Euclid's Algorithm - JavaScript

Question

I'm new to JavaScript and I'm learning about recursive functions. Specifically, I'm working on Euclid's algorithm. It all makes sense to me except for the base case on line 2 "if ( ! b) { return a; }. I understand that at some point a % b will be equal to NaN and this is when the recursive call should stop. But what does "if ( ! b)" mean in it's simplest form? I can't wrap my head around this. I appreciate the feedback in advance!

// Euclid's Algorithm 

var gcd = function(a, b) {  
   if (!b) {  
       return a;  
   }  

   return gcd(b, a % b);  
};  
console.log(gcd(462, 910));

Answer 1

This is the rationale behind Euclid's algorithm.

gcd(a, b) = gcd(b, a%b)

But except when b is 0. What is the result in this case? You can imagine that 0 has actually infinite factors in it: you can divide 0 by anything and the remainder will always be 0.

From this, we can derive that

gcd(a, 0) = a

And that's the stop case of the algorithm. if (!b) is actually checking if b===0, and returning a in this case.

Answer 2

(! b) is evaluating the variable b to return the value of false. In JavaScript NaN is falsey which means it's not false, but it will evaluate to false in a Boolean evaluation.

As others have mentioned, the variable b will equal 0 and not NaN. I was just explaining how NaN evaluates for the sake of the original question.