51. N-Queens 回溯算法浅谈

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.

代码分析：

这题更是典型的回溯算法，主要是加了一个向量用来存各个位置。不管怎样我都觉得回溯算法很神奇。

代码如下：

static int x[1000];

class Solution {

private:

    bool Place(int k)

    {

        for(int i=0;i<k;++i)

        {if((abs(i-k)==abs(x[i]-x[k]))||(x[i]==x[k])) return false;}

        return true;

    }

    void Backtrack(int t,int n,vector<string>q,vector< vector<string>>& v1,string s){

    if(t==n)

    {v1.push_back(q);}

    else

    {

        for(int i=0;i<n;++i)

        {

            string s1=s;

            s1[i]='Q';

            q.push_back(s1);

            x[t]=i;

            if(Place(t)) Backtrack(t+1,n,q,v1,s);

            q.pop_back();

        }

    }

}

public:

    vector<vector<string>> solveNQueens(int n) {

        vector< vector<string>> v1;

        vector<string> q;

        string s(n,'.');

        for(int i=0;i<n;++i)

        {

            x[0]=i;

            string s1=s;

            s1[i]='Q';

            q.push_back(s1);

            Backtrack(1,n,q,v1,s);

            q.pop_back();

        }

        return v1;

    }

};