**Which Data Structure Is Used for Priority Queue?**

A priority queue is a data structure that allows elements to be inserted with an associated priority and retrieved according to their priority. It differs from a regular queue, where elements are retrieved in the order they were added. In a priority queue, the element with the highest priority is always at the front of the queue.

## Binary Heap

The most common data structure used for implementing a priority queue is a binary heap. A binary heap is a complete binary tree where every node satisfies the heap property. The heap property states that for any given node X, the key in X is greater than or equal to the keys in its children.

### Max Heap

In a max heap, the key of each node is greater than or equal to the keys of its children. This means that the element with the highest priority will always be at the root of the tree. When an element is inserted into a max heap, it is placed at the next available position and then “bubbled up” until it satisfies the heap property again.

### Min Heap

In a min heap, the key of each node is less than or equal to the keys of its children. This means that the element with the lowest priority will always be at the root of the tree. Similar to a max heap, when an element is inserted into a min heap, it is placed at the next available position and then “bubbled up” until it satisfies the heap property again.

## Implementation Details

A binary heap can be implemented using an array or a linked list. However, using an array has several advantages in terms of memory efficiency and access time. By storing elements in an array, we can easily calculate the parent and child indices of a node using simple arithmetic operations.

When implementing a binary heap as a priority queue, we typically use an array where the first element (index 0) is unused. This allows us to perform simple calculations for accessing parent and child nodes without the need for additional checks.

## Conclusion

In conclusion, the most commonly used data structure for implementing a priority queue is a binary heap. The binary heap can be either a max heap or a min heap, depending on whether we want the element with the highest or lowest priority at the front of the queue. The binary heap can be efficiently implemented using an array, making it an ideal choice for priority queue implementations.