited/they have value false
+            # append the dogs that have not been visited to the queue
+            if visited[enemy_dog] == False:
+                queue.append(enemy_dog)
+                # check current dog's group and assign the enemy dog the opposite group
+                if visited[current_dog] == "group_1":
+                    visited[enemy_dog] = "group_2" 
+                elif visited[current_dog] == "group_2":
+                    visited[enemy_dog] = "group_1"
+            #check if current dogs group matches the enemy dog's group
+            elif visited[current_dog] == visited[enemy_dog]:
+                return False
+    return True
+
+    
 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: ?
-    """
-    pass
+        Time Complexity: O(N)
+        Space Complexity: O(N)
+    """  
+    # if empty array return True
+    if not dislikes:
+        return True
+        
+
+    visited = [False] * ((len(dislikes)+1))
+    # return partition_helper(visited,dislikes, 0)
+    
+    for i in range(len(dislikes)):
+        #dislike[i] i is not connected to any other node empty list for adjacency 7.  [] means it has no adjacencey. dog i does not dislike any other dog or you have visited dog you skip it.  
+        if not visited[i]:
+            #continue means you skip.return flow to the start of the loop while break is exit the loop
+            # continue
+        # i index of the dogs, breadth first search (done with queue)  i nodes of the dog 
+            result = partition_helper(visited,dislikes, i)
+            if not result:
+                return False 
+    return True