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]++;        }    }};