> For the complete documentation index, see [llms.txt](https://kseb0.gitbook.io/whiteboard/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://kseb0.gitbook.io/whiteboard/arrays-and-strings/design-a-circular-queue.md).

# Design a Circular Queue

### Approach1: Array

Based on the description of the problem, an intuitive data structure that meets all the requirements would be a **ring** where the head and the tail are adjacent to each other. 

Since there does not exist such data structure, we will use an array to simulate such behavior. I've also inserted a pictorial representation in the below.

#### Visual:

As seen in the below example, the below circular Queue is of a maximum capacity of 4. 

Since we follow the FIFO properties in a Queue, Index 0 is empty due to a Deque operation being called. 

The maximum capacity is 4 however it's current size is 3. In order to take advantage of the empty space, we need to access the first index. 

**Since we insert at the rear in a Queue**, we use the below formula to access the 0th index.

`Enque: (Rear + 1) % capacity` 

Since we dequeue from the front in a Queue 

`Deque: (Front + 1) % capacity`

![](/files/-Mg2mxBYbtKRrDoPGp8j)

```python
class MyCircularQueue:

     def __init__(self, k: int):
        self.capacity = k 
        self.size = 0
        self.t = [0] * self.capacity 
        self.front, self.rear = 0, -1

     def enQueue(self, value: int) -> bool:
        if self.isFull(): return False
        
        self.rear = (self.rear + 1) % self.capacity 
        self.t[self.rear] = value
        self.size += 1
        return True

     def deQueue(self) -> bool:
        if self.isEmpty(): return False
        
        self.front = (self.front + 1) % self.capacity
        self.size -= 1
        return True

     def Front(self) -> int:
        if self.isEmpty(): return -1
        
        return self.t[self.front]

     def Rear(self) -> int:
        if self.isEmpty(): return -1
        
        return self.t[self.rear]

     def isEmpty(self) -> bool:

        return self.size == 0

     def isFull(self) -> bool:
        return self.size == self.capacity 

```

### Approach2: Linked List

![](/files/-Mg2nLhMIN_nmCGvi2Rs)

```python
class ListNode:

    def __init__(self, value=-1, next=None):
        self.value =value
        self.next = next

class MyCircularQueue:

     def __init__(self, k: int):
        self.head = self.tail = None
        self.size = 0
        self.k = k

     def enQueue(self, value: int) -> bool:

        if self.isFull(): return False
        
        node = ListNode(value)
        if self.size == 0:
            self.head = self.tail = node
        else:
            self.tail.next = node
            self.tail = node
            
        self.size += 1
        return True

     def deQueue(self) -> bool:

        if self.isEmpty(): return False
        
        self.head = self.head.next
        self.size -= 1
        return True
        
     def Front(self) -> int:
        return -1 if self.isEmpty() else self.head.value

     def Rear(self) -> int:
        return -1 if self.isEmpty() else self.tail.value

     def isEmpty(self) -> bool:
        return self.size == 0

     def isFull(self) -> bool:
        return self.size == self.k
```


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