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MediumArray

Kth Smallest Element in a Sorted Matrix

arraybinary searchsorting

Problem Statement

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

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

You must find a solution with a memory complexity better than O(n ^2 ) .

Examples

Example 1
Input: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8
Output: 13
The elements in the matrix are [1,5,9,10,11,12,13, 13 ,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
-10 ^9 <= matrix[i][j] <= 10 ^9
All the rows and columns of matrix are guaranteed to be sorted in non-decreasing order .
1 <= k <= n ^2
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.
🤔
Medium
Difficulty
Topic Info
ModuleDSA
CategoryArray
Sub-topicBinary Search
Tags
arraybinary searchsortingheap (priority queue)matrix
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