【leetcode】N-Queens I & II

II:

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

 

问题是求N皇后的解，可以采用回溯法解决。 

 

class Solution {
public:

bool isSafe(vector<int> &A,int r){
    for(int i=0;i<r;i++){
        if((A[i]==A[r])||(abs(A[i]-A[r]))==(r-i))
            return false;
    }
    return true;
}

void queen(int n,int &result,int cur,vector<int> &A){
    if(cur==n){
        result++;
        return ;
    }else{
        for(int i=0;i<n;i++){
            A[cur]=i;
            if(isSafe(A,cur))
                queen(n,result,cur+1,A);
        }
    }
}

    int totalNQueens(int n) {
        int result=0;
        vector<int> A(n,-1);
        queen(n,result,0,A);
        return result;
    }
};

 

 

I:

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.

For example,
There exist two distinct solutions to the 4-queens puzzle:

[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],

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

 

class Solution {
public:
    void printQueen(vector<int> &A,int n,vector<vector<string> >&res)
    {
        vector<string> r;
        for(int i=0;i<n;i++)
        {
            string str(n,'.');
            str[A[i]]='Q';
            r.push_back(str);
        }
        res.push_back(r);
    }
    bool isValidQueens(vector<int>A,int r)
    {
        for(int i=0;i<r;i++)
        {
            if((A[i]==A[r])||(abs(A[i]-A[r]))==(r-i))
                return false;
        }
        return true;
    }
    void nqueens(vector<int> A,int cur,int n,vector<vector<string> >&res)
    {
        if(cur==n)
        {
            printQueen(A,n,res);
        }else{
            for(int i=0;i<n;i++)
            {
                A[cur]=i;
                if(isValidQueens(A,cur))
                    nqueens(A,cur+1,n,res);
            }
        }
    }

    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string> >res;
        res.clear();
        vector<int> A(n,-1);
        nqueens(A,0,n,res);
        return res;
    }
};