Merge pull request #1 from tanhongit/main

840. Magic Squares In Grid

Author: tanhongit

.github/workflows/fork.yml

@@ -0,0 +1,42 @@
+name: 'Upstream Sync'
+
+on:
+  push:
+    branches:
+      - '*'
+  schedule:
+    - cron: '0 0 * * *'
+
+  workflow_dispatch:
+  
+jobs:
+  sync_latest_from_upstream:
+    runs-on: ubuntu-latest
+    name: Sync latest commits from upstream repo
+
+    steps:
+    - name: Checkout target repo
+      uses: actions/checkout@v4
+      with:
+        ref:  main
+
+    - name: Sync upstream changes
+      id: sync
+      uses: aormsby/[email protected]
+      with:
+        target_sync_branch: main
+        target_repo_token: ${{ secrets.GITHUB_TOKEN }}
+        upstream_sync_branch: main
+        upstream_sync_repo: Algorithms-and-Chickens/leetcode
+        upstream_repo_access_token: ${{ secrets.UPSTREAM_REPO_SECRET }}
+      
+    - name: New commits found
+      if: steps.sync.outputs.has_new_commits == 'true'
+      run: echo "New commits were found to sync."
+    
+    - name: No new commits
+      if: steps.sync.outputs.has_new_commits == 'false'
+      run: echo "There were no new commits."
+      
+    - name: Show value of 'has_new_commits'
+      run: echo ${{ steps.sync.outputs.has_new_commits }}

medium/840. Magic Squares In Grid/assets/img.png

@@ -0,0 +1,39 @@
+URL: [840. Magic Squares In Grid
+](https://leetcode.com/problems/magic-squares-in-grid/description/)
+
+A `3 x 3` magic square is a `3 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.
+
+![img.png](assets/img.png)
+
+**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:
+
+![img_1.png](assets/img_1.png)
+
+while this one is not:
+
+![img_2.png](assets/img_2.png)
+- 
+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`

medium/840. Magic Squares In Grid/assets/img_1.png

@@ -0,0 +1,113 @@
+# Solution URL
+
+https://leetcode.com/discuss/topic/5611092/solution-100-beats-in-php-with-explanation/
+
+# 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**: $O(\text{m} \times \text{n})$ 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 an upvote. Thank you so much for reading!

medium/840. Magic Squares In Grid/assets/img_2.png

@@ -11,19 +11,23 @@ Return an array of coordinates representing the positions of the grid in the ord
 
 Example 1:
 
+![img.png](assets/img.png)
+
 > **Input:** rows = 1, cols = 4, rStart = 0, cStart = 0
 > 
 > **Output:** [[0,0],[0,1],[0,2],[0,3]]
 
 Example 2:
 
+![img_1.png](assets/img_1.png)
+
 > **Input:** rows = 5, cols = 6, rStart = 1, cStart = 4
 > 
 > **Output:** [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]
 
 
 Constraints:
 
-- 1 <= rows, cols <= 100
-- 0 <= rStart < rows
-- 0 <= cStart < cols
+- `1 <= rows, cols <= 100`
+- `0 <= rStart < rows`
+- `0 <= cStart < cols`

medium/840. Magic Squares In Grid/description.md

@@ -4,7 +4,7 @@ https://leetcode.com/problems/spiral-matrix-iii/solutions/5606322/solution-beat-
 
 # Intuition
 <!-- Describe your first thoughts on how to solve this problem. -->
-- To traverse all the cells in a grid of size `rows * cols` starting from a specific position (`rStart`, `cStart`) in a spiral order, we can use an array of directions and a variable to keep track of the number of steps needed in each direction.
+- To traverse all the cells in a grid of size `rows * cols` starting from a specific position (`rStart`, `cStart`) in spiral order, we can use an array of directions and a variable to keep track of the number of steps needed in each direction.
 - We will move in sequential directions: **right, down, left, and up**, increasing the number of steps after every two directions (one complete cycle).
 
 # Approach
@@ -17,11 +17,11 @@ https://leetcode.com/problems/spiral-matrix-iii/solutions/5606322/solution-beat-
 - After every two directions, increment the number of steps required.
 
 # Complexity
-- Time complexity: **O(n×m)**
+- Time complexity: $O(n \times m)$
 
 We will traverse all cells in the grid once, so the time complexity is linear with respect to the number of cells in the grid, or `O(n×m)`, where `n` is the number of rows and `m` is the number of columns.
 
-- Space complexity: **O(n×m)**
+- Space complexity: $O(n \times m)$
 
 The result array `ans` will contain all positions of the grid, so the space complexity is also linear with respect to the number of cells in the grid, or `O(n×m)`.
 
@@ -63,3 +63,5 @@ class Solution
 }
 
 ```
+
+If it can help you, please give me an upvote. Thank you so much for reading!