Update Longest_movie_title.md

Author: Joseph Luce

real_interview_questions/Google/Longest_movie_title.md

@@ -5,18 +5,21 @@ import copy
 def concat_longest_title(titles):
     adj_list = create_adj_list(titles)
     global_visit = set()
-    global_title = list()
+    longest_title = list()
+    memo = dict()
     for title in adj_list.keys():
         if title not in global_visit:
             local_visit = set()
             local_title = list()
-            visit_title(title, 
-                        local_title,
-                        global_title,
-                        adj_list, 
-                        local_visit, 
-                        global_visit)
-    return ' '.join(global_title)
+            local_result = visit_title(title, 
+                                        local_title,
+                                        adj_list, 
+                                        local_visit, 
+                                        global_visit,
+                                        memo)
+            if len(local_result) > len(longest_title):
+                longest_title = copy.deepcopy(local_result)
+    return longest_title
 
 def create_adj_list(titles):
     firstWord_to_titles_hash = dict()
@@ -39,25 +42,32 @@ def create_adj_list(titles):
                 result[title] = list()
     return result
         
-def visit_title(title, stack, longest_title, adj_list, local_visit, global_visit):
-    print longest_title
+def visit_title(title, stack, adj_list, local_visit, global_visit, memo):
+    if title in memo:
+        return memo[title]
     result = list()
     if title not in local_visit:
         local_visit.add(title)
         stack.append(title)
-        if len(stack) > len(longest_title):
-            longest_title = copy.deepcopy(stack)
         neighbors = adj_list[title]
         for next_title in neighbors:
-            visit_title(next_title, 
-                        stack,
-                        longest_title,
-                        adj_list, 
-                        local_visit, 
-                        global_visit)
+            local_result = visit_title(next_title, 
+                                        stack,
+                                        adj_list, 
+                                        local_visit, 
+                                        global_visit,
+                                        memo)
+            if len(local_result) > len(result):
+                result = copy.deepcopy(local_result)
+        if len(stack) > len(result):
+                result = copy.deepcopy(stack)
         stack.pop()
+    memo[title] = result 
+    return result
         
 Input = ['OF MICE AND MEN', 'BLACK MASS', 'MEN IN BLACK']
-        
+Input = ['a b', 'b c', 'c d', 'c e', 'e f']  
+Input = ['a b', 'b c', 'c a'] 
+    
 print concat_longest_title(Input)
 ```