51. N-Queens

来源：互联网发布：手机阿里云os登录编辑：程序博客网时间：2024/06/07 03:11

problem：

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.."]]

n皇后问题使用递归方法,对每行进行判断，如果可以就放置，如果不行则返回上一层

class Solution {  private:      vector<vector<string>>result;      bool check(int row,int col, int n,vector<string>m)//检测每行，每列，左右两个斜行      {          if (row == 0)              return true;          int i;          int j;          for (i = 0; i < row; i++)          {              if (m[i][col] == 'Q')                  return false;          }          i = row - 1;          j = col - 1;          while (i >= 0 && j >= 0)          {              if (m[i][j] == 'Q')                  return false;              i--;              j--;          }          i = row - 1;          j = col + 1;          while (i >= 0 && j < n)          {              if (m[i][j] == 'Q')                  return false;              i--;              j++;          }          return true;      }      void add(vector<string>m)      {          result.push_back(m);      }      void solve(int row,int n,vector<string>m)      {          int col;          if (row == n )//所有行已经全部放置          {              add(m);              return;          }          for (col = 0; col<n; col++)          {              if (check(row, col,n,m) == true)//查看row行col列              {                      m[row][col] = 'Q';//放置一枚Q                      solve(row + 1,n,m);//往下行继续递归放置                      m[row][col] = '.';//如果没有达到递归到返回条件，将之前放置的Q取消              }          }      }  public:      vector<vector<string>> solveNQueens(int n) {          vector<string>m(n,string(n,'.'));//Init          solve(0, n,m);          return result;      }  };

0 0