Heap vs. priority queues

Heap and priority queues are both data structures that are used to manage elements with some priority. They are useful when elements require some priority to perform any kind of operation, including insertion, deletion, etc.

Heap

A heap is a tree-based data structure that satisfies the following properties:

• Heap must be a complete binary tree.

• The nodes must be ordered according to the heap order.

There are two kinds of heap orders: min-heap and max-heap. Let’s discuss them below:

• Min-heap: In a min-heap, a parent node key is less than or equal to their child node keys. The root node key will be the smallest element in a min-heap.

• Max-heap: In a max-heap, a parent node key is greater than or equal to their child node keys. The root node key will be the largest element in a min-heap.

Heaps are commonly implemented using arrays, where we can find the parent-child relationship easily. For example, if the root node is at index 0, then its left and right children are at index 1 and 2, respectively.

Benefits of using a heap

A heap comes up with many benefits. Here are some of them:

• Heap provides an efficient way of finding the minimum or maximum elements in $O(1)$ time complexity.

• A heap can be used for sorting or merging sort lists.

• The array-based implementation of the heap is quite simple.

Limitations of using a heap

Let’s discuss some limitations of using a heap:

• The heap is not suitable for quick search, update, or delete operations.

• The time complexity of finding an element in the heap is $O(n)$.

Priority queue

A priority queue is a type of queue data structure that arranges the elements in a queue with some priority. Whenever we perform a dequeue operation, it returns the element based on the priority. There are two kinds of priority queues:

• Min priority queue: A min priority queue is a type of priority queue in which the element with the lowest priority is dequeued first.

• Max priority queue: A min priority queue is a type of priority queue in which the element with the highest priority is dequeued first.

Priority queues can be implemented using various data structures: heap, array, queue, etc.

Benefits of using a priority queue

A priority queue offers many benefits. Here are some of them:

• A priority queue can be used to implement a priority-based selection algorithm.

• Tasks such as scheduling or routing packets can be implemented using a priority queue.

• We can also implement algorithms such as Dijkstra’s or Huffman’s using priority queues.

Limitations of using a priority queue

Let’s discuss some limitations of using a priority queue:

• The implementation of a priority queue requires an understanding of the underlying data structure.

• The time complexity of finding an element in the priority queue is $O(n)$.

Heap vs. priority queue

Heaps are designed for efficient insertion and extraction of the minimum and maximum elements, while priority queues manage the elements based on their priority. Besides their difference, we can relate the heap and a priority queue. We can implement a priority using a heap by storing the elements as nodes of the heap and the priorities to determine the heap priority. Using this method, we can insert and remove elements in $O(\log n)$ time complexity.

Use cases

Before selecting the right data structure, it’s important to consider the data type, data size, required operations, and functions. Let’s discuss where each data structure is preferable to the other.

Heap

A heap can be utilized over a priority queue in the following situations:

• Heaps are memory-efficient because they are implemented using an array. It can be used where memory usage is a concern.

• A heap is a good choice if we need an efficient way to find the minimum or maximum values of a dataset.

• We can use two heaps to maintain the median of a dynamically changing dataset: the max-heap to store the lower half of the data and the min-heap to store the upper half.

• We can utilize the heap for sorting or merging data in ascending or descending order, such as heap sort.

Priority queue

A priority queue is more suitable over a heap in the following scenarios:

• A priority queue is a better choice if we want to prioritize and process data based on some criteria, such as, task scheduling or event-driven simulations.

• In the implementation of Dijkstra’s algorithm, we can utilize the priority queue to find the shortest path in the graph and select the next node with the smallest tentative distance.

• We can use a priority queue to build a Huffman tree for optimal prefix coding, where characters with lower frequencies have higher priorities.

Comparison

Let’s draw a comparison between the heap and the priority queue.

Conclusion

In this Answer, we’ve explored the heap and priority queue along with their benefits, limitations, and use cases. The heap is designed to return the maximum or minimum value, while the priority queue provides the element with the highest or lowest priority. Heap is memory efficient, and it could be a better choice for memory usage concerns. The priority queue is a better choice for priority-based applications. Understanding the strengths and limitations of both allows for selecting the right data structure for the right problem, leading to more efficient and effective solutions.