LRU cache design with hash map and doubly linked list in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the role of the hash map in LRU cache

In an LRU cache implemented with a hash map and a doubly linked list, what is the primary purpose of the hash map?

A To store the order of usage of cache items

B To provide fast access to cache items by key

C To remove the least recently used item from the cache

D To maintain the size limit of the cache

💡 Hint

Think about how you find an item quickly by its key.

The hash map allows quick lookup of cache items by their keys, enabling O(1) access time. The doubly linked list manages the order of usage.

🧠 Conceptual

intermediate

Purpose of the doubly linked list in LRU cache

Why is a doubly linked list used in an LRU cache alongside a hash map?

A To quickly find cache items by key

B To store the cache items in sorted order by key

C To maintain the order of items from most to least recently used

D To limit the cache size automatically

💡 Hint

Consider how the cache knows which item to remove when full.

The doubly linked list keeps track of the usage order, allowing quick updates when items are accessed or removed, supporting O(1) insertion and deletion.

🔍 Analysis

advanced

Effect of accessing a cache item on the doubly linked list

In an LRU cache, when a cache item is accessed, what change happens to the doubly linked list?

A The accessed item is moved to the front of the list

B The accessed item is moved to the end of the list

C The accessed item is removed from the list

D No change happens to the list

💡 Hint

Think about which item should be considered most recently used after access.

Accessing an item updates its usage status, so it is moved to the front of the doubly linked list to mark it as most recently used.

❓ Reasoning

advanced

Why does the LRU cache remove the tail node when full?

When the LRU cache reaches its capacity and needs to add a new item, why is the tail node of the doubly linked list removed?

A Because the tail node is the least recently used item

B Because the tail node is the most recently used item

C Because the tail node is the largest key value

D Because the tail node is the oldest inserted item regardless of usage

💡 Hint

Consider which item should be discarded to make space.

The tail node represents the least recently used item, so removing it frees space for new items while preserving the most recently used ones.

❓ Comparison

expert

Comparing time complexities of operations in LRU cache

Which statement correctly compares the time complexities of the main operations (get and put) in an LRU cache implemented with a hash map and doubly linked list?

A Get runs in O(n) time, but put runs in O(1) time

B Get runs in O(1) time, but put runs in O(n) time due to list updates

C Both get and put operations run in O(n) time because of list traversal

D Both get and put operations run in O(1) time due to hash map and linked list usage

💡 Hint

Think about how the hash map and doubly linked list work together to optimize operations.

The hash map provides O(1) access to nodes, and the doubly linked list allows O(1) insertion and deletion, so both get and put run in constant time.

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