[LeetCode] N-Queens N皇后问题

时间:2022-04-10 11:07:34

 

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

[LeetCode] N-Queens N皇后问题

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.."]
]

 

经典的N皇后问题,基本所有的算法书中都会包含的问题,经典解法为回溯递归,一层一层的向下扫描,需要用到一个pos数组,其中pos[i]表示第i行皇后的位置,初始化为-1,然后从第0开始递归,每一行都一次遍历各列,判断如果在该位置放置皇后会不会有冲突,以此类推,当到最后一行的皇后放好后,一种解法就生成了,将其存入结果res中,然后再还会继续完成搜索所有的情况,代码如下:

 

class Solution {
public:
    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string> > res;
        vector<int> pos(n, -1);
        solveNQueensDFS(pos, 0, res);
        return res;
    }
    void solveNQueensDFS(vector<int> &pos, int row, vector<vector<string> > &res) {
        int n = pos.size();
        if (row == n) {
            vector<string> out(n, string(n, '.'));
            for (int i = 0; i < n; ++i) {
                out[i][pos[i]] = 'Q';
            }
            res.push_back(out);
        } else {
            for (int col = 0; col < n; ++col) {
                if (isValid(pos, row ,col)) {
                    pos[row] = col;
                    solveNQueensDFS(pos, row + 1, res);
                    pos[row] = -1;
                }
            }
        }
    }
    bool isValid(vector<int> &pos, int row, int col) {
        for (int i = 0; i < row; ++i) {
            if (col == pos[i] || abs(row - i) == abs(col - pos[i])) {
                return false;
            }
        }
        return true;
    }
};

 

此题还有非递归的解法,请参见网友JustDoIt的博客

 

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