N-Queens

N-Queens

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.



Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 

'Q'

 and 

'.'

 both
indicate a queen and an empty space respectively.

For example,

There exist two distinct solutions to the 4-queens puzzle:

[
[".Q..",  // Solution 1
"...Q",
"Q...",
"..Q."],

["..Q.",  // Solution 2
"Q...",
"...Q",
".Q.."]
]

Solution 

This problem is kind of difficult to solve. The general thought is that for every row, we use a loop to put queen
to each column. If the queens do not attack each other, entering next row recursively. This solution refers to the Code Gankers' blog http://blog.csdn.net/linhuanmars/article/details/20667175

1. keep an array to store the queen column position for every row. For example, for the 4-queens puzzle, we have
two solutions. For the first solution, the array should be [1,3,0,2] and for the second solution, the array should be [2,0,3,1].

2. For the queen column position for each row, we need to check whether the position is valid to put the queen.
For example, if the array is [1,1,0,2], it is invalid, because two queens appear at the same column. For another example, [2,3,3,1] is also invalid, because for the first row and second row, the two queens share the same diagonal. We need a private method
to check whether the column position is valid or not.

public class Solution {
public List<List<String>> solveNQueens(int n) {
List<List<String>> ret = new ArrayList<List<String>>();

helper(n,0,new int
,ret);
return ret;
}

private void helper(int n, int row, int[] columnForRow, List<List<String>> ret) {
if (n == row) {
ArrayList<String> list = new ArrayList<String>();;
for (int i = 0; i < n; i++) {
StringBuilder sb = new StringBuilder();
for (int j = 0; j < n; j++) {
if (columnForRow[i] == j)
sb.append("Q");

else
sb.append(".");
}
list.add(sb.toString());
}

ret.add(list);
return;
} else {
for (int i = 0; i < n; i++) {
columnForRow[row] = i;

if (check(row, columnForRow)) {
helper(n, row + 1, columnForRow, ret);
}
}
}
}

private boolean check(int row, int[] columnForRow) {
for (int i = 0; i < row; i++) {
if (columnForRow[i] == columnForRow[row] || Math.abs(columnForRow[i] - columnForRow[row]) == row - i)
return false;
}

return true;
}
}