LearnViz CompSci
Home / Learn / Data Structures / Heaps

Intermediate Topic 22 of 52 Data Structures

Heaps

Complete trees satisfying a parent-versus-child ordering property.

How it works

A heap is a complete binary tree in which each parent is ordered with respect to its children: in a max-heap it is at least as large as both, in a min-heap at most. The root is therefore always the extreme element. Because it is complete, it is stored compactly in an array, with children of index i at 2i+1 and 2i+2, and the root is readable in O(1).

Where it is used

Priority queues, heapsort, finding the k smallest or largest elements, merging sorted streams, Dijkstra's algorithm and memory allocators use heaps. Heaps are not related to the program heap memory.

Common pitfall

A heap is only partially ordered, so it cannot search for arbitrary keys quickly or iterate in sorted order. Off-by-one errors in index arithmetic are common between zero-based and one-based layouts. Building from n items with the bottom-up method is O(n), faster than n separate inserts.

Where it fits in the course

Heaps is topic 22 of 52 in Data Structures, rated Intermediate. It follows B+ Trees. The next topic is Binary Heap Operations.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Data Structures quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Heaps?
Complete trees satisfying a parent-versus-child ordering property. It belongs to Data Structures and is an intermediate-level topic.
Where do people use Heaps?
Priority queues, heapsort, finding the k smallest or largest elements, merging sorted streams, Dijkstra's algorithm and memory allocators use heaps.
What is the most common mistake with Heaps?
A heap is only partially ordered, so it cannot search for arbitrary keys quickly or iterate in sorted order.
What should I learn before this topic?
Start with B+ Trees, the topic just before it in Data Structures.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Data Structures quiz. You can also explore Binary Search Tree in the Visual Lab.
Is Heaps hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Heaps?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Heaps?
B+ Trees, Binary Heap Operations, B-Trees are closely connected. The full list is in the related topics section of this page.
What should I study after Heaps?
Continue with Binary Heap Operations, the next topic in Data Structures.

Related topics