Finding kth smallest number from n sorted arrays

Question

So, you have n sorted arrays (not necessarily of equal length), and you are to return the kth smallest element in the combined array (i.e the combined array formed by mergin

Answer 1

You could look at my recent answer on the related question here. The same idea can be generalized to multiple arrays instead of 2. In each iteration you could reject the second half of the array with the largest middle element if k is less than sum of mid indexes of all arrays. Alternately, you could reject the first half of the array with the smallest middle element if k is greater than sum of mid indexes of all arrays, adjust k. Keep doing this until you have all but one array reduced to 0 in length. The answer is kth element of the last array which wasn't stripped to 0 elements.

Run-time analysis:

You get rid of half of one array in each iteration. But to determine which array is going to be reduced, you spend time linear to the number of arrays. Assume each array is of the same length, the run time is going to be cclog(n), where c is the number of arrays and n is the length of each array.