I was asked to think about the drop down search box in a browser like Firefox or Chrome. The question was, given that the user types a few characters and we present them with suggestions, how do we decide what suggestions to give them, what order to present them in, and finally, how do we know if we did a good job? Once we had discussed this for a bit, I was then asked to actually come up with an algorithm for finding suggestions quickly, with out having to search through all the possible suggestions for each character the user typed.
