What's the motivation behind the problem? How could you use it to solve real-world problems? What are the insights, the clever observations made on the problem's constraints that make the solution possible? What details of the problem does the solution take advantage of to get that extra performance gain / space saving? Where does the algorithm / data-structure / solution suck? How could you make it better? What do you lose and gain by doing so? For the specific problem at hand, which solution presents the most acceptable trade-offs?