N皇后解决方法

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.."]
]
思路：回溯法去遍历一遍。

#include<iostream>
#include<vector>
#include<string>
using namespace std;
class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>>res;
        vector<string> nQueens(n, string(n, '*'));
        solveNqueens(res, nQueens, 0, n);
        return res;
    }
    void solveNqueens(vector<vector<string>>&res, vector<string>&nQueens, int row, int &n)
    {
        if (row == n)
        {
            res.push_back(nQueens);
            //vector<string> tmp(n, string(n, '****'));
            //res.push_back(tmp);
            return;
        }
        for (int i = 0; i<n; i++)
        {
            if (isValid(nQueens, row, i, n))
            {
                nQueens[row][i] = 'Q';
                solveNqueens(res, nQueens, row + 1, n);
                nQueens[row][i] = '*';
            }
        }
    }
    bool isValid(vector<string>&nQueens, int row, int col, int n)
    {
        for (int i = 0; i<row; i++)
        {
            if (nQueens[i][col] == 'Q')return false;
        }
        for (int j = 0; j < col; j++)
        {
            if (nQueens[row][j] == 'Q')return false;
        }
        //check if the 45° diagonal had a queen before.
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; --i, --j)
        if (nQueens[i][j] == 'Q')
            return false;
        //check if the 135° diagonal had a queen before.
        for (int i = row - 1, j = col + 1; i >= 0 && j < n; --i, ++j)
        if (nQueens[i][j] == 'Q')
            return false;
        return true;
    }
};
int main()
{
    Solution a;
    vector<vector<string>>res = a.solveNQueens(4);
    for (int i = 0; i < res.size(); i++)
    {
        for (int j = 0; j < res[i].size(); j++)
            cout << res[i][j] <<endl;
        cout << endl;
    }
    cin.get();
    return 0;
}