JQUERY Time complexity

I tried the following code for updating the value of an element:

first:

$(this).parent().prev().children(':selected').val();

then: I tried with following code:

$(this).parent().prev().children('.pgs').val();//`.pgs` is class of `select` drop down

last:

I also tried with following code:

$(this).parent().prev().find('.pgs').val();

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Here, first snippet of code took little more time than the last two snippets. Why did the first snippet show such behavior? How do I find out more about jQuery operations time complexity?

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:selected is not a CSS selector the browser understands, it's specificly implemented via Sizzle (the selector engine jQuery's uses), so it goes through a very different code path.

.pgs however is a perfectly valid CSS selector, something that the browser can optimize heavily, since jQuery can use native cSS selection methods, for instance querySelector() and querySelectorAll().

As for more research here, I don't have a great resource for you. However, the general rule is if it's a jQuery selector but not a valid CSS selector it's going to be slower, since it can't take advantage of several native code paths in the browser.