. Magic Squares In Grid

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:

1. 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.

2. 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

  
  
  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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