51. N-Queens II

Follow up for N-Queens problem.

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

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跟50 -Queue思路一样

问题是那个不能用int total带入，而是int[] 即便是一位数组，

如果只是int作为参数，只是copy the value to the function, total本身没有变，

如果是int[], 相当吧variable's reference带入， 可以改变参数本身的值，

试过 Integer,也不行，所以用int[1]吧

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public class Solution {
    public int totalNQueens(int n) {
        
        int[] total = new int[1];
        int[] cols = new int[n];   
        placeQ(n, 0, cols, total);
        return total[0];
    }
    
    
    private void placeQ(int n, int r, int[] cols, int[] total){
        
        if(r == n){ //Found one!      
           total[0]++;
        
        }else{
            for(int c=0; c < n; c++){
                if(checkValid(cols,r,c)){// if Valid
                    cols[r] = c; // place a Q
                    placeQ(n, r+1, cols, total);// go to next row
                }
            }
        }
    }
    
    private boolean checkValid(int[] cols, int r1, int c1){
        for(int r2=0; r2<r1; r2++){
            int c2 = cols[r2];
            //check if at some col
            if(c2 == c1)    return false;
        }
        return true;
    }
}