N-Queens II

题目

Follow up for N-Queens problem.

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

方法

和上题方法一样，使用回溯法。结构基本同样。仅仅须要返回数量。

    public int totalNQueens(int n) {
        int[] queenAtCol = new int[n];
        int total = getNQueens(0, n, queenAtCol);
        return total;
    }
    public List<String[]> solveNQueens(int n) {
        List <String[]> list = new ArrayList<String[]>();

        return list;
    }
	private int getNQueens(int row, int n, int[] queenAtCol) {
		if (row == n) {
			return 1;
		} else {
			int tempSum = 0;
			for (int col = 0; col < n; col++) {
				if (isValid(row,col,queenAtCol)) {
					queenAtCol[row] = col;
					tempSum += getNQueens(row + 1, n, queenAtCol);
				}
			}
			return tempSum;
		}
	}
	
	private boolean isValid(int row, int col,int[] queenAtCol) {
		//row is valid.
		//column 
		for (int i = 0; i < row; i++) {
			if (queenAtCol[i] == col) {
				return false;
			}
		}
		
		for (int i = 0; i < row; i++) {
			if (i + queenAtCol[i] == row + col) {
				return false;
			}
		}
		
		for (int i = 0; i < row; i++) {
			if (col - row == queenAtCol[i] - i) {
				return false;
			}
		}
		return true;
	}