Question

for example, how to detect the index of the li elem in it’s parent ul?

Answer 1

<ul>
    <li>this</li>
    <li>is</li>
    <li>ul</li>
</ul>

<ul>
    <li>this</li>
    <li>is</li>
    <li>another</li>
    <li>ul</li>
</ul>

if you have something like above, you could do jQuery as:

$(function(){
  $('li').click(function(){ alert('the index is '+$(this).index()) })

})

this will alert the index of the li element based on its parent ul

more on index() here.