Largest Local Values in a Matrix

Largest Local Values in a Matrix - Problem

Array Matrix Easy

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.

Input & Output

Example 1 — Basic 4x4 Grid

$ Input: grid = [[9,9,8,1],[5,6,2,6],[8,2,6,4],[6,2,2,2]]

› Output: [[9,9],[8,6]]

💡 Note: For position (0,0): 3x3 window has max value 9. For position (0,1): 3x3 window has max value 9. For position (1,0): 3x3 window has max value 8. For position (1,1): 3x3 window has max value 6.

Example 2 — Minimum 3x3 Grid

$ Input: grid = [[1,1,1],[1,1,1],[1,1,1]]

› Output: [[1]]

💡 Note: Only one 3x3 window possible, and the maximum value in all 1s is 1.

Example 3 — Larger Grid with Negatives

$ Input: grid = [[-1,2,-3],[4,-5,6],[-7,8,-9]]

› Output: [[8]]

💡 Note: The single 3x3 window contains all elements, and the maximum is 8.

Constraints

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

Visualization

Tap to expand

Asked in

G Google 45 a Amazon 35 M Microsoft 28 A Apple 22

The key insight is that each output position corresponds to the maximum value in a 3x3 sliding window. Best approach is the brute force iteration which directly checks each 3x3 window. Time: O(n²), Space: O(1).

Common Approaches

✓ Two Pointers

⏱️ Time: N/A Space: N/A

Brute Force - Check All 3x3 Windows

⏱️ Time: O(n²) Space: O(1)

For each position in the result matrix, examine the corresponding 3x3 window in the original grid by checking all 9 cells to find the maximum value.

Optimized Single Pass

⏱️ Time: O(n²) Space: O(1)

Instead of using nested loops to find max, we can calculate the maximum while iterating through the 3x3 window, avoiding redundant comparisons and making the code more efficient.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚠ Quadratic Growth

Space Complexity

✓ Linear Space

89.2K Views

Medium Frequency

~15 min Avg. Time

1.8K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen