#### Overview of this book

Choosing the right data structure is pivotal to optimizing the performance and scalability of applications. This new edition of Hands-On Data Structures and Algorithms with Python will expand your understanding of key structures, including stacks, queues, and lists, and also show you how to apply priority queues and heaps in applications. You’ll learn how to analyze and compare Python algorithms, and understand which algorithms should be used for a problem based on running time and computational complexity. You will also become confident organizing your code in a manageable, consistent, and scalable way, which will boost your productivity as a Python developer. By the end of this Python book, you’ll be able to manipulate the most important data structures and algorithms to more efficiently store, organize, and access data in your applications.
Preface
Free Chapter
Python Data Types and Structures
Introduction to Algorithm Design
Algorithm Design Techniques and Strategies
Stacks and Queues
Trees
Heaps and Priority Queues
Hash Tables
Graphs and Algorithms
Searching
Sorting
Selection Algorithms
String Matching Algorithms
Other Books You May Enjoy
Index

# Heaps

A heap data structure is a specialization of a tree in which the nodes are ordered in a specific way. A heap is a data structure where each data elements satisfies a `heap` property, and the `heap` property states that there must be a certain relationship between a parent node and its child nodes. According to this certain relationship in the tree, the heaps can be of two types, in other words, `max` heaps and `min` heaps. In a `max` heap, each parent node value must always be greater than or equal to all its children. In this kind of tree, the `root` node must be the greatest value in the tree. For example, see Figure 7.1 showing the `max` heap in which all the nodes have greater values compared to their children:

Figure 7.1: An example of a max heap

In a `min` heap, the relationship between parent and children is that the value of the parent node must always be less than or equal to its children. This rule should be followed by all the nodes in the tree. In the `min` heap, the...