LeetCode 52: N-Queens II

Follow up for N-Queens problem.
Now, instead outputting board configurations, return the total number of distinct solutions.

public class Solution {
    private int num; // Number of lines of board
    private int nSolution; // Number of solutions
    private int[] x; // Position of queens
    
    public int totalNQueens(int n) {
        // Backtracking problem
        // Construct a (n+1) level tree: The ith (i = 0,1,...,n) level has n^i nodes
        // x[i] also represents there is a queen on the ith row x[i]th column
        num = n;
        nSolution = 0;
        x = new int[n];
        
        backTrack(0);
        
        return nSolution;
    }
    
    private void backTrack(int cnt)
    {
        if (cnt == num) // Passed the last row and get a possible solution
            nSolution++;
        else
        {
            for (int j = 0; j < num; j++)
            {
                x[cnt] = j;
                
                // Test if x[cnt] can be positioned
                if (place(cnt))
                    backTrack(cnt+1);
            }
        }
    }
    
    // Constrained rule: The queens can be be put in the same row, column or line with slope (-1 or +1)
    private boolean place(int j)
    {
        for (int i = 0; i < j; i++)
            if (x[i]==x[j] || Math.abs(i-j)==Math.abs(x[i]-x[j]))
                return false;
                
        return true;
    }
}