Question

Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Example:

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

return 13.
Note:
You may assume k is always valid, 1 ≤ k ≤ n2.

Quick Hints

• PriorityQueue for row or column
• Keep popping and updating till k

Solution

Time complexity

O (n + k log(n)) where n is the number of columns

Space complexity

O (n) taken by the priority queue

Notes