Leetcode题解（７）L51/N-Queens

L51: 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.

For example,

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

[

　 [“.Q..”, // Solution 1

　 “…Q”,

　 “Q…”,

　 “..Q.”],

　 [“..Q.”, // Solution 2

　 “Q…”,

　 “…Q”,

　 “.Q..”]

]

解题思路：典型的回溯法，可用递归或非递归解决

class Solution {
public:
    bool isAttack(vector<int> queens, int k)
    {
        if(k == 0)
            return false;
        for (int i=0; i<k; i++)
        {
            if(queens[k] == queens[i] || abs(k-i) == abs(queens[k]-queens[i]))
                return true;
        }
        return false;
    }

    void showQueens(vector<int> queens, vector<vector<string> >& result){
        int n = queens.size();
        vector<string> vec(n, string(n,‘.‘));

        for(int i = 0; i < n; i++)
            vec[i][queens[i]] = ‘Q‘;

        result.push_back(vec);
    }

    vector<vector<string> > solveNQueens(int n) {
        vector<vector<string> > result;
        vector<int> queens(n,0);

        if(n == 1)
        {
            vector<string> vec(1, string(‘Q‘));
            result.push_back(vec);
            return result;
        }

        int i = 0;

        while(1)
        {
            while(i < n)
            {
                while(queens[i] == n)
                {
                    queens[i--] = 0;
                    if(i == -1)
                        return result;
                    queens[i]++;
                }
                if(isAttack(queens,i))
                    queens[i]++;
                else
                    i++;
            }
            showQueens(queens,result);

            queens[n-1] = 0;
            i = n-2;
            queens[i]++;
        }
    }
};