# 51. N-Queens

## 刷题内容

• https://leetcode.com/problems/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.


˼·1 **- ʱ�临�Ӷ�: O(2^n)*- �ռ临�Ӷ�: O(n)***

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class Solution {
public:
void travel(int* d,vector<string>& ret,int level,int n,vector<vector<string> >& ans,int* l,int* r)
{
if(level >= n)
ans.push_back(ret);
for(int i = 0;i < n;++i)
if(!d[i] && !r[level + i] && !l[i - level + n])
{
d[i] = 1;
r[level + i] = 1;
l[i- level + n] = 1;
ret[level][i] = 'Q';
travel(d,ret,level + 1,n,ans,l,r);
d[i] = 0;
r[level + i] = 0;
l[i- level + n] = 0;
ret[level][i] = '.';
}
}
vector<vector<string>> solveNQueens(int n) {
int d[n];
int l[2 * n];
int r[2 * n];
memset(d,0,sizeof(d));
memset(l,0,sizeof(l));
memset(r,0,sizeof(r));
vector<string> temp;
vector<vector<string> > ans;
string s(n,'.');
for(int i = 0;i < n;++i)
temp.push_back(s);
for(int i = 0;i < n;++i)
{
temp[0][i] ='Q';
d[i] = 1;
r[i] = 1;
l[i + n] = 1;
travel(d,temp,1,n,ans,l,r);
temp[0][i] = '.';
d[i] = 0;
r[i] = 0;
l[i + n] = 0;
}
return ans;
}
};


apachecn/AiLearning