Leetcode #1439: Find the Kth Smallest Sum of a Matrix With Sorted Rows
In this guide, we solve Leetcode #1439 Find the Kth Smallest Sum of a Matrix With Sorted Rows in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an m x n matrix mat that has its rows sorted in non-decreasing order and an integer k. You are allowed to choose exactly one element from each row to form an array.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Binary Search, Matrix, Heap (Priority Queue)
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: mat = [[1,3,11],[2,4,6]], k = 5
Output: 7
Explanation: Choosing one element from each row, the first k smallest sum are:
[1,2], [1,4], [3,2], [3,4], [1,6]. Where the 5th sum is 7.
Python Solution
class Solution:
def kthSmallest(self, mat: List[List[int]], k: int) -> int:
pre = [0]
for cur in mat:
pre = sorted(a + b for a in pre for b in cur[:k])[:k]
return pre[-1]
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.