52. N-Queens II

weixin_30751947

于 2019-07-25 20:49:00 发布

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原文链接：http://www.cnblogs.com/forPrometheus-jun/p/11246876.html

本文详细解析了八皇后问题的求解算法，采用递归回溯的方法，通过判断每个皇后放置位置的合法性来寻找所有可能的解决方案。示例中展示了4皇后问题的两种解，并提供了完整的C++代码实现。

description:

八皇后
Note:

Example:

Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

answer:

class Solution {
public:
    int totalNQueens(int n) {
        int res = 0;
        vector<int> pos(n, -1);
        helper(pos, 0, res);
        return res;
    }
    void helper(vector<int>& pos, int row, int& res) {
        int n = pos.size();
        if (row == n) ++res;
        for (int col = 0; col < n; ++col) {
            if (isValid(pos, row, col)) {
                pos[row] = col;
                helper(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;
    }
};