LeetCode: 【L4】N-Queens 解题报告

 1 public class Solution {
 2     public List<String[]> solveNQueens(int n) {
 3         List<String[]> ret = new ArrayList<String[]>();
 4         
 5         if (n == 0) {
 6             return ret;
 7         }
 8         
 9         dfs(n, new ArrayList<Integer>(), ret);
10         return ret;
11     }
12     
13     public String[] createSolution(ArrayList<Integer> path) {
14         /*
15         [
16          [".Q..",  // Solution 1
17           "...Q",
18           "Q...",
19           "..Q."],
20         
21          ["..Q.",  // Solution 2
22           "Q...",
23           "...Q",
24           ".Q.."]
25         ]
26         */
27         int size = path.size();
28         String[] ret = new String[size];
29         
30         for (int i = 0; i< size; i++) {
31             StringBuilder sb = new StringBuilder();
32             for (int j = 0; j < size; j++) {
33                 // a queen.
34                 if (j == path.get(i)) {
35                     sb.append(‘Q‘);
36                 } else {
37                     sb.append(‘.‘);
38                 }
39             }
40             
41             ret[i] = sb.toString();
42         }
43         
44         return ret;
45     }
46     
47     //ArrayList<Integer> path: store the index of the columns of one solution.
48     public void dfs(int n, ArrayList<Integer> path, List<String[]> ret) {
49         if (path.size() == n) {
50             String[] solution = createSolution(path);
51             ret.add(solution);
52             return;
53         }
54         
55         for (int i = 0; i < n; i++) {
56             // Judge if this is a solution;
57             if (!isValid(path, i)) {
58                 continue;
59             }
60             
61             path.add(i);
62             dfs(n, path, ret);
63             path.remove(path.size() - 1);
64         }
65     }
66     
67     public boolean isValid(ArrayList<Integer> path, int index) {
68         int size = path.size();
69         for (int i = 0; i < size; i++) {
70             // Same column as one queen.
71             if (index == path.get(i)) {
72                 return false;
73             }
74             
75             // 在两条对角线之上
76             // bug 3: 少一个)
77             if (size - i == Math.abs(index - path.get(i))) {
78                 return false;
79             }
80         }
81         
82         return true;
83     }
84 }