Java for LeetCode 052 N-Queens II

Follow up for N-Queens problem.

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

解题思路：和上题一样《JAVA语言程序设计》中exerice6-22已经给出了计算count的代码，直接拿来用即可，JAVA实现如下：

static public int totalNQueens(int n) {
	 if(n==1)
		 return 1;
	 int count = 0; 
	    int[] queens = new int[n]; // queens are placed at (i, queens[i])
	    for (int i = 0; i < n; i++)
	      queens[i] = -1; 
	    queens[0] = 0; 
	    int k = 1;
	    while (k >=0) {
	      int j = findPosition(k, queens,n);
	      if (j ==-1) {
	        queens[k] = -1;
	        k--; // back track to the previous row
	      } else {
	        queens[k] = j;
	        if (k == n-1) 
	          count++;  
	        else {
	          k++;
	        }
	      }
	    }
     return count; 
  }
  public static int findPosition(int k, int[] queens,int n) {
    int start = queens[k] == -1 ? 0 : queens[k] + 1;
    for (int j = start; j < n; j++) {
      if (isValid(k, j, queens,n))
        return j; 
    }
    return -1;
  }

  public static boolean isValid(int k, int j, int queens[],int n) {
    for (int i = 0; i < k; i++)
      if (queens[i] == j)
        return false;
    for (int row = k - 1, column = j - 1; row >= 0 && column >= 0; row--, column--)
      if (queens[row] == column)
        return false;
    for (int row = k - 1, column = j + 1; row >= 0 && column <= n-1; row--, column++)
      if (queens[row] == column)
        return false;
    return true;
  }