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.."]
]

解法简单，贪心算法，从第1行到第n行遍历，每次保证不会被前面的皇后杀到，如果能遍历到最后一行，就代表当前的解法可行。这里需要设置一个n长的标志数组，存放皇后所在的位置，用于检测后面放置的皇后是否会被杀到。从下图可以看到，这种解法的时间复杂度不高。

Java代码：

public class Solution{
    public List<String[]> solveNQueens(int n) {
        int []flag = new int[n];
        for(int i = 0; i < n; i ++){
            flag[i] = -1;
        }
        List<String[]> result = new ArrayList<String[]>();
        for(int i = 0; i < n; i ++){
            flag[0] = i;
            queens(n, 1, flag, result);
        }
        return result;
    }
    public void queens(int n, int curRow, int []flag, List<String[]> result)
    {
        if(curRow == n){
            String []solution = new String[n];
            for(int i = 0; i < n; i ++){
                String rowSol = "";
                for(int j = 0;j < n; j ++){
                    if(flag[i] != j){
                        rowSol += '.';
                    }else{
                        rowSol += 'Q';
                    }
                }
                solution[i] = rowSol;
            }
            result.add(solution);
            return;
        }
        for(int i = 0; i < n; i ++){
            int j = 0;
            for(; j < curRow;j++){
                if((i == flag[j]) || (i == flag[j] + (curRow - j)) || (i == flag[j] - (curRow - j))){
                    break;
                }
            }
            if(j == curRow){
                flag[curRow] = i;
                queens(n, curRow + 1, flag, result);
            }
        }
    }
}