LeetCode（51） N-Queens

题目

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:

分析

一个经典N皇后问题，这种棋盘类的题目一般是回溯法, 依次放置每行的皇后。要求在放置的时候，要保持当前的状态为合法，即当前放置位置的同一行、同一列、两条对角线上都不存在皇后。

多种解法请参考

AC代码

class Solution {
private:
    vector<vector<string> > ret;
public:
    vector<vector<string>> solveNQueens(int n) {
        if (n <= 0)
            return vector<vector<string>>();

        //二维字符矩阵，存储当前满足N皇后的解
        vector<string> cur(n, string(n, '.'));

        //调用主函数
        set_queens(cur, 0);
        return ret; 
    }

    void set_queens(vector<string> &cur, int row)
    {
        int size = cur.size();
        if (row == size)
        {
            ret.push_back(cur);
            return;
        }
        else{
            for (int col = 0; col < size; col++)
            {
                if (isValid(cur, row, col))
                {
                    cur[row][col] = 'Q';
                    //安置下一个皇后
                    set_queens(cur, row + 1);
                    cur[row][col] = '.';
                }//for
            }//for
        }
    }

    //判断在cur[row][col]位置放一个皇后，是否是合法的状态
    //已经保证了每行一个皇后，只需要判断列是否合法以及对角线是否合法。
    bool isValid(vector<string> &cur, int row, int col)
    {
        //判断是否同列
        for (int i = 0; i < row; i++)
        {
            if (cur[i][col] == 'Q')
                return false;
        }//for

        //判断是否同一左对角线
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; --i, --j)
        {
            if (cur[i][j] == 'Q')
                return false;
        }

        //判断是否同一右对角线
        for (int i = row - 1, j = col + 1; i >= 0 && j <= cur.size(); --i, ++j)
        {
            if (cur[i][j] == 'Q')
                return false;
        }

        return true;
    }
};

GitHub测试程序源码