378 - Kth Smallest Element in a Sorted Matrix.

Medium

Given an n x n matrix where each of the rows and columns is sorted in ascending order, return the <code>k^th</code> smallest element in the matrix.

Note that it is the <code>k^th</code> smallest element in the sorted order , not the <code>k^th</code> distinct element.

You must find a solution with a memory complexity better than <code>O(n²)</code>.

Example 1:

Input: matrix = \[\[1,5,9],10,11,13,12,13,15], k = 8

Output: 13

Explanation: The elements in the matrix are 1,5,9,10,11,12,13,<ins> **13** </ins>,15, and the 8^th smallest number is 13

Example 2:

Input: matrix = \[\[-5]], k = 1

Output: -5

Constraints:

• n == matrix.length == matrix[i].length

• 1 <= n <= 300

• <code>-10⁹<= matrixj<= 10⁹</code>

• All the rows and columns of matrix are guaranteed to be sorted in non-decreasing order.

• <code>1 <= k <= n²</code>

Follow up:

• Could you solve the problem with a constant memory (i.e., O(1) memory complexity)?

• Could you solve the problem in O(n) time complexity? The solution may be too advanced for an interview but you may find reading this paper fun.