My favourite fiz-buzz problem for Senior Programmers

This post, I will be discussing one of my favourite fiz-buzz problems for senior programmers/engineers. 

Find Kth largest element from a list of 1 million integers. 

Or

Find Kth largest element at any given point of time from a stream of integers, count is not known. 

This problem is interesting as it has multiple approaches to solve and it checks the fundamentals of algorithms and data structure. Quite often, candidate start with asking questions like is the list sorted? Or can I sort the list ? In such case, I go and check on which sorting algorithm the candidate proposes. This gives me an opportunity to start conversation around complexity of the approach (particularly, time complexity). Most of the candidates are quick to point out algorithms (like Quick Sort , Merge Sort) which take O(NlogN) for sorting a list. This is right time to point out that why do you need to sort the complete array/list if you just need to find out 100th or kth largest/smallest element. Now the conversation usually go in either of the direction - 

1. Candidate sometime suggest that, sorting is more quicker way to solve this problem - missing altogether the complexity aspect. If someone doesn't even realize that sorting is not the right way to handle this problem, then it kind of red signal for me. 
2. At times candidates acknowledge the in-efficiency of sorting approach and then start looking for better approach. I suggest, candidates to think out loud which will give me insight about their thought process and how are they approaching it. When I see them not moving ahead; I suggest them on optimizing Quick sort approach ? Is there any way to cut down the problem size in half in every iteration ? Can you use divide and concur to improve on your O(NlogN) complexity ?   

This problem can be solved by Quick Select as well as using Heap data structure. This problem also has a brute force approach (i.e. run loop for k time; in each iteration find the maximum number lower than the last one). 

If the candidate doesn't make much progress then I try to simplify the problem by saying - find 3rd or 2nd largest element. I have seen some of the senior programmers failing to solve this trivial version as well. This is clear Reject sign for me.

Also, sometime I don't even ask candidate to code. I use this problem to just get an idea and skip the coding part if i see a programmer sitting right across me :)

-Happy problem solving !