Search a string as you type the character

Question

I have contacts stored in my mobile. Lets say my contacts are

Ram

Hello

Hi

Feat

Eat

At

When I type letter \'A\' I should get

Answer 1

Look up "generalized suffix tree", e.g. https://en.wikipedia.org/wiki/Generalized_suffix_tree . For a fixed alphabet size this data structure gives asymptotically optimal solution to find all z matches of a substring of length m in a set of strings in O(z + m) time. Thus you get the same sort of benefit as if you restricted your search to the matches for the previous prefix. Also the structure has optimal O(n) space and build time where n is the total length of all your contacts. I believe you can modify the structure so that you just find the k strings that contain the substring in O(k + m) time, but in general you probably shouldn't have too many matches per contact that have a match, so this may not even be necessary.