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2373 - Largest Local Values in a Matrix (Easy)

https://leetcode.com/problems/largest-local-values-in-a-matrix/

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.

In other words, we want to find the largest value in every contiguous 3 x 3 matrix in grid.

Return the generated matrix.

Example 1:

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.

Example 2:

Input: grid = [[1,1,1,1,1],[1,1,1,1,1],[1,1,2,1,1],[1,1,1,1,1],[1,1,1,1,1]]
Output: [[2,2,2],[2,2,2],[2,2,2]]
Explanation: Notice that the 2 is contained within every contiguous 3 x 3 matrix in grid.

Constraints:

  • n == grid.length == grid[i].length
  • 3 <= n <= 100
  • 1 <= grid[i][j] <= 100

Approach 1: Simulation​

Written by @wingkwong
class Solution:
    def largestLocal(self, grid: List[List[int]]) -> List[List[int]]:
        n = len(grid)
        # the result matrix is always (n - 2) * (n - 2)
        res = [[0] * (n - 2) for _ in range(n - 2)]
        # iterate all possible 3 x 3 grids
        for i in range(n - 2):
            for j in range(n - 2):
                # for (i, j) being at top-left, 
                # iterate to check the max in this 3 x 3 grid
                for ii in range(i, i + 3):
                    for jj in range(j, j + 3):
                        res[i][j] = max(res[i][j], grid[ii][jj])
        return res