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Basics of Recursive Programming (recitation)

madooei
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Recursion

A recursive function is a function that calls itself. Here’s a recursive function:

// REQUIRES: n >= 0
// EFFECTS: returns n!
public static long factorial (int n) {
    if (n == 0) {
        return 1;
    } else {
        return factorial(n-1) * n;
    }
}

Now we can compute factorial(4) in terms of factorial(3), and factorial(3) in terms of factorial(2), and factorial(2) – well, you get the idea.

Recall, a recursive function is defined in terms of base cases and recursive steps.

  • In a base case, we compute the result immediately given the inputs to the function call. For example, factorial(0) is 1 by definition.
  • In a recursive step, we compute the result with the help of one or more recursive calls to this same function, but with the inputs somehow reduced in size or complexity, closer to a base case. For factorial, we reduce the problem by calling factorial(n-1).

There are three common steps in a recursive definition:

  1. Figure out your base case: What is the simplest argument we could possibly get?
  2. Make a recursive call with a simpler argument: Simplify your problem, and assume that a recursive call for this new problem will simply work. This is called the "leap of faith."
  3. Use your recursive call to solve the full problem: Remember that we are assuming the recursive call works. With the result of the recursive call, how can you solve the original problem you were asked? For factorial, we just multiply (n1)! by n.
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