Kth smallest element in sorted matrix

Question

This is an interview question.

Find the K^th smallest element in a matrix with sorted rows and columns.
Is it correct that the K^th small

Answer 1

O(k log(k)) solution.

• Build a minheap.

• Add (0,0) to the heap. While, we haven't found the kth smallest element, remove the top element (x,y) from heap and add next two elements [(x+1,y) and (x,y+1)] if they haven't been visited before.

We are doing O(k) operations on a heap of size O(k) and hence the complexity.