Sometimes you need to look ahead or behind the current element you're on when iterating through an array. This is a neat trick for doing that quickly, without stepping outside the bounds of your array.

arraynavigation.js

var arr = ['a','b','c'];


// 1. LOOKING AHEAD
// -----------------------------
for (var i=0; i<arr.length; i++) {
	var next = arr[ (i+1) % arr.length ]; // <= THE MAGIC
	console.log(arr[i], "->", next);
}

/*
Output:
  a -> b
  b -> c
  c -> a (important one)
*/





// 2. LOOKING BEHIND
// -----------------------------
// We have do to a bit more work to work with going backwards.
// Mod isn't well defined for negative numbers 
// See: (http://en.wikipedia.org/wiki/Modulo_operation)

// Here's a hack for JS
Number.prototype.mod = function(n) {
	return ((this % n) + n) % n;
}

// Now let's use it
for (var i=0; i<arr.length; i++) {
	// Find the element before the current one
	var prev = arr[ (i-1).mod(arr.length) ]; // <= MORE MAGIC
	console.log(prev, "<-", arr[i]);
}

/*
Output:
  c <- a (important one)
  a <- b
  b <- c
*/

Is it possible that

 ((this % n) + n) % n

can be changed to

 (this + n) % n

I come back to this gist once in a while. I now understand why you need ((this % n) + n) % n