LRU cache design with hash map and doubly linked list in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does LRU stand for in LRU cache?

LRU stands for Least Recently Used. It is a cache eviction policy that removes the least recently accessed item when the cache is full.

beginner

Why is a hash map used in an LRU cache design?

A hash map provides fast access to cache items by their keys, allowing O(1) average time complexity for lookups.

intermediate

What role does a doubly linked list play in an LRU cache?

The doubly linked list keeps track of the order of item usage. The most recently used item is moved to the front, and the least recently used item is at the end, enabling quick removal.

intermediate

How do the hash map and doubly linked list work together in an LRU cache?

The hash map stores keys and pointers to nodes in the doubly linked list. This allows quick access and updates of the usage order when items are accessed or added.

beginner

What happens when the LRU cache reaches its capacity and a new item is added?

The least recently used item (at the end of the doubly linked list) is removed from both the list and the hash map to make space for the new item, which is added to the front.

What is the main purpose of using a doubly linked list in an LRU cache?

A To track the order of item usage for quick eviction

B To store cache keys in sorted order

C To speed up hash map lookups

D To reduce memory usage

The doubly linked list tracks the order of usage, allowing quick updates when items are accessed or evicted.

Which data structure provides O(1) average time complexity for key lookups in an LRU cache?

A Hash map

B Doubly linked list

C Array

D Stack

A hash map allows fast key lookups, which is essential for efficient cache access.

When an item is accessed in an LRU cache, what happens to its position in the doubly linked list?

A It stays in the same place

B It moves to the front

C It moves to the end

D It is removed

Accessed items are moved to the front to mark them as most recently used.

What is removed from the cache when it reaches capacity and a new item is added?

A Most recently used item

B Random item

C All items

D Least recently used item

The least recently used item is removed to make space for the new item.

Which two data structures are combined to implement an efficient LRU cache?

A Array and linked list

B Stack and queue

C Hash map and doubly linked list

D Binary tree and hash map

A hash map and doubly linked list together provide fast access and efficient order tracking.

Explain how a hash map and a doubly linked list work together to implement an LRU cache.

Think about fast access and order management.

Describe the process that happens when the LRU cache is full and a new item needs to be added.

Focus on eviction and insertion steps.

Practice

1. What is the main purpose of using a doubly linked list in an LRU cache design?

easy

A. To hash keys for constant time access

B. To store key-value pairs for fast lookup

C. To sort items by their values

D. To keep track of the order of item usage for quick updates

Solution

1. Step 1: Understand the role of doubly linked list in LRU cache

   The doubly linked list maintains the order of items from most recently used to least recently used.

2. Step 2: Explain why order tracking is important

   This order allows quick removal of the least recently used item when the cache is full.

3. Final Answer:

   To keep track of the order of item usage for quick updates -> Option D

4. Quick Check:

   Doubly linked list = usage order tracking [OK]

Hint: Doubly linked list tracks usage order in LRU cache [OK]

Common Mistakes:

• Confusing hash map role with doubly linked list
• Thinking doubly linked list stores key-value pairs
• Assuming it sorts items by value

2. Which of the following correctly describes the time complexity of the get operation in an LRU cache implemented with a hash map and doubly linked list?

easy

A. O(n), where n is the number of items in the cache

B. O(1), constant time

C. O(log n), due to sorting

D. O(n^2), because of list traversal

Solution

1. Step 1: Analyze the get operation components

   The hash map provides direct access to the node in constant time.

2. Step 2: Consider the doubly linked list update

   Moving the accessed node to the front is done in constant time using pointers.

3. Final Answer:

   O(1), constant time -> Option B

4. Quick Check:

   Hash map + doubly linked list = O(1) get [OK]

Hint: Hash map lookup + list update = O(1) get [OK]

Common Mistakes:

• Assuming list traversal causes O(n) time
• Confusing sorting with LRU operations
• Thinking get requires scanning all items

3. Consider an LRU cache with capacity 2. After these operations: put(1, 1), put(2, 2), get(1), put(3, 3), what will get(2) return?

medium

A. 2

B. 1

C. -1

D. 3

Solution

1. Step 1: Track cache state after each operation

   After put(1,1) and put(2,2), cache has keys 1 and 2. get(1) makes key 1 most recently used.

2. Step 2: Insert put(3,3) and evict least recently used

   Key 2 is least recently used and gets evicted. Cache now has keys 1 and 3.

3. Step 3: Check get(2) result

   Key 2 was evicted, so get(2) returns -1.

4. Final Answer:

   -1 -> Option C

5. Quick Check:

   Evicted key 2, so get(2) = -1 [OK]

Hint: Evicted least used key returns -1 on get [OK]

Common Mistakes:

• Forgetting eviction after capacity reached
• Assuming get updates usage but doesn't evict
• Returning wrong value for evicted key

4. In an LRU cache implementation, a developer notices that the cache never evicts any items even after exceeding capacity. What is the most likely cause?

medium

A. The eviction logic is missing or not triggered when capacity is exceeded

B. The doubly linked list is not updated to move recently used items to front

C. The hash map is not updated when items are accessed

D. The cache capacity is set to zero

Solution

1. Step 1: Understand eviction role in LRU cache

   Eviction removes the least recently used item when capacity is exceeded.

2. Step 2: Identify why eviction might not happen

   If eviction logic is missing or not triggered, items will never be removed despite capacity limits.

3. Final Answer:

   The eviction logic is missing or not triggered when capacity is exceeded -> Option A

4. Quick Check:

   Missing eviction = no item removal [OK]

Hint: Eviction missing means cache never removes items [OK]

Common Mistakes:

• Blaming hash map updates for eviction issues
• Ignoring eviction step in put operation
• Assuming capacity zero means no eviction

5. You want to extend an LRU cache to also support a peekLeastUsed() operation that returns the least recently used key without removing it. Which data structure property allows this operation to be efficient?

hard

A. The tail pointer of the doubly linked list points to the least recently used item

B. The hash map stores keys in sorted order

C. The doubly linked list is singly linked for fast traversal

D. The cache uses a priority queue to track usage

Solution

1. Step 1: Identify how least recently used item is tracked

   The doubly linked list keeps most recently used at head and least recently used at tail.

2. Step 2: Explain how to access least used without removal

   Using the tail pointer, we can directly access the least recently used key efficiently.

3. Final Answer:

   The tail pointer of the doubly linked list points to the least recently used item -> Option A

4. Quick Check:

   Tail pointer = least recently used access [OK]

Hint: Tail of doubly linked list = least recently used key [OK]

Common Mistakes:

• Assuming hash map stores sorted keys
• Thinking singly linked list is used
• Confusing priority queue with LRU structure