How to Solve Design Front Middle Back Queue

This problem requires designing a FrontMiddleBackQueue class that supports inserting and removing elements from the front, middle, and back efficiently. Correct handling of middle positions, especially when there are two choices, is key. Using linked-list pointer manipulation or a dual-array approach ensures operations maintain expected ordering and performance.

Problem Statement

Design a queue that allows adding and removing elements from three positions: the front, the middle, and the back. Implement a FrontMiddleBackQueue class with methods to pushFront, pushMiddle, pushBack, popFront, popMiddle, and popBack. When the queue has two middle choices, always operate on the frontmost middle.

For example, performing pushMiddle or popMiddle must correctly identify the frontmost middle index in cases of even length. You must ensure all operations maintain correct element ordering and handle empty states properly. Optimize for clarity and pointer manipulation, as naive indexing may fail in middle operations.

Examples

Example 1

Input: ["FrontMiddleBackQueue", "pushFront", "pushBack", "pushMiddle", "pushMiddle", "popFront", "popMiddle", "popMiddle", "popBack", "popFront"] [[], [1], [2], [3], [4], [], [], [], [], []]

Output: [null, null, null, null, null, 1, 3, 4, 2, -1]

FrontMiddleBackQueue q = new FrontMiddleBackQueue(); q.pushFront(1); // [1] q.pushBack(2); // [1, 2] q.pushMiddle(3); // [1, 3, 2] q.pushMiddle(4); // [1, 4, 3, 2] q.popFront(); // return 1 -> [4, 3, 2] q.popMiddle(); // return 3 -> [4, 2] q.popMiddle(); // return 4 -> [2] q.popBack(); // return 2 -> [] q.popFront(); // return -1 -> [] (The queue is empty)

Constraints

• 1 <= val <= 109
• At most 1000 calls will be made to pushFront, pushMiddle, pushBack, popFront, popMiddle, and popBack.

Solution Approach

Use a Linked List with Pointers

Maintain a doubly linked list to track elements, keeping pointers to the head, tail, and middle. Update the middle pointer whenever an element is added or removed to ensure middle operations access the correct node. This approach emphasizes pointer manipulation and avoids array shifting overhead.

Dual-Deque Approach

Split the queue into two deques representing the front and back halves. Maintain balance such that the front deque always contains the frontmost half of elements. Middle insertions and removals then correspond to pushing or popping from the end of the front deque, simulating pointer-based middle access efficiently.

Array-Based Brute Force

For low operation constraints, a single array can be used. Perform pushFront, pushMiddle, pushBack, popFront, popMiddle, and popBack via array inserts and removals. Be careful with middle index calculation to always select the frontmost middle. This approach is simple but emphasizes failure modes if middle positions are miscalculated.

Complexity Analysis

Time and space depend on the implementation. A naive array-based solution has O(n) per middle operation due to shifting, while linked list or dual-deque approaches achieve O(1) amortized operations. Space is O(n) for storing all elements.

What Interviewers Usually Probe

• Pay attention to correctly identifying the frontmost middle for even-length queues.
• Emphasize pointer updates and balancing after each operation.
• Check boundary cases where the queue becomes empty or has only one element.

Common Pitfalls or Variants

Common pitfalls

• Misidentifying the frontmost middle during pushMiddle or popMiddle.
• Forgetting to update the middle pointer after front or back operations.
• Assuming array indices map directly to middle positions without adjustments.

Follow-up variants

• Implement a FrontBackQueue supporting only front and back operations for simplified pointer management.
• Support multiple middle operations in batch and analyze pointer consistency under bulk updates.
• Extend to a priority FrontMiddleBackQueue where elements have weights affecting their middle placement.

How GhostInterview Helps

• Automatically computes correct middle positions, preventing common index miscalculations.
• Guides pointer updates and deque balancing for reliable front, middle, and back operations.
• Highlights failure modes in naive array or pointer approaches, ensuring robust solution strategies.

Topic Pages

• Array
• Linked List
• Design
• Queue
• Data Stream

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FAQ

What is the best way to handle the middle element in Design Front Middle Back Queue?

Track a middle pointer or maintain two balanced deques so that pushMiddle and popMiddle always operate on the frontmost middle node.

Can I solve this problem using only arrays?

Yes, for small constraints a single array works, but you must handle middle index carefully to avoid off-by-one errors and inefficient shifts.

Why is pointer manipulation important in this problem?

Pointer manipulation allows O(1) insertion and removal at middle positions, preventing costly array shifts and maintaining element order.

How do I maintain the correct middle after popFront or popBack?

Update the middle pointer according to the queue size after every operation, moving it forward or backward based on even or odd length changes.

Is there a dual-deque solution for Design Front Middle Back Queue?

Yes, splitting the queue into front and back halves allows efficient middle operations by treating the front deque's end as the middle, balancing after each insertion or removal.