840. Magic Squares In Grid solution with php

Author: tanhongit

medium/840. Magic Squares In Grid/splution-php.md

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+# Intuition
+
+To determine how many `3x3` subgrids within a given grid are magic squares, we need to check each possible `3x3` subgrid.
+
+**A magic square** is defined as a grid where the sums of rows, columns, and diagonals are all equal and contain the numbers from 1 to 9 exactly once.
+
+# Approach
+
+1. **Grid Size Check**:
+
+   First, we check if the grid has fewer than 3 rows or columns.
+
+   If it does, return 0 because no `3x3` subgrid can exist.
+
+2. **Iterate Over Subgrids**:
+   Use nested loops to iterate over all possible `3x3` subgrids in the grid.
+
+3. **Helper Function**:
+   For each subgrid, use a helper function to:
+    - Ensure all numbers from 1 to 9 are present exactly once.
+    - Check if the sums of all rows, columns, and diagonals are equal.
+
+4. **Count Valid Subgrids**:
+   Increment a counter for each valid magic square subgrid found.
+    If the helper function returns true, increment the counter `$res`.
+
+# Complexity
+- **Time complexity**:
+
+`O(m×n)` is the number of rows and (n) is the number of columns in the grid. We iterate over each possible `3x3` subgrid and check if it is a magic square.
+
+- **Space complexity**:
+
+`O(1)`, aside from the input grid, as we use a constant amount of extra space to store the set of numbers and the sums.
+
+# Code
+```php
+class Solution {
+    /**
+     * @param Integer[][] $grid
+     * @return Integer
+     */
+    public static function numMagicSquaresInside($grid) {
+        $m = count($grid);
+        $n = count($grid[0]);
+        $res = 0;
+        if ($m < 3 || $n < 3) {
+            return 0;
+        }
+
+        for ($row = 0; $row <= $m - 3; $row++) {
+            for ($col = 0; $col <= $n - 3; $col++) {
+                $set = array_fill(0, 10, 0);
+                if (self::helper($grid, $row, $col, $set)) {
+                    $res++;
+                }
+            }
+        }
+
+        return $res;
+    }
+
+    /**
+     * @param Integer[][] $grid
+     * @param Integer $row
+     * @param Integer $col
+     * @param Integer[] $set
+     * @return Boolean
+     */
+    private static function helper($grid, $row, $col, &$set) {
+        for ($i = 0; $i < 3; $i++) {
+            for ($j = 0; $j < 3; $j++) {
+                $val = $grid[$row + $i][$col + $j];
+                if ($val > 9 || $val < 1 || $set[$val] > 0) {
+                    return false;
+                }
+                $set[$val]++;
+            }
+        }
+
+        $sum_row1 = $grid[$row][$col] + $grid[$row][$col + 1] + $grid[$row][$col + 2];
+        $sum_row2 = $grid[$row + 1][$col] + $grid[$row + 1][$col + 1] + $grid[$row + 1][$col + 2];
+        $sum_row3 = $grid[$row + 2][$col] + $grid[$row + 2][$col + 1] + $grid[$row + 2][$col + 2];
+
+        if ($sum_row1 != $sum_row2 || $sum_row1 != $sum_row3) {
+            return false;
+        }
+
+        $sum_col1 = $grid[$row][$col] + $grid[$row + 1][$col] + $grid[$row + 2][$col];
+        $sum_col2 = $grid[$row][$col + 1] + $grid[$row + 1][$col + 1] + $grid[$row + 2][$col + 1];
+        $sum_col3 = $grid[$row][$col + 2] + $grid[$row + 1][$col + 2] + $grid[$row + 2][$col + 2];
+
+        if ($sum_col1 != $sum_col2 || $sum_col1 != $sum_col3) {
+            return false;
+        }
+
+        $diag1 = $grid[$row][$col] + $grid[$row + 1][$col + 1] + $grid[$row + 2][$col + 2];
+        $diag2 = $grid[$row][$col + 2] + $grid[$row + 1][$col + 1] + $grid[$row + 2][$col];
+
+        if ($diag1 != $diag2) {
+            return false;
+        }
+
+        if ($sum_col1 != $sum_row1 || $sum_row1 != $diag1) {
+            return false;
+        }
+
+        return true;
+    }
+}
+```
+
+If it can help you, please give me a upvote. Thank you so for reading!