Kth Smallest Element in a Sorted Matrix — LeetCode 378 Python Solution

The problem

Given an n x n matrix where each of the rows and columns is sorted in ascending order, return 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

Input

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

Output

13

Explanation

The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13

Python solution

class Solution:
    def kthSmallest(self, matrix: List[List[int]], k: int) -> int:
        def check(matrix, mid, k, n):
            count = 0
            i, j = n - 1, 0
            while i >= 0 and j < n:
                if matrix[i][j] <= mid:
                    count += i + 1
                    j += 1
                else:
                    i -= 1
            return count >= k

        n = len(matrix)
        left, right = matrix[0][0], matrix[n - 1][n - 1]
        while left < right:
            mid = (left + right) >> 1
            if check(matrix, mid, k, n):
                right = mid
            else:
                left = mid + 1
        return left

Complexity

Pattern: Heap / Priority Queue

Keep only the best k elements, or always pull the smallest, in log time. LeetCode 378. Kth Smallest Element in a Sorted Matrix is filed here because LeetCode tags it Heap (Priority Queue), which is the vocabulary this hub collects.

The heap / priority queue guide has the Python template for the pattern and the 163 LeetCode problems that use it.

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