Selection algorithms on sorted matrix

Question

this is a google interview question :

Given a N*N Matrix. All rows are sorted, and all columns are sorted. Find the Kth Largest element of the matrix.

doing

Answer 1

You can find the k^th smallest element in time O(n log n) expected, if you notice that:

1. Generating a random number that lies between Array[i][j] and Array[k][l] such that Array[i][j] < Array[k][l] takes O(n) time (expected) and

Using [1] as a subroutine, you can use a procedure similar to RANDOMIZED-SELECT to generate the k^th smallest number in the whole array.