Magic Squares in Grid in C++

Suppose we have a grid we have to find the number of magic square sub-grid into that grid. A 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.

So, if the input is like

then the output will be 1, as the magic square is

To solve this, we will follow these steps −

• Define one set with values: [816357492, 834159672, 618753294, 672159834,492357816, 438951276, 294753618, 276951438]
• Define an array offset of size: 9 x 2 := {{-2,-2},{-2,-1},{-2,0},{-1,-2},{-1,-1},{-1,0},{0,-2},{0,-1},{0,0}}
• ans := 0
• for initialize i := 2, when i < grid row count, update (increase i by 1), do −
  • for initialize j := 2, when j < grid row count, update (increase j by 1), do −
    • sum := 0
    • for initialize k := 0, when k < 9, update (increase k by 1), do −
      • sum := sum * 10
      • sum := sum + grid[i + offset[k, 0], j + offset[k, 1]]
    • ans := ans + occurrence of sum in s
• return ans

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   int numMagicSquaresInside(vector<vector<int>>& grid) {
      const unordered_set<int> s{816357492, 834159672, 618753294,
      672159834,492357816, 438951276, 294753618,276951438};
      const int offset[][2] = {{-2, -2}, {-2, -1}, {-2, 0},{-1, -2}, {-1, -1}, {-1, 0},
{ 0, -2}, { 0, -1}, { 0, 0}};
      int ans = 0;
      for(int i = 2; i< grid.size(); i++)
      {
         for(int j = 2; j<grid.size(); j++)
         {
            int sum = 0;
            for(int k = 0; k<9; k++)
            {
               sum *= 10;
               sum += grid[i + offset[k][0]][j+offset[k][1]];
            }
            ans += s.count(sum);
         }
      }
      return ans;
   }
};
main(){
   Solution ob;
   vector<vector<int>> v = {{4,3,8,4},{9,5,1,9},{2,7,6,2}};
   cout << (ob.numMagicSquaresInside(v));
}

Input

{{4,3,8,4},{9,5,1,9},{2,7,6,2}}

Output

1