840. Magic Squares In Grid

Medium

Topics: Array, Hash Table, Math, Matrix

A 3 x 3 magic square is a3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum.

Given a row x col grid of integers, how many 3 x 3 contiguous magic square subgrids are there?

Note: while a magic square can only contain numbers from 1 to 9, grid may contain numbers up to 15.

Example 1:

Input: grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
Output: 1
Explanation: The following subgrid is a 3 x 3 magic square:

while this one is not:

In total, there is only one magic square inside the given grid.

Example 2:

Input: grid = [[8]]
Output: 0

Constraints:

row == grid.length.
col == grid[i].length
1 <= row, col <= 10
0 <= grid[i][j] <= 15

Solution:

We need to count how many 3x3 contiguous subgrids in the given grid form a magic square. A magic square is a 3x3 grid where all rows, columns, and both diagonals sum to the same value, and it contains the distinct numbers from 1 to 9.

To solve this problem, we can follow these steps:

Check if a Subgrid is Magic:
- The subgrid must contain all distinct numbers from 1 to 9.
- The sum of each row, column, and diagonal should be 15.
Iterate through the Grid:
- Since we need to check 3x3 subgrids, we will iterate from 0 to row-2 for rows and from 0 to col-2 for columns.
- For each top-left corner of the 3x3 subgrid, extract the subgrid and check if it's a magic square.

Let's implement this solution in PHP: 840. Magic Squares In Grid

<?php
// Example usage:
$grid1 = [
    [4, 3, 8, 4],
    [9, 5, 1, 9],
    [2, 7, 6, 2]
];

echo numMagicSquaresInside($grid1); // Output: 1

$grid2 = [
    [18]
];

echo numMagicSquaresInside($grid2); // Output: 0
?>

Explanation:

isMagic function:
- Extracts the 3x3 subgrid.
- Checks if all numbers are distinct and between 1 to 9.
- Verifies that the sums of the rows, columns, and diagonals are all 15.
numMagicSquaresInside function:
- Iterates over all possible 3x3 subgrids in the given grid.
- Counts how many of those subgrids are magic squares.

This code works efficiently within the constraints, counting all 3x3 magic square subgrids in the given grid.

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