leetcode--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.."]
]


dfs method.

public class Solution {
    public List<String[]> solveNQueens(int n) {
       List<String[]> placement = new ArrayList<String[]>();
		if(n == 1){
			placement.add(new String[]{"Q"});
	        return placement;
	    }
		if(n >= 4){
			List<Integer> position = new ArrayList<Integer>();
			dfs(n, 0, position, placement);
		}
		return placement;	
	}
		
	private boolean dfs(int n, int row, List<Integer> position, List<String[]> placement){
		if(row == n) return true; 
		for(int i = 0; i < n; ++i) {
			if(isValidPosition(row * n + i, position, n)){
				position.add(row * n + i);
				if(dfs(n, row + 1, position, placement))
					generateSolution(position,placement, n);
				position.remove(row);
			}
		}
		return false;
	}
		
	private boolean isValidPosition(int k, List<Integer> position, int n){
		for(int i = 0; i < position.size(); ++i){
			if( k % n == position.get(i) % n || Math.abs( k % n - position.get(i) % n) == k / n - i) 
				return false;
		}
		return true;
	}
		
	private void generateSolution(List<Integer> position, List<String[]> placement, int n){
		char[] oneRow = new char[n];
		for(int i = 0; i < n; ++i)
			oneRow[i] = '.';
		String[] oneSolution = new String[n];
		for(int i = 0; i < n; ++i){
			oneRow[position.get(i) % n] = 'Q';
			oneSolution[i] = new String(oneRow);
			oneRow[position.get(i) % n] = '.';
		}
		placement.add(oneSolution);     
    }
}