refactor(datastructures, lru-cache): refactor lru cache

datastructures/lfucache/README.md

@@ -1,3 +1,5 @@
+# LFU Cache
+
 Design and implement a data structure for a Least Frequently Used (LFU) cache.
 
 Implement the LFUCache class:

datastructures/lrucache/README.md

@@ -1,9 +1,67 @@
-Design an LRU cache
+# Design an LRU cache
+
+## Constraints and assumptions
 
-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
+    Yes
+
+## Solution
+
+A hash map alone gives us `O(1)` key-value lookup, but doesn't track order. An array tracks order, but inserting/removing
+from the middle is `O(n)`. We need a data structure that supports `O(1)` insertion, deletion, AND reordering. This
+points us toward a structure where we can move items to the front/back instantly. Think of a playlist where songs move
+to the top when played: - When you play a song (access), it jumps to position #1 - When you add a new song and the
+playlist is full, the song at the bottom (least recently played) gets removed - You need to find any song by name
+instantly (hash map), but also know which song is at the bottom (ordering) This dual requirement - fast lookup by key
+AND fast reordering - suggests combining two data structures: one for `O(1)` key access, another for `O(1)` position
+changes.
+
+### HashMap + Doubly Linked List hybrid
+
+When you need O(1) access AND O(1) ordering operations (move to front/back, remove),
+combine a hash map for lookups with a doubly linked list for order tracking. The hash map stores pointers to list nodes,
+enabling instant node location and manipulation.
+
+### Sentinel nodes eliminate edge cases
+
+Use dummy head and tail nodes in your doubly linked list to avoid null checks when adding/removing nodes at boundaries.
+This means every real node always has non-null prev/next pointers, simplifying insertion and deletion logic dramatically.
+
+### Access equals update pattern:
+
+In LRU cache, every get() operation must update recency by moving the accessed node to the most-recent position
+(typically the head or tail). Forgetting this is the most common bug - reads aren't passive in cache implementations.
+
+### Capacity check timing matters
+
+Always check capacity and evict after inserting the new element, not before. For updates (key exists), no eviction is
+needed. For new insertions at capacity, evict the LRU item, then add - this handles the edge case where capacity=1
+correctly.
+
+### Bidirectional pointer maintenance
+
+When manipulating doubly linked list nodes, always update four pointers in the correct order: the node's prev/next AND
+its neighbors' pointers. A common pattern is to extract a node (reconnect its neighbors), then insert it elsewhere
+(update new neighbors and the node itself).
+
+### Cache eviction policy abstraction
+
+This LRU pattern extends to LFU (Least Frequently Used), MRU (Most Recently Used), and TTL caches. The core insight -
+combining hash map for O(1) lookup with an auxiliary structure (list, heap, or multiple lists) for O(1) policy
+enforcement - applies broadly to cache replacement algorithms.
+
+## Complexity Analysis
+
+### Time Complexity
+
+O(1) Both get and put operations involve hash map lookup (O(1)), and linked list node 
+insertion/deletion/movement (O(1) with doubly linked list). No iteration through the cache is needed.
+
+### Space Complexity
+
+O(capacity) We store at most 'capacity' key-value pairs in the hash map, and the same number of nodes in the doubly
+linked list. Space grows linearly with capacity.

datastructures/lrucache/with_internal_linked_list.py

@@ -1,54 +1,51 @@
-class Node:
-    def __init__(self, key=0, data=0):
-        self.data = data
-        self.key = key
-        self.prev = None
-        self.next = None
-
+from typing import Dict, Optional, Any
+from datastructures.linked_lists.doubly_linked_list.node import DoubleNode
 
 class LRUCache:
     def __init__(self, capacity: int):
         self.capacity = capacity
-        self.lookup = {}
+        self.lookup: Dict[str | int, DoubleNode] = {}
         self.size = 0
-        self.head = Node()
-        self.tail = Node()
+        # Using sentinel head and tail nodes avoids null checks when adding/removing nodes at boundaries. This means
+        # every real node always has non-null prev/next pointers, simplifying insertion and deletion logic dramatically
+        self.head = DoubleNode(0)
+        self.tail = DoubleNode(0)
         self.head.next = self.tail
-        self.tail.prev = self.head
+        self.tail.previous = self.head
 
     @staticmethod
-    def __delete_node(node):
+    def __delete_node(node: DoubleNode):
         node.previous.next = node.next
         node.next.previous = node.previous
 
-    def __add_to_head(self, node):
+    def __add_to_head(self, node: DoubleNode):
         node.next = self.head.next
         node.next.previous = node
         node.previous = self.head
         self.head.next = node
 
-    def get(self, key: int) -> int:
+    def get(self, key: str | int) -> Optional[Any]:
         if key in self.lookup:
             node = self.lookup[key]
             data = node.data
             self.__delete_node(node)
             self.__add_to_head(node)
             return data
-        return -1
+        return None
 
-    def put(self, key: int, value: int) -> None:
+    def put(self, key: str | int, value: int) -> None:
         if key in self.lookup:
             node = self.lookup[key]
             node.data = value
             self.__delete_node(node)
             self.__add_to_head(node)
         else:
-            node = Node(key, value)
+            node = DoubleNode(key=key, data=value)
             self.lookup[key] = node
             if self.size < self.capacity:
                 self.size += 1
                 self.__add_to_head(node)
             else:
-                del self.lookup[self.tail.prev.key]
-                self.__delete_node(self.tail.prev)
+                del self.lookup[self.tail.previous.key]
+                self.__delete_node(self.tail.previous)
                 self.__add_to_head(node)