CareerCup

Given huge database of songs design search data structure and algorithm to search all songs with words starting with the letters entered and words matching the sequence of words entered.
Suppose the songs are:
1. Every night in my dreams
2. Listen to my heart
3. Show me the meaning
4. Night in London
5. Night changes

Entering "m" should list 1,2 and 3. "my" should list 1 and 2. "Night" should list 1,4 and 5. "Night in" should list 1 and 4.

Given access to live stream of purchases, design the algorithm to list the top 100 products in past X minutes/hours/days.

Implement a meeting organizer

Given a binary tree (not search tree), find the path which adds up to given sum.

Given a array of numbers, find all the numbers which add up to given sum.

There are buses taking various routes and each route has some stops. Given a matrix of stops and distances (distance between two stops for connected stops), find all cluster of stops of any size with all stops in a cluster fully connected and are at a distance not greater than D.

Assume that the routes are bi-directional.