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Design Circular Queue

Expert Answer & Key Takeaways

# System & Data Structure Design Design problems in DSA interviews test your ability to translate requirements into a functional, efficient, and maintainable class structure. Unlike standard algorithmic problems, the focus here is on State Management and API Design. ### Core Principles 1. Encapsulation: Keep data private and expose functionality through well-defined methods. 2. Trade-offs: Every design choice has a cost. Is it better to have O(1)O(1) read and O(N)O(N) write, or vice versa? 3. State Consistency: Ensure that your internal data structures (e.g., a Map and a List) stay in sync after every operation. ### Common Design Patterns #### 1. HashMap + Doubly Linked List (DLL) The "Gold Standard" for O(1)O(1) caching (LRU/LFU). ```text [Head] <-> [Node A] <-> [Node B] <-> [Node C] <-> [Tail] ^ ^ ^ ^ ^ (MRU) (Data) (Data) (Data) (LRU) ``` - HashMap: Provides O(1)O(1) lookups for keys to their corresponding nodes. - DLL: Provides O(1)O(1) addition/removal of nodes at both ends, maintaining the order of access. #### 2. Amortized Analysis (Rebalancing) Commonly used in Queue using Stacks or Dynamic Arrays. - Instead of doing heavy work on every call, we batch it. Pushing to a stack is O(1)O(1), and "flipping" elements to another stack happens only when necessary, averaging O(1)O(1) per operation. #### 3. Ring Buffers (Circular Arrays) Used for fixed-size memory management (e.g., Circular Queue, Hit Counter). ```text [0] [1] [2] [3] [4] [5] ^ ^ ^ Head (Data) Tail (Pops) (Next Push) ``` - Use `(index + 1) % capacity` to wrap around the array. #### 4. Concurrency & Thread Safety For "Hard" design problems (e.g., Bounded Blocking Queue). - Use Mutexes (Locks) to prevent data races. - Use Condition Variables (`wait`/`notify`) to manage producer-consumer logic efficiently without busy-waiting. ### How to Approach a Design Problem 1. Identify the API: What methods do you need to implement? (`get`, `put`, `push`, etc.) 2. Define the State: What variables represent the current state? (Size, Capacity, Pointers). 3. Choose the Data Structures: Select the combination that minimizes time complexity for the most frequent operations. 4. Dry Run: Trace the state changes through a sequence of operations based on your chosen structure.

Design Circular Queue

Design your implementation of the circular queue. The circular queue is a linear data structure in which the operations are performed based on FIFO (First In First Out) principle and the last position is connected back to the first position to make a circle.
Medium
Approach 1

Level I: Array with Front/Rear Pointers

Intuition

Use a fixed-size array and two pointers, head and tail. Use modulo arithmetic to wrap around the array. We use a size variable to easily distinguish between empty and full states.
⏱ O(1) for all ops.💾 O(N).

Detailed Dry Run

Enqueue(1), Enqueue(2), Dequeue()...
OpArrayHeadTailSize
init(3)[0,0,0]0-10
enq(1)[1,0,0]001
enq(2)[1,2,0]012
deq()[1,2,0]111
java
class MyCircularQueue {
    private int[] q; private int head, tail, size, k;
    public MyCircularQueue(int k) { this.k = k; q = new int[k]; head = 0; tail = -1; size = 0; }
    public boolean enQueue(int val) {
        if (isFull()) return false;
        tail = (tail + 1) % k; q[tail] = val; size++; return true;
    }
    public boolean deQueue() {
        if (isEmpty()) return false;
        head = (head + 1) % k; size--; return true;
    }
    public int Front() { return isEmpty() ? -1 : q[head]; }
    public int Rear() { return isEmpty() ? -1 : q[tail]; }
    public boolean isEmpty() { return size == 0; }
    public boolean isFull() { return size == k; }
}
Approach 2

Level II: Linked List Implementation

Intuition

Instead of an array, use a Doubly Linked List. This avoids modulo arithmetic but uses more memory for pointers. To make it 'circular' in memory, we can limit the number of nodes to k.
⏱ O(1) all ops.💾 O(k) where k is max size.

Detailed Dry Run

Head -> [1] <-> [2] <-> [3] <- Tail Enqueue(4) if size < k: Add new node after tail, move tail.
java
class MyCircularQueue {
    class Node { int val; Node next; Node(int v) { val = v; } }
    Node head, tail; int count, capacity;
    public MyCircularQueue(int k) { capacity = k; }
    public boolean enQueue(int value) {
        if (isFull()) return false;
        Node newNode = new Node(value);
        if (isEmpty()) head = tail = newNode;
        else { tail.next = newNode; tail = newNode; }
        count++; return true;
    }
    public boolean deQueue() {
        if (isEmpty()) return false;
        head = head.next; count--; return true;
    }
    public int Front() { return isEmpty() ? -1 : head.val; }
    public int Rear() { return isEmpty() ? -1 : tail.val; }
    public boolean isEmpty() { return count == 0; }
    public boolean isFull() { return count == capacity; }
}

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