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 ‘.‘

Example:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

首先用了最直白最經典的方法，還是學計概的時候寫過的

 1 class Solution {
 2 public:
 3     bool valid(vector<string>a, int x, int y,int n) {
 4         int i = 1;
 5         while (x - i >= 0 && y - i >= 0) {
 6             if (a[x - i][y - i] == ‘Q‘)return false;
 7             i++;
 8         }
 9         i = 1;
10         while
 
(x-i>=0&&y+i<=n) {
11             if (a[x - i][y + i] == ‘Q‘)return false;
12             i++;
13         }
14         return true;
15     }
16     void build(vector<vector<string>>&ans,vector<string>now, int n, vector<bool>line,int row) {
17         if (row >= n) {
18             ans.push_back(now);
19             return;
20         }
21         for(int i=0;i<n;i++)
22             if (!line[i] && valid(now, row, i, n)) {
23                 now[row][i] = ‘Q‘;
24                 line[i] = true;
25                 build(ans, now, n, line, row + 1);
26                 line[i] = false;
27                 now[row][i] = ‘.‘;
28             }
29     }
30     vector<vector<string>> solveNQueens(int n) {
31         vector<vector<string>>ans;
32         string str = "";
33         for (int i = 0; i < n; i++)str += ‘.‘;
34         vector<string>now(n, str);
35         vector<bool>line(n, false);
36         build(ans, now, n, line, 0);
37         return ans;
38     }
39 };

當然非常慢

然後看了別人的帖子想起來還有用一維數組存圖的方法，但是還是很慢，用的方法和別人完全一樣但是慢了很多是怎麽回事……

 1 class Solution {
 2 public:
 3     bool valid(vector<int>a, int x, int y) {
 4         for (int i = 0; i < x; i++)
 5             if (y == a[i] || abs(a[i] - y) == x - i)
 6                 return false;
 7         return true;
 8     }
 9     void build(vector<vector<string>>&ans,vector<int>&now,int row) {
10         int n = now.size();
11         if (row == n) {
12             vector<string>res(n, string(n,‘.‘));
13             for (int i = 0; i < n; i++)
14                 res[i][now[i]] = ‘Q‘;
15             ans.push_back(res);
16             return;
17         }
18         for(int i=0;i<n;i++)
19             if (valid(now, row, i)) {
20                 now[row] = i;
21                 build(ans, now, row + 1);
22             }
23     }
24     vector<vector<string>> solveNQueens(int n) {
25         vector<vector<string>>ans;
26         vector<int>pos(n, -1);
27         build(ans,pos, 0);
28         return ans;
29     }
30 };

19.2.8 [LeetCode 51] N-Queens