19.2.8 [LeetCode 51] N-Queens

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.

Example:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

首先用了最直白最经典的方法，还是学计概的时候写过的

class Solution {
public:
    bool valid(vector<string>a, int x, int y,int n) {
        int i = 1;
        while (x - i >= 0 && y - i >= 0) {
            if (a[x - i][y - i] == 'Q')return false;
            i++;
        }
        i = 1;
        while(x-i>=0&&y+i<=n) {
            if (a[x - i][y + i] == 'Q')return false;
            i++;
        }
        return true;
    }
    void build(vector<vector<string>>&ans,vector<string>now, int n, vector<bool>line,int row) {
        if (row >= n) {
            ans.push_back(now);
            return;
        }
        for(int i=0;i<n;i++)
            if (!line[i] && valid(now, row, i, n)) {
                now[row][i] = 'Q';
                line[i] = true;
                build(ans, now, n, line, row + 1);
                line[i] = false;
                now[row][i] = '.';
            }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>>ans;
        string str = "";
        for (int i = 0; i < n; i++)str += '.';
        vector<string>now(n, str);
        vector<bool>line(n, false);
        build(ans, now, n, line, 0);
        return ans;
    }
};

当然非常慢

然后看了别人的帖子想起来还有用一维数组存图的方法，但是还是很慢，用的方法和别人完全一样但是慢了很多是怎么回事……

class Solution {
public:
    bool valid(vector<int>a, int x, int y) {
        for (int i = 0; i < x; i++)
            if (y == a[i] || abs(a[i] - y) == x - i)
                return false;
        return true;
    }
    void build(vector<vector<string>>&ans,vector<int>&now,int row) {
        int n = now.size();
        if (row == n) {
            vector<string>res(n, string(n,'.'));
            for (int i = 0; i < n; i++)
                res[i][now[i]] = 'Q';
            ans.push_back(res);
            return;
        }
        for(int i=0;i<n;i++)
            if (valid(now, row, i)) {
                now[row] = i;
                build(ans, now, row + 1);
            }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>>ans;
        vector<int>pos(n, -1);
        build(ans,pos, 0);
        return ans;
    }
};