Strange behavior when iterating over HTMLCollection from getElementsByClassName

What's going on is an odd side effect. When you reassign className for each element of elements, the element gets removed from the array! (Actually, as @ user2428118 points out, elements is an array-like object, not an array. See this thread for the difference.) This is because it no longer has the classOne class name. When your loop exits (in the second case), the elements array will be empty.

You could write your loop as:

while (elements.length) {
    elements[0].className = 'classTwo'; // removes elements[0] from elements!
}

In your first case, by incrementing i, you are skipping half of the (original) elements that have class classOne.

Excellent question, by the way. Well-researched and clear.

getElementsByClassName returns a NodeList. A NodeList collection is a live collection, which means that the modification of the document affects the collection. more