The Self-Taught Computer Scientist

2Recursion

To understand recursion, one must first understand recursion.

Anonymous

An iterative algorithm solves problems by repeating steps over and over, typically using a loop. Most of the algorithms you've written in your programming journey so far are likely iterative algorithms. Recursion is a method of problem-solving where you solve smaller instances of the problem until you arrive at a solution. Recursive algorithms rely on functions that call themselves. Any problem you can solve with an iterative algorithm, you can also solve with a recursive one; however, sometimes, a recursive algorithm is a more elegant solution.

You write a recursive algorithm inside of a function or method that calls itself. The code inside the function changes the input and passes in a new, different input the next time the function calls itself. Because of this, the function must have a base case: a condition that ends a recursive algorithm to stop it from continuing forever. Each time the function calls itself, it moves closer to the base case. Eventually, the base case condition is satisfied, the problem is solved, and the function stops calling itself. An algorithm that follows these rules satisfies the three laws of recursion:

• A recursive algorithm must have a base case.
• A recursive algorithm must change its state and move toward the base case.
• A recursive algorithm must call itself recursively.

To help you understand how a recursive algorithm works, let's take a look at finding the ...