As a programmer, you've most likely come across the terms “heap” and “stack.” It's a widespread practice for beginners to use these two terms interchangeably and incorrectly.
While students of a Data Structures course and experienced programmers will distinguish between these two data structures easily, they can seem the same to others.
Programmers need to differentiate between the two and use them appropriately in practical programming situations. Interviewers are often keen on giving applicants a scenario and then asking for the most appropriate data structure.
Read on as we take a detailed look at heaps, stacks, their differences, and relevant applications.
What Is a Heap?
A heap for programmers is typically a special tree data structure often called a "priority queue". Heaps that are a completely balanced binary tree structure (recall that all levels of a complete binary tree are filled except the last level) and follow a heap property are called Binary Heaps.
The heap property structures the tree in a manner that places the maximum or the minimum value at the root.
In a Max Heap, the value of the parent nodes is greater than the child nodes, and the root of the tree contains the maximum value. Alternatively, a Min Heap is structured to have the minimum value as the root, and each child node has a greater value than its parent. The heap property must be recursively true for every node in the binary tree.
Heaps are generally implemented through linear arrays, with the first element of the array (Arr) representing the root. For a specific node i, you can retrieve the child nodes at Arr[ (2*i) + 1 ] and Arr[ (2*i) + 2], similarly the parent node is located at the Arr[ (i-1)/2 ] index. Most languages such as Java and C++ contain libraries that provide users with ready-to-use min and max heaps.
What Is a Stack?
Stacks are one of the first data structures taught to students, and they should not be overlooked. A stack is a data structure that behaves like any real-life stack (cards, plates, etc.). Stacks allow operations only on one end, and as a result, they have a LIFO (Last-In-First-Out) characteristic. In contrast, queues have a FIFO (First-In-First-Out) characteristic and allow operations on both ends.
Typical stack operations consist of push (inserting data into the top of the stack) and pop (removing the topmost data element). You can implement stacks through pointers, arrays, or even linked lists, depending on your requirements. C++, C#, and Java all contain libraries that have already implemented a stack, so you can use them whenever you need.
Heaps vs. Stacks
If you’ve read this far, you have a pretty good idea of the differences between a stack and a heap. Stacks are linear and have a LIFO characteristic, whereas heaps have a tree structure and follow the heap property. They both have different applications that we'll discuss in the next section.
In terms of an asymptotic time complexity analysis, you can build a binary heap in O(n) and extract the minimum or maximum value in O(1). Insertions and deletions can be achieved in O(log N) time. In contrast, insertion and deletion take O(1) time in a stack.
For the reasons discussed above, heaps are very efficient when used as a priority queue. Graph algorithms such as Prim’s Minimum Spanning Tree and Dijkstra's Shortest Path typically utilize heaps as the priority queue. Another important application of heaps is to sort an array efficiently in just O(N logN) time; this sorting technique is known as "Heap Sort".
Stacks, too, have a variety of critical applications such as memory management and expression evaluation. If you face a backtracking coding problem, it might be a good idea to save the day using a stack.
Prioritize Data Structures
Every successful programmer will tell you the importance of becoming proficient with data structures. It's a great idea to try to understand and get comfortable using different data structures as and when required since it's a vital concept for every programmer out there.