Solve N-Queens Problem?

List<List<string>> SolveNQueens(int n)
{
List<List<string>> results = new List<List<string>>();
int[] board = new int[n]; // board[i] = column position of queen

in row i

Solve(0, board, results, n);

return results;
}

void Solve(int row, int[] board, List<List<string>> results, int n)

{
if (row == n)
{

results.Add(GenerateBoard(board, n));

return;
}
for (int col = 0; col < n; col++)
{
if (IsSafe(row, col, board))
{
board[row] = col;

Solve(row + 1, board, results, n);

}
}
}

bool IsSafe(int row, int col, int[] board)

{
for (int i = 0; i < row; i++)

Follow on:

{
if (board[i] == col || Math.Abs(board[i] - col) ==

Math.Abs(i - row))

return false;
}
return true;
}
List<string> GenerateBoard(int[] board, int n)
{
List<string> res = new List<string>();
for (int i = 0; i < n; i++)
{
char[] row = new char[n];
for (int j = 0; j < n; j++)
row[j] = '.';
row[board[i]] = 'Q';

res.Add(new string(row));

}
return res;
}

Explanation:

Backtracking places queens row by row while checking columns and diagonals.