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[n],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;    }}