This lesson introduces a new problem solving strategy called recursion. Recursion represents an exciting new addition to our algorithm toolbox. It can be hard to wrap your head around at first. But we'll go slow and, as always, use lots of examples. What are we waiting for?
So far we've looked exclusively at iterative algorithms that solve a problem by repeating a series of steps.
The implementations of iterative algorithms are characterized by the use of looping constructs such as
Recursive algorithms work differently. They solve problems by breaking them down into smaller yet similar pieces, and the reassembling the solutions to the smaller problems into a solution to the larger problem. This will make more sense once we look at some examples!
Learning to think recursively takes time and practice. You'll get both!
But let's start by comparing and contrasting an iterative and recursive solution to the same problem. That will both help us start to learn to think recursively, and identify the differences between the two approaches.
Let's write an algorithm to determine if a
String is a palindrome, that is, whether it reads the same forwards and backwards.
First, let's design an iterative algorithm:
Next, let's try and approach the problem recursively.
What does that mean? A recursive solution tries to make the problem smaller in each step until it is trivial to solve. Let's think about how to apply that to palindrome detection.
To wrap up, let's put the two approaches side by side and discuss the differences.
A recursive implementation contains a function that calls itself. At first, this may seem really weird. But the trick is not to not let that throw you, and to just consider what happens.
Successful recursive algorithms must do three things correctly:
Let's examine another recursive implementation. We'll identify the three requirements enumerated above, and trace its execution.
Today's homework problem has you complete a recursive implementation of factorial. For reference, here is the iterative implementation that matches the homework problem:
To complete the recursive implementation, consider the following questions: