Add prev to Node class (#82)

For managing an LRU cache, we need to use a doubly linked list for move_to_front() operation.

solutions/object_oriented_design/lru_cache/lru_cache.ipynb

@@ -56,7 +56,8 @@
     "\n",
     "    def __init__(self, results):\n",
     "        self.results = results\n",
-    "        self.next = next\n",
+    "        self.prev = None\n",
+    "        self.next = None\n",
     "\n",
     "\n",
     "class LinkedList(object):\n",
 %% Cell type:markdown id: tags:
 
 This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/system-design-primer-primer).
 
 %% Cell type:markdown id: tags:
 
 # Design an LRU cache
 
 %% Cell type:markdown id: tags:
 
 ## Constraints and assumptions
 
 * What are we caching?
     * We are cahing the results of web queries
 * Can we assume inputs are valid or do we have to validate them?
     * Assume they're valid
 * Can we assume this fits memory?
     * Yes
 
 %% Cell type:markdown id: tags:
 
 ## Solution
 
 %% Cell type:code id: tags:
 
 ``` python
 %%writefile lru_cache.py
 class Node(object):
 
     def __init__(self, results):
         self.results = results
-        self.next = next
+        self.prev = None
+        self.next = None
 
 
 class LinkedList(object):
 
     def __init__(self):
         self.head = None
         self.tail = None
 
     def move_to_front(self, node):  # ...
     def append_to_front(self, node):  # ...
     def remove_from_tail(self):  # ...
 
 
 class Cache(object):
 
     def __init__(self, MAX_SIZE):
         self.MAX_SIZE = MAX_SIZE
         self.size = 0
         self.lookup = {}  # key: query, value: node
         self.linked_list = LinkedList()
 
     def get(self, query)
         """Get the stored query result from the cache.
 
         Accessing a node updates its position to the front of the LRU list.
         """
         node = self.lookup[query]
         if node is None:
             return None
         self.linked_list.move_to_front(node)
         return node.results
 
     def set(self, results, query):
         """Set the result for the given query key in the cache.
 
         When updating an entry, updates its position to the front of the LRU list.
         If the entry is new and the cache is at capacity, removes the oldest entry
         before the new entry is added.
         """
         node = self.lookup[query]
         if node is not None:
             # Key exists in cache, update the value
             node.results = results
             self.linked_list.move_to_front(node)
         else:
             # Key does not exist in cache
             if self.size == self.MAX_SIZE:
                 # Remove the oldest entry from the linked list and lookup
                 self.lookup.pop(self.linked_list.tail.query, None)
                 self.linked_list.remove_from_tail()
             else:
                 self.size += 1
             # Add the new key and value
             new_node = Node(results)
             self.linked_list.append_to_front(new_node)
             self.lookup[query] = new_node
 ```
 
 %%%% Output: stream
 
     Overwriting lru_cache.py