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.."]]

public class Solution {    public List<String[]> solveNQueens(int n) {        ArrayList<String[]> result=new ArrayList<String[]>();        Integer []columns=new Integer[n];        placeQueens(0,n,columns,result);        return result;    }    //dfs    public void placeQueens(int row,int n,Integer[] columns,ArrayList<String[]> result){        if(row==n){            String[] arr=new String[n];            for(int i=0;i<n;i++){                StringBuffer sb=new StringBuffer();                for(int j=0;j<n;j++){                    if(columns[i]==j) sb.append("Q");                    else sb.append(".");                }                arr[i]=sb.toString();            }            result.add(arr);        } else {            for(int col=0;col<n;col++){                if(isValid(columns,row,col)){                    columns[row]=col;                    placeQueens(row+1,n,columns,result);                }            }        }    }    public boolean isValid(Integer[] columns,int row1,int column1){        for(int row2=0;row2<row1;row2++){            int column2=columns[row2];            //check column            if(column1==column2) return false;            //check duijiaoxian            int colDistance=Math.abs(column1-column2);            int rowDistance=row1-row2;            if(colDistance==rowDistance) return false;        }        return true;    }}