Real Python: Recursion in Python: An Introduction

If you’re familiar with functions in Python, then you know that it’s quite common for one function to call another. In Python, it’s also possible for a function to call itself! A function that calls itself is said to be recursive, and the technique of employing a recursive function is called recursion.

It may seem peculiar for a function to call itself, but many types of programming problems are best expressed recursively. When you bump up against such a problem, recursion is an indispensable tool for you to have in your toolkit.

By the end of this tutorial, you’ll understand:

• What it means for a function to call itself recursively
• How the design of Python functions supports recursion
• What factors to consider when choosing whether or not to solve a problem recursively
• How to implement a recursive function in Python

Then you’ll study several Python programming problems that use recursion and contrast the recursive solution with a comparable non-recursive one.

What Is Recursion?

The word recursion comes from the Latin word recurrere, meaning to run or hasten back, return, revert, or recur. Here are some online definitions of recursion:

• Dictionary.com: The act or process of returning or running back
• Wiktionary: The act of defining an object (usually a function) in terms of that object itself
• The Free Dictionary: A method of defining a sequence of objects, such as an expression, function, or set, where some number of initial objects are given and each successive object is defined in terms of the preceding objects

A recursive definition is one in which the defined term appears in the definition itself. Self-referential situations often crop up in real life, even if they aren’t immediately recognizable as such. For example, suppose you wanted to describe the set of people that make up your ancestors. You could describe them this way:

Notice how the concept that is being defined, ancestors, shows up in its own definition. This is a recursive definition.

In programming, recursion has a very precise meaning. It refers to a coding technique in which a function calls itself.

Why Use Recursion?

Most programming problems are solvable without recursion. So, strictly speaking, recursion usually isn’t necessary.

However, some situations particularly lend themselves to a self-referential definition—for example, the definition of ancestors shown above. If you were devising an algorithm to handle such a case programmatically, a recursive solution would likely be cleaner and more concise.

Traversal of tree-like data structures is another good example. Because these are nested structures, they readily fit a recursive definition. A non-recursive algorithm to walk through a nested structure is likely to be somewhat clunky, while a recursive solution will be relatively elegant. An example of this appears later in this tutorial.

On the other hand, recursion isn’t for every situation. Here are some other factors to consider:

• For some problems, a recursive solution, though possible, will be awkward rather than elegant.
• Recursive implementations often consume more memory than non-recursive ones.
• In some cases, using recursion may result in slower execution time.

Typically, the readability of the code will be the biggest determining factor. But it depends on the circumstances. The examples presented below should help you get a feel for when you should choose recursion.

Recursion in Python

When you call a function in Python, the interpreter creates a new local namespace so that names defined within that function don’t collide with identical names defined elsewhere. One function can call another, and even if they both define objects with the same name, it all works out fine because those objects exist in separate namespaces.

The same holds true if multiple instances of the same function are running concurrently. For example, consider the following definition:

deffunction():x=10function()

When function() executes the first time, Python creates a namespace and assigns x the value 10 in that namespace. Then function() calls itself recursively. The second time function() runs, the interpreter creates a second namespace and assigns 10 to x there as well. These two instances of the name x are distinct from each another and can coexist without clashing because they are in separate namespaces.