Leetcode #2373: Largest Local Values in a Matrix
In this guide, we solve Leetcode #2373 Largest Local Values in a Matrix 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 n x n integer matrix grid. Generate an integer matrix maxLocal of size (n - 2) x (n - 2) such that: maxLocal[i][j] is equal to the largest value of the 3 x 3 matrix in grid centered around row i + 1 and column j + 1.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Matrix
Intuition
Grid problems are easiest when you define clear row/column boundaries.
A consistent traversal order prevents off-by-one errors.
Approach
Iterate by rows, columns, or layers depending on the requirement.
Keep bounds updated as the traversal progresses.
Steps:
- Define bounds or directions.
- Visit cells in order.
- Update result and move bounds.
Example
Input: grid = [[9,9,8,1],[5,6,2,6],[8,2,6,4],[6,2,2,2]]
Output: [[9,9],[8,6]]
Explanation: The diagram above shows the original matrix and the generated matrix.
Notice that each value in the generated matrix corresponds to the largest value of a contiguous 3 x 3 matrix in grid.
Python Solution
class Solution:
def largestLocal(self, grid: List[List[int]]) -> List[List[int]]:
n = len(grid)
ans = [[0] * (n - 2) for _ in range(n - 2)]
for i in range(n - 2):
for j in range(n - 2):
ans[i][j] = max(
grid[x][y] for x in range(i, i + 3) for y in range(j, j + 3)
)
return ans
Complexity
The time complexity is O(m·n). The space complexity is O(1) to O(m·n).
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.