#### 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

# Asymptotic notation

To analyze the time complexity of an algorithm, the rate of growth (order of growth) is very important when the input size is large. When the input size becomes large, we only consider the higher-order terms and ignore the insignificant terms. In asymptotic analysis, we analyze the efficiency of algorithms for large input sizes considering the higher order of growth and ignoring the multiplicative constants and lower-order terms.

We compare two algorithms with respect to input size rather than the actual runtime and measure how the time taken increases with an increased input size. The algorithm which is more efficient asymptotically is generally considered a better algorithm as compared to the other algorithm. The following asymptotic notations are commonly used to calculate the running time complexity of an algorithm:

• θ notation: It denotes the worst-case running time complexity with a tight bound.
• Ο notation: It denotes the...