【leetcode刷题笔记】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.."]
]

1. private String[] PrintBoard(int n,List<Integer> cols)：当搜索到一个答案的时候，根据cols将棋盘打印成题目要求的字符串数组的格式；
2. private boolean isValid(List<Integer> cols,int col)：当前的棋盘状态记录在cols中，需要在第cols.size()行col列放置一个皇后，该函数检查这种放置是否合理；
3. private void QueenDfs(int n,int level,List<Integer> cols,List<String[]> result)：深度优先搜索函数，level表示当前搜索到第level行，当level==n的时候，完成一次搜索；否则尝试将皇后放置在level行的0~n-1列，用isValid函数判断是否合理，如果合理，就放置皇后，并继续递归搜索棋盘下一行皇后放置的位置。
4. public List<String[]> solveNQueens(int n)：直接调用QueenDfs函数完成搜索。

代码如下：

 1 public class Solution {
 2     private String[] PrintBoard(int n,List<Integer> cols){
 3         String[] answer= new String[n];
 4         for(int i = 0;i < n;i++){
 5             StringBuffer temp = new StringBuffer();
 6             for(int j = 0;j < n;j ++){
 7                 temp.append(j == cols.get(i) ? "Q":".");
 8             }
 9             answer[i] = temp.toString();
10         }
11
12         return answer;
13     }
14     private boolean isValid(List<Integer> cols,int col){
15         for(int i = 0;i < cols.size();i++){
16             if(cols.get(i) == col)
17                 return false;
18             if(cols.size() - i == Math.abs(cols.get(i) - col))
19                 return false;
20         }
21         return true;
22     }
23     private void QueenDfs(int n,int level,List<Integer> cols,List<String[]> result){
24         if(level == n){
25             String[] s = PrintBoard(n,cols);
26             result.add(s);
27             return;
28         }
29
30         for(int i = 0;i < n;i++){
31             if(isValid(cols, i)){
32                 cols.add(i);
33                 QueenDfs(n, level+1, cols,result);
34                 cols.remove(cols.size()-1);
35             }
36         }
37     }
38     public List<String[]> solveNQueens(int n) {
39         List<String[]> result = new ArrayList<String[]>();
40         List<Integer> cols = new ArrayList<Integer>();
41         QueenDfs(n, 0, cols, result);
42
43         return result;
44     }
45 }

【leetcode刷题笔记】N-Queens