图搜索-DFS-N皇后(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.

非常典型的回溯问题，需要注意的点：
1、剪枝（确定性优化：不需要的就砍掉）；
2、A*（不确定性优化：改变搜索顺序，不改变搜索的结果，不一定更优）;
3、DFS限制搜索长度，探测长度寻找最优解—>判定问题.

    //记录每列走第几行    public static int[] path= new int[100];    public static List<List<String>> res = new ArrayList<>();    //记录历史上走过的行    public static boolean[] row = new boolean[100];    //辅助判断对角线是否被走过,例如 x+y=k,记录所有已走的 x+y的和,不能有两个点该和相同,例如 colIdx +    public static boolean[] diagonal = new boolean[100];    //辅助判断反对角线是否被走过,例如 y = x + colIdx - i, 记录所有已走的 x + colIdx = y + i 的点的值,    //例如 colIdx - i + n -1 为避免负数    public static boolean[] reverse = new boolean[100];    public List<List<String>> solveNQueens(int n) {        res.clear();        dfs(0,n);        return res;    }    public void dfs(int colIdx, int n){        if(colIdx >= n){            //根据 path 信息记录该组结果,之后返回好进行其它结果的回溯探测            List<String> chess = new ArrayList<String>();            for(int i = 0 ;i < n; i++) {                String tmpRow = "";                for (int j = 0; j < n; j++) {                    if (path[i] == j)                        tmpRow += 'Q';                    else tmpRow += '.';                }                chess.add(tmpRow);            }            res.add(chess);            return;        }        //对某一列而言,任意行都有可能走        for(int i = 0 ; i < n; i++){            if(!row[i] && !diagonal[colIdx + i] && !reverse[colIdx - i + n -1]){                path[colIdx] = i;                row[i] = true;                diagonal[colIdx + i] = true;                reverse[colIdx - i + n -1] = true;                dfs(colIdx+1,n);                row[i] = false;                diagonal[colIdx + i] = false;                reverse[colIdx - i + n -1] = false;            }        }    }