Find the largest k numbers in k arrays stored across k machines

Question

This is an interview question. I have K machines each of which is connected to 1 central machine. Each of the K machines have an array of 4 byte numbers in file. You can use

Answer 1

I would suggest something like this:

• take the k largest numbers on each machine in sorted order O(Nk) where N is the number of element on each machine

• sort each of these arrays of k elements by largest element (you will get k arrays of k elements sorted by largest element : a square matrix kxk)

• take the "upper triangle" of the matrix made of these k arrays of k elements, (the k largest element will be in this upper triangle)

• the central machine can now find the k largest element of these k(k+1)/2 elements