#### 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
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Index

# Composing complexity classes

Normally, we need to find the total running time of complex operations and algorithms. It turns out that we can combine the complexity classes of simple operations to find the complexity class of more complex, combined operations. The goal is to analyze the combined statements in a function or method to understand the total time complexity of executing several operations. The simplest way to combine two complexity classes is to add them. This occurs when we have two sequential operations. For example, consider the two operations of inserting an element into a list and then sorting that list. Assuming that inserting an item occurs in O(n) time, and sorting in O(nlogn) time, then we can write the total time complexity as O(n + nlogn); that is, we bring the two functions inside the O(…), as per Big O computation. Considering only the highest-order term, the final worst-case complexity becomes O(nlogn).

If we repeat an operation, for example in...