cpp-flashcards/org/study_deck_02/dsa/math-geometry/0840-magic-squares-in-grid.org

#+ANKI_DECK: study_deck_02
* TODO 0840. Magic Squares In Grid :medium:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*0840. Magic Squares In Grid][0840. Magic Squares In Grid]]
:END:

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~ 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:*


#+begin_src
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.
#+end_src


*Example 2:*


#+begin_src
Input: grid = [[8]]
Output: 0
#+end_src


*Constraints:*

 - ~row == grid.length~

 - ~col == grid[i].length~

 - ~1 <= row, col <= 10~

 - ~0 <= grid[i][j] <= 15~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python :lc-problem 840 :lc-lang python3
class Solution:
    def numMagicSquaresInside(self, grid: List[List[int]]) -> int:
#+end_src

** TODO C++
#+begin_src cpp :lc-problem 840
class Solution {
public:
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        
    }
};
#+end_src