Recursion

recursion is when a function calls itself

(like this pair of hands drawing themselves)

Infinite Recursion

Here's a not very useful recursive function:

function go() {
  console.log("Go!");
  go();                // do it all again
}

To stop this function, press CTRL-C.

Recursion Requires Termination

For recursion to be useful, it needs to (eventually) stop.

The standard way to stop is called a guard clause.

Also called a base case or a terminator.

function countdown(seconds) {
  if (seconds === 0) {
    console.log("Blastoff!");
  }
}

Recursion is Reduction

In addition to the base case, a recursive function needs to define at least one other case; this case wraps around the base case like a Russian doll.

You can think of a recursive function as starting with a large problem, and gradually reducing the problem until it reaches the base case.

Since the base case has a known solution, every other step can then be built back up on top of it -- which is why it's called the base.

In this way, recursion is an example of the divide and conquer approach to problem-solving.

Countdown

The simplest form of recursion uses a counter; in this example we are counting down the seconds until a rocket launches.

function countdown(seconds) {
  if (seconds == 0) {
    console.log("Blastoff!");
  } else {
    console.log("" + seconds + "...");
    let nextCount = seconds - 1;
    countdown(nextCount);
  }
}

countdown(10);

Put the above in a source file called countdown.js and try it now.

Note that when recursing, you must change the value of the counter, else recurse forever.

Exercise: Draw It Out

Please dive into the above countdown function in excruiciating detail.

Fill out the cells of the following table for the call countdown(5):

Lab: Recursive Factorial

To find the factorial of a number N, you take all the counting numbers between 1 and N and multiply them together.

Write a function called factorial that takes a number and returns its factorial.

Remember to start with the base case!

factorial(1)    // 1
factorial(2)    // 2
factorial(3)    // 6
factorial(10)   // 3628800

Solution: Factorial

function factorial(n) {
    if (n == 1) {
        return 1;
    } else {
        return n * factorial(n - 1);
    }
}

Exercise: Draw It Out

Please dive into the above factorial function in excruiciating detail.

Fill out the cells of the following table for the call factorial(5):

Recursion vs Loops

Recursion can be seen as another kind of loop, like for or while or reduce.

In fact, most recursive functions can be "unrolled" and rewritten using a loop and a stack.

For example, here is factorial using a stack instead of recursion:

function factorial(n) {
    let stack = [];
    while (n >= 1) {
        stack.push(n);
        n = n - 1;
    }
    let f = 1;
    while (stack.length > 0) {
        f = f * stack.pop();
    }
    return f;
} 

What do you think about this implementation compared to the previous one? What are the advantages and disadvantages of recursion vs. loops?

Lab: Recursive Fibonacci

Using recursion, write a program called fib.js so that running node fib.js 10 prints

[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ]

which are the first 10 elements of the Fibonacci sequence.

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