Design Circular Queue (LC 622)

What does it solve?

Implement a queue on a fixed-size array without shifting elements. When the tail reaches the end it wraps around to reuse freed slots at the front, forming a ring.

Key insight: keep a head index (front), a count of items, and capacity k. Enqueue writes at (head + count) % k; dequeue advances head = (head + 1) % k. The modulo is what makes it circular. Empty when count = 0, full when count = k. All ops are O(1).

The core idea

enqueue(x): if full → false
buf[(head+count)%k] = x; count++
dequeue(): if empty → false
head = (head+1)%k; count--
// full: count==k · empty: count==0

Complexity

All operations

O(1)

enqueue, dequeue, front, rear, isEmpty, isFull are all constant time. No element ever moves.

Space complexity

O(k)

One fixed array of capacity k, reused indefinitely as items cycle through.

Scenarios

Live animation — head & tail wrap with modulo

filled slot head (front) tail (next write) dequeued / rejected

Ring buffer (arranged in a circle to show the wrap)

Same array, laid out linearly (index 0 → k−1)

Press Play to run the scenario…

Current op detail

head = — tail = — count = — state = —

Step — of —

head index

—

front slot

tail index

—

(head+count)%k

count

—

of k

last op

—

result

Select a scenario and press Play to start.

✓ Done

SpeedMedium

Step-by-step table

Step	op	arg	head	tail	count	result

C++ implementation

circular_queue.cpp

class MyCircularQueue {
    vector<int> buf;
    int head = 0, cnt = 0, k;
public:
    MyCircularQueue(int k) : buf(k), k(k) {}

    bool enQueue(int x) {
        if (cnt == k) return false;      // full
        buf[(head + cnt) % k] = x;         // wrap with modulo
        cnt++;
        return true;
    }
    bool deQueue() {
        if (cnt == 0) return false;      // empty
        head = (head + 1) % k;             // advance front
        cnt--;
        return true;
    }
    int  Front() { return cnt == 0 ? -1 : buf[head]; }
    int  Rear()  { return cnt == 0 ? -1 : buf[(head + cnt - 1) % k]; }
    bool isEmpty() { return cnt == 0; }
    bool isFull()  { return cnt == k; }
};

My Notes

📝Notes✅

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