Python: Find the kth smallest element in the matrix

Last update on April 23 2025 12:58:59 (UTC/GMT +8 hours)

12. Kth Smallest in Sorted Matrix

Given a n x n matrix where each of the rows and columns is sorted in ascending order, write a Python program to find the kth smallest element in the matrix using the heap queue algorithm.

Assume k is always valid, 1 ≤ k ≤ n² .

Sample Solution:

Python Code:

import heapq
class Solution(object):
    def find_Kth_Smallest(self, matrix, k):
        """
        :type matrix: List[List[int]]
        :type k: int
        :rtype: int
        """
        m, n = len(matrix), len(matrix[0])
        temp = [[False] * n for _ in range(m)]
        q = [(matrix[0][0], 0, 0)]
        ans = None
        temp[0][0] = True
        for _ in range(k):
            ans, i, j = heapq.heappop(q)
            if i + 1 < m and not temp[i + 1][j]:
                temp[i + 1][j] = True
                heapq.heappush(q, (matrix[i + 1][j], i + 1, j))
            if j + 1 < n and not temp[i][j + 1]:
                temp[i][j + 1] = True
                heapq.heappush(q, (matrix[i][j + 1], i, j + 1))
        return ans

matrix = [
   [0, 5, 9],
   [11, 12, 13],
   [15, 17, 19]   
]
k = 1
s = Solution()
result = s.find_Kth_Smallest(matrix, k)
print("First smallest element:",result)
k = 2
s = Solution()
result = s.find_Kth_Smallest(matrix, k)
print("\nSecond smallest element:",result)
k = 3
s = Solution()
result = s.find_Kth_Smallest(matrix, k)
print("\nThird smallest element:",result)

Sample Output:

First smallest element: 0

Second smallest element: 5

Third smallest element: 9

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to find the kth smallest element in an n x n matrix (with each row and column sorted) using a min-heap.
• Write a Python script to implement a function that extracts the kth smallest value from a sorted matrix by using heapq to manage candidates.
• Write a Python program to compare the kth smallest element in a matrix found via heapq with that from a complete flatten-and-sort approach.
• Write a Python function to use a min-heap to determine the kth smallest element in a matrix and then print the element along with its matrix position.

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Python Code Editor:

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