[leetcode] 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.."]
]

思路：深度搜索，属于经典问题了，定义两个数组，行数组和列数组，行数组用来存储该行摆放位置，列数组用来存储该列是否已经摆放过了，本代码参考了大神的代码
代码：

class Solution {
int row[1000],col[1000];
vector<vector<string> > res;
public:
vector<vector<string> > solveNQueens(int n) {
res.clear();
dfs(0,n);
return res;
}
void dfs(int step, int n){
int i,j;
if(step==n){
vector<string> rows;
for(i=0;i<n;i++){
string temp(n,'.');
temp[row[i]]='Q';
rows.push_back(temp);
}
res.push_back(rows);
}
for(i=0;i<n;i++){
if(col[i]==0){
for(j=0;j<step;j++){
if(abs(j-step)==abs(i-row[j])) break;//列之间的距离与行之间的距离相等；
}
if(j==step){
row[step]=i;
col[i]=1;
dfs(step+1,n);
row[step]=0;
col[i]=0;
}
}
}
}
};