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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:
while this one is not:
In total, there is only one magic square inside the given grid.
Example 2:
Constraints:
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:
Iterate through the Grid:
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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