What is the time complexity of HTML DOM lookups [closed]

Question

Assuming there are no crazy optimizations (I'm looking at you Chrome).

I'm talking about raw, nasty, ain't-broke-don't-fix-it, ie v6 javascript, cost.

The lower limit being:

document.getElementById() 

Versus:

document.getElementsByTagName('div') lookup.

Answer 1

getElementById can safely assumed to be O(1) in a modern browser as a hashtable is the perfect data structure for the id=>element mapping.

Without any optimizations any simply query - be it a css selector, an id lookup, a class or tag name lookup - is not worse than O(n) since one iteration over all elements is always enough.

However, in a good browser I'd expect it to have a tagname=>elements mapping, so getElementsByTagName would be O(1) too.