n皇后问题的递归和迭代版 leetcode N-Queens

题目如下图：

递归版

class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<int> dict(n, 0);

        dfs(0, dict, n);

        return res;
    }

private:
    void dfs(int cur, vector<int> & dict, int n)
    {
        if (cur == n)
        {
            fillRes(dict);
            return;
        }
        for (int i = 0; i < n; i++)
        {
            dict[cur] = i;
            if (check(dict, cur))
                dfs(cur + 1, dict, n);
        }
    }

    void fillRes(vector<int> & dict)
    {
        vector<string> tmp;
        for (int i = 0; i < dict.size(); i++)
        {
            string s(dict.size(), ‘.‘);
            s[dict[i]] = ‘Q‘;
            tmp.push_back(s);
        }

        res.push_back(tmp);
    }

    bool check(vector<int> & dict, int cur)
    {
        for (int i = 0; i < cur; i++)
        {
            if (dict[i] == dict[cur] || abs(dict[cur] - dict[i]) == abs(cur - i))
                return false;

        }
        return true;
    }
    vector<vector<string>> res;
};

迭代版

class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> res;
        vector<int> nums(n, 0);

        int cur = 0;
        while (cur >= 0)
        {
            if (check(nums, cur))
                cur = cur + 1;
            else
            {
                int carry = 1;
                for (; cur >= 0 && carry != 0;)
                {
                    nums[cur] += carry;
                    if (nums[cur] == n)
                    {
                        nums[cur--] = 0;
                        carry = 1;
                    }
                    else
                    {
                        carry = 0;
                    }

                }
            }
            if (cur == n)
            {
                fillRes(res, nums);
                int carry = 1;
                for (cur--; cur >= 0 && carry != 0;)
                {
                    nums[cur] += carry;
                    if (nums[cur] == n)
                    {
                        nums[cur--] = 0;
                        carry = 1;
                    }
                    else
                    {
                        carry = 0;
                    }
                }
            }
        }

        return res;
    }

private:
    void fillRes(vector<vector<string>> & res, vector<int> & dict)
    {
        vector<string> tmp;
        for (int i = 0; i < dict.size(); i++)
        {
            string s(dict.size(), ‘.‘);
            s[dict[i]] = ‘Q‘;
            tmp.push_back(s);
        }

        res.push_back(tmp);
    }

    bool check(vector<int> & dict, int cur)
    {
        for (int i = 0; i < cur; i++)
        {
            if (dict[i] == dict[cur] || abs(dict[cur] - dict[i]) == abs(cur - i))
                return false;

        }
        return true;
    }
};