#### Overview of this book

If you’re a Python developer who wants to discover how to take the power of functional programming (FP) and bring it into your own programs, then this book is essential for you, even if you know next to nothing about the paradigm. Starting with a general overview of functional concepts, you’ll explore common functional features such as first-class and higher-order functions, pure functions, and more. You’ll see how these are accomplished in Python 3.6 to give you the core foundations you’ll build upon. After that, you’ll discover common functional optimizations for Python to help your apps reach even higher speeds. You’ll learn FP concepts such as lazy evaluation using Python’s generator functions and expressions. Moving forward, you’ll learn to design and implement decorators to create composite functions. You'll also explore data preparation techniques and data exploration in depth, and see how the Python standard library fits the functional programming model. Finally, to top off your journey into the world of functional Python, you’ll at look at the PyMonad project and some larger examples to put everything into perspective.
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Understanding Functional Programming
Introducing Essential Functional Concepts
Functions, Iterators, and Generators
Working with Collections
Recursions and Reductions
The Itertools Module
More Itertools Techniques
The Functools Module
Decorator Design Techniques
Conditional Expressions and the Operator Module
A Functional Approach to Web Services
Optimizations and Improvements
Other Books You May Enjoy
Index

## Generating all combinations

The `itertools` module also supports computing all combinations of a set of values. When looking at combinations, the order doesn't matter, so there are far fewer combinations than permutations. The number of combinations is often stated as

. This is the number of ways that we can take combinations of `r` things at a time from a universe of `p` items overall.

For example, there are 2,598,960 five-card poker hands. We can actually enumerate all 2 million hands by executing the following command:

```hands = list(
combinations(tuple(product(range(13), '♠♥♦♣')), 5))```

More practically, assume we have a dataset with a number of variables. A common exploratory technique is to determine the correlation among all pairs of variables in a set of data. If there are v variables, then we will enumerate all variables that must be compared by executing the following command:

`combinations(range(v), 2)`

Let's get some sample data from http://www.tylervigen.com to show how this will work. We...