How do they perform auto complete of code in eclipse or other ides? What is basic principle behind it?
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You know how you have to explicitly attach source code to non-standard libraries you imported in Eclipse? When you do that, text-search index is built over that source and this way IDE knows to offer you auto-complete feature. Roughly, I suppose it is something as associative array where key is the prefix of method you typed, and value is description of that method.
Now what is important for this functionality is to be implemented efficiently regarding both time and memory consumption. It would be very inefficient to store the same entry for every possible prefix of some method. (Or even to store every prefix!)
One of interesting structures that could be suitable for this problem is Trie, which is inherently optimized for prefix search while keeping acceptable memory usage.
Take a look here for a simple example:
http://www.sarathlakshman.com/2011/03/03/implementing-autocomplete-with-trie-data-structure/