Find the largest Magic Square - c++

Question

Given an m x n integer grid, return the size (i.e., the side length k) of the largest magic square that can be found within this grid.
The question can be found here on leetcode
I first wanted to see if a naive brute force approach would pass, so I came up with the following algorithm
Iterate through all values of k (from min(rows,cols) of the matrix to 1)
For each of the k values, check if it's possible to create a magic of square of dimensions kxk by checking all possible sub matrices and
return k if it's possible. This would be O(rows*cols*k^2)
So that would make the overall complexity O(k^3*rows*cols). (Please correct me if I am wrong)
I have attached my code in C++ below
class Solution {
public:
int largestMagicSquare(vector<vector<int>>& grid) {
int rows = grid.size(),cols = grid[0].size();
for(int k = min(rows,cols); k >= 2; k--){ // iterate over all values of k
for(int i = 0; i < rows-k+1; i++){
for(int j = 0; j < cols-k+1; j++){
int startX = i, startY = j, endX = i+k-1, endY = j+k-1;
int diagSum = 0, antiDiagSum = 0;
bool valid = true;
// calculate sum of diag
for(int count = 0; count < k; count++){
diagSum += grid[startX][startY];
startX++,startY++;
}
// this is the sum that must be same across all rows, cols, diag and antidiag
int sum = diagSum;
// calculate sum of antidiag
for(int count = 0; count < k; count++){
antiDiagSum += grid[endX][endY];
endX--,endY--;
}
if(antiDiagSum != sum) continue;
// calculate sum across cols
for(int r = i; r <=i+k-1; r++){
int colSum = 0;
for(int c = j; c <= j+k-1; c++){
colSum += grid[r][c];
}
if(colSum != sum){
valid = false;
break;
}
}
if(!valid) continue;
// calculate sum across rows
for(int c = j; c <= j+k-1; c++){
int rowSum = 0;
for(int r = i; r <= i+k-1; r++){
rowSum += grid[r][c];
}
if(rowSum != sum){
valid = false;
break;
}
}
if(!valid) continue;
return k;
}
}
}
return 1;
}
};
I thought I would optimize the solution once this works (Maybe binary search over the values of k). However, my code is failing for a really large test case for a matrix of dimension 50x50 after passing 74/80 test cases on Leetcode.
I tried to find out the source(s) that could be causing it to fail, but I am not really sure where the error is.
Any help would be appreciated. Thanks!
Please do let me know if further clarification about the code is needed

Answer 1

The calculation of antiDiagSum is wrong: it actually sums the values on the same diagonal as diagSum, just in reverse order. To traverse the opposite diagonal, you need to increment the Y coordinate and decrement the X coordinate (or vice versa), but your code decrements both of them.
It is probably easiest if you fix this by calculating both diagonal sums in the same loop:
for(int count = 0; count < k; count++){
diagSum += grid[startX][startY];
antiDiagSum += grid[endX][startY];
startX++, startY++, endX--;
}