N-Queens II

Link:http://oj.leetcode.com/problems/n-queens-ii/

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

public class Solution {
    public int num = 0;
    public int totalNQueens(int n) {
        if (n < 1)
            return 0;
        num = 0;
        int[] queens = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            queens[1] = i;
            dfs(2, n, queens);
        }
        return num;
    }
    public void dfs(int col, int size, int[] queens) {
        if (col > size) {
            num++;
            return;
        }
        // here i means row number;
        for (int i = 1; i <= size; i++) {
            if (isValid(i, col, queens)) {
                queens[col] = i;
                dfs(col + 1, size, queens);
                queens[col] = 0;
            }
        }
    }

    public boolean isValid(int row, int col, int[] queens) {
        for (int i = 1; i < col; i++) {
            // queens should not be in the same row,
            // queens should not be placed in the duijiaoxian...
            // which means |x1-x2|==|y1-y2|
            if (queens[i] != 0
                    && (queens[i] == row || (Math.abs(i - col) == Math
                            .abs(queens[i] - row))))
                return false;
        }
        return true;
    }
}