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Find the first id of any descendant using jQuery

For draggable divs in JS on my page, I want to store the last location in local storage so that when a user refreshes, the draggable elements on the page stay put.
My HTML is in general like this:
<div id="some_id" class="draggable">
<p>I am a draggable thing.</p>
</div>
I then use the id of the div as a key in local storage so that having multiple draggable objects on the page doesn't result in them all being given the same position on refresh.
However, templates like this are sometimes used inside a template which handles visibility, so sometimes they'll be like this:
<div class="visibility_container draggable">
<button class="close_button">Close</button>
<div id="some_id">
<p>I am a draggable thing.</p>
</div>
</div>
Note that the draggable class is added programmatically each time.
These templates may vary but will never have ids within them – they'd be pretty terrible templates if they did – so I only need to find the first descendant element which has an id and use the value of that id as my local storage key.
How can I find the nearest element with JS? I'm aware that jQuery has a .closest() method which finds the nearest ancestor – I need to go in the opposite direction. I'm also aware of jQuery's .find() which can find me all descendants matching a selector, but I'm unsure I can guarantee the order in which jQuery returns these children as the API docs were not clear on that point.

I'm also aware of jQuery's .find() which can find me all descendants matching a selector, but I'm unsure I can guarantee the order in which jQuery returns these children as the API docs were not clear on that point.
find lists elements in document order (aka "DOM order") (and you're right, I'm surprised not to see a clear statement of that in the docs). "Document order" is a well-defined DOM term, it means a depth-first search of the descendant elements. Or put it another way: The one whose text is first in the markup.
So for instance:
<div id="container">
<div>
<div>
<div id="one"></div>
</div>
<div id="two"></div>
</div>
...then
console.log($("#container").find("[id]").first().attr("id"));
...will log one, not two.
This document order thing is common across most of the jQuery API and DOM methods like querySelectorAll, getElementsByTagName, and such. I'm not having any luck finding a clear statement of it in the jQuery documentation, though, which seems like an oversight. The closest I've found so far is a bit documenting an exception to that (e.g., saying here that "The second and third...create a jQuery object using one or more DOM elements that were already selected in some other way...unlike most other multi-element jQuery operations, the elements are not sorted in DOM order." [my emphasis].) The multiple selector docs also point out that the results will be in document order (not the order of the selectors).

How is the jQuery selector $('#foo a') evaluated?

As a example of jQuery code (https://coderwall.com/p/7uchvg), I read that the expression $('#foo a'); behaves like this:
Find every a in the page and then filter a inside #foo.
And it does not look efficient.
Is that correct? And if yes, how should we do that in a better way?

That is correct - Sizzle (jQuery's selector engine) behaves the same way as CSS selectors. CSS and Sizzle selectors are evaluated right-to-left, and so #foo a will find all a nodes, then filter those by nodes that descend from #foo.
You improve this by ensuring that your leaf selectors have a high specificity, usually by giving them a class or ID.

how should we do that in a better way?
Use the context parameter from jQuery.
$('a', '#foo');
Now jQuery will search all anchors within the context of the element with id: foo.
In your query the context is defaulted to document when omitted:
$('#foo a'); == $('#foo a', document);
In this case, your query is indeed not efficient.
You might take a look at this article.

While it is true that Sizzle is a right-to-left engine (which is the same way css is interpreted), it is not true that the specific selector in your example would select all anchor elements on the page and then filter their parents to match the id of "foo". Sizzle actually optimizes any selector that starts with an ID and uses that as the context for the entire selection, rather than using the document. In other words, the selector you've chosen basically translates to:
document.getElementById("foo").getElementsByTagName("a")
Really, that's not a bad selector at all.
However, given the other things jQuery needs to do (which includes looping over the elements to merge them onto the jQuery instance), jQuery("#foo").find("a") will always be the fastest because jQuery implements a jQuery object creation shortcut for id-only selectors, and then it does the find rooted from #foo.
In other words, Sizzle itself is not much different when doing Sizzle("#foo a") and Sizzle("a", document.getElementById("foo")), but jQuery("#foo").find... will be faster because of jQuery's own ID shortcut.
By the way, my remarks on Sizzle is assuming querySelectorAll is not being used. If it is, Sizzle just passes it on to qsa, which still isn't as fast as using jQuery's ID shortcut.

You can use find() for more granular control on your selector order:
$('#foo').find('a');
This will of course be more impressive with more complex selectors, where you can chain find() and filter().
For the record $('#foo').find('a') === $('a','#foo')
[Update] ok, I realized later that it's exactly what your link says...
The jQuery selector engine (Sizzle) has been refactored last year, you'll find detailed explanations here:
http://www.wordsbyf.at/2011/11/23/selectors-selectoring/

Instead of filtering with a inside #foo elements, simply attach a class to a elements and get a elements with class like $("a.class");. This would be more efficient.

Yet another "try it for yourself":
jsperf for various selectors on 10000 elements
jsperf for various selectors on 300 elements
jsperf for various selectors on a "more representative DOM"
Doesn't seem to be much difference with a "flat" DOM (1 & 2), but the performance varies much more with a nested DOM.
Also note that some of the test cases aren't selecting the correct elements (i.e. $('.a') vs $('.a', context)), but I left them from the original tests just for comparison.

This example will retrieve the all anchors elements a in an element called foo, to Find every a in the page and then filter a inside #foo as you want u should select a #foo
$("a #foo");
this will retrieve all the foo elements inside a elements.

access child DOM object from parent in dotted notation

Is there a way to select a child DOM object by treating it as data member of its parent DOM object? Imagine I have this code:
<div id=div1>
<div id=innerdiv1></div>
<div id=innerdiv2></div>
</div>
<div id=div2>
<div id=innerdiv1></div>
<div id=innerdiv2></div>
</div>
This example won't work in real life because both pairs of child divs have the same id's (innerdiv1, innerdiv2), but that's exactly what bothers me about the "id" thing.
Is there some way in javascript to access a child element as a data member, something like document.getElementById('div1.innerdiv1'), which would return a different object from document.getElementById('div2.innerdiv1').
I can't stand that each id has to be unique throughout the document. It becomes a major issue when you have a lot of code and you accidentally use the same id twice. It makes for really nasty bugs that are difficult to squash.

You can use document.querySelector in modern browsers. document.getElementById is pretty much obsolete.
document.querySelector('#div1 #innerdiv1')

You can use classes for the inner divs instead of ids, which do not need to be unique.

The document object has a getElementById method, but the returned elements do not have this method, and it couldn't take a string that isn't exactly the id of an element [if that's what you want try a library, like jQuery or Pumbaa80's suggestion of document.querySelector].
In some browsers you can try:
document.getElementById('div1').getElementsByTagName('div')[0]
As a side note, try dropping these two html documents into html5.validator.nu or http://validator.w3.org/#validate_by_input
<!DOCTYPE html><head><title>t</title></head><body>
<div id=div1><div id=d1>one</div><div id=d2>two</div>three</div>
<div id=div2><div id=d1>four</div><div id=d2>five</div>six</div>
</body>
Now you can totally avoid using the same id twice by just using classes instead.
<!DOCTYPE html><head><title>t</title></head><body>
<div id=div1><div class=d1>one</div><div class=d2>two</div>three</div>
<div id=div2><div class=d1>four</div><div class=d2>five</div>six</div>
</body>
For the first one, you could use document.querySelector('#div2 #d1') or $('#div2 #d1')
but I don't think the result would be guaranteed across all browsers due to the fact that this should be equivalent to writing document.querySelector('#d1') which you can see returns the first occurring id that matches, or $('#d1') which returns both id matching elements in an array.
And for the second one you could use document.querySelector('#div2 .d1') or $('#div2 .d1') or the other statements for very similar results, except that your html is valid this time. You don't even have to have css that defines d1 and d2 and if you used an attribute like class="d1 mySubHeading" and class="d2 mySubHeading" you could style both with mySubHeading and leave d1 and d2 there purely for selection via these methods.

Selecting previous anchor tag and adding a class to it with jQuery

Basically I've got two anchor tags separated by a div.
<a class="foo"></a>
<div class="count">0</a>
<a class="bar"></a>
and I'm doing something like this:
var addClass = $(this).parent().children('a:first-child').addClass('new');
It will then add it to the first anchor tag like so:
<a class="foo new"></a>
I know using the nth:child selector is pretty expensive, so I was wondering if there was an easier way to select that previous anchor node, (while ignoring the second one).

You could do this
$(this).parent().children('a:eq(0)').addClass('new');
Learn more about :eq()
Alternatively, if there are no elements between the <a> and the <div>, you could do
$(this).prev('a');
Learn more about .prev()

I'd probably combine prevAll with first (or eq(0), since first just calls eq(0) — but I find first more readable):
$(this).prevAll("a").first().addClass("new");
// or
$(this).prevAll("a").eq(0).addClass("new");
prevAll returns all of the element's preceding siblings, in order starting with the closest sibling, and of course first / eq(0) reduces the set to the first element.
You might be tempted to use the :first selector with prevAll to avoid building up an unnecessary list of siblings, but to my surprise it works better to use first after-the-fact.

How about:
$(this).siblings('a').eq(0).addClass(0);
Actually, if your structure is as simple as in your example, you can just do a simple:
$(this).prev().addClass(0);
jQuery's traversal methods give you lots of ways to get to any given destination.

Performance of jQuery selectors

HTML markup:
<div>
<a id="foo"> </a>
</div>
jQuery:
$('div').each(function(){
$('#foo', this).dosmth(); // 1
$('#foo').dosmth(); // 2
});
Which method would be faster to run dosmth?

Since we're getting a variety of answers, hopefully here's some clarity (check the examples here):
The fastest - There's no need to loop. Skip the $("div").each part and just do $("#foo"). foo is an ID, and thus lookup is instantaneous.
Middling - $("#foo") in a loop. Note that you also don't want this because it will execute the function for every div on the page (and for this reason on a larger document with a lot of divs this would be the slowest).
Slowest - $("#foo", this). The context node doesn't help in the first place, and then consider that jQuery will first build a jQuery object out of this and turn it into $(this).find("#foo"). That's all unnecessary, of course.
Bottom line: in most cases (e.g. sometimes when confirming that an ID is in one context and not another) context nodes are unnecessary with ID lookup.
Here are some resources from the jQuery source:
Handling for most of the cases here - note that $("#id") is singled out for handling as document.getElementById
find - what happens when you pass a context

Since an #id should be unique in the DOM your markup will be invalid (I am assuming more than one <div/> based upon using .each())
Change the id to a class and use the following:
<div>
<a class="foo"> </a>
</div>
<div>
<a class="foo"> </a>
</div>
And the script
$('div').each(function(){
$('.foo', this).dosmth(); //or $(this).find(".foo");
});
But if you only have one element with an id of foo selecting by id will be the fastest, plus you can drop the need for using .each()
$('#foo').dosmth(); //or document.getElementById("foo");

jquery selectors by id only is the fastest way to search because it uses getElementbyId in javascript.
so this one is the fastest:
$('#foo').dosmth();
if you use a context like:
$('#foo', this).dosmth();
it is translated into:
$(this).find('#foo').dosmth();
so that will make another useless operation because your #foo is unique
Regards,
Max

$('#foo', this).dosmth();
This will search within the context of the div and not the whole DOM, which will make the selector faster. This only makes sense to use when the DOM is large, otherwise, just use the normal selector: $('#foo').dosmth();

If you're using an id there's only ever going to be one. So you can just do:
$('a#foo').dosmth();
You don't need to use each() to go through each div and get all the a#foo's out of it. That WILL waste time, creating loops for no reason. Instead use:
$('a#foo').each(function(){ ... });
or even just:
$('a#foo').dosmth();
You can also do $('div a#foo').dosmth(); if you want.

Please read the discussion below regarding this answer or check Bryan answer above about the differences in speed of the selectors.
I would go with
$('a#foo', this).dosmth();
Update But instead of retrieving all the divs before, I would check for
only the desired one at the first time
like this
$('div a#foo').each(function(){
}