[LeetCode][JavaScript]N-Queens

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.."]
]

https://leetcode.com/problems/n-queens/

不就是dfs嘛。

一行行地做dfs。每一轮先找这一行有哪些地方可以放Queen，把这些点置成Q，循环递归这些点，最后不要忘记把默认值‘.‘写回去。

如果到了最后一行，并且可以放得下Queen，这就是一个正确的解。

因为每一行只能放一个，如果遇到放不下的情况，说明已经错了。

找行上的候选人的时候，第一眼看上去要找8个方向。

但首先，行上就不用找了，列方向上和2个斜的方向上只需要找上半部分，因为下面都没开始放Q，肯定不冲突的。

因为js没有二维数组，写了2个方法构造数组，所以看上去代码很长...

 1 /**
 2  * @param {number} n
 3  * @return {string[][]}
 4  */
 5 var solveNQueens = function(n) {
 6     var map = [];
 7     var result = [];
 8     buildMap();
 9     dfs(0);
10     return result;
11
12     function dfs(row){
13         var i = 0, j = 0;
14         var candidates = [];
15         for(i = 0; i < n; i++){
16             if(canPlaceQueen(row, i)){
17                 candidates.push(i);
18             }
19         }
20         if(row === n -1 && candidates.length !== 0){ //found
21             map[row][candidates[0]] = ‘Q‘;
22             result.push(formatMap(map));
23             map[row][candidates[0]] = ‘.‘;
24             return;
25         }
26         for(i = 0; i < candidates.length; i++){
27             map[row][candidates[i]] = ‘Q‘;
28             dfs(row + 1);
29             map[row][candidates[i]] = ‘.‘;
30         }
31     }
32     function canPlaceQueen(x, y){
33         var cell = "";
34         var i = 0, j = 0;
35         for(i = 0; i < n; i++){
36             cell = map[i][y];
37             if(cell === ‘Q‘){
38                 return false;
39             }
40         }
41         for(i = x, j = y; i >=0 && j >= 0; i--, j--){
42             cell = map[i][j];
43             if(cell === ‘Q‘){
44                 return false;
45             }
46         }
47         for(i = x, j = y; i >=0 && j < n; i--, j++){
48             cell = map[i][j];
49             if(cell === ‘Q‘){
50                 return false;
51             }
52         }
53         return true;
54     }
55     function buildMap(){
56         var i = 0, j = 0;
57         for(i = 0; i < n; i++){
58             map[i] = [];
59         }
60         for(i = 0; i < n; i++){
61             for(j = 0; j < n; j++){
62                 map[i][j] = ‘.‘;
63             }
64         }
65     }
66     function formatMap(map){
67         var res = [];
68         var i = 0, j = 0;
69         for(i = 0; i < n; i++){
70             var tmp = "";
71             for(j = 0; j < n; j++){
72                 tmp += map[i][j];
73             }
74             res.push(tmp);
75         }
76         return res;
77     }
78 };