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.."]
]

class Solution {
private:
std::vector<std::vector<std::string> > res;
public:
std::vector<std::vector<std::string> > solveNQueens(int n) {
std::vector<std::string>cur(n, std::string(n,'.'));
dfs(cur, 0);
return res;
}
void dfs(std::vector<std::string> &cur, int row)
{
if(row == cur.size())
{
res.push_back(cur);
return;
}
for(int col = 0; col < cur.size(); col++)
if(isValid(cur, row, col))
{
cur[row][col] = 'Q';
dfs(cur, row+1);
cur[row][col] = '.';
}
}

//推断cur[row][col]位置放置皇后。是否合法。
bool isValid(std::vector<std::string> &cur, int row, int col)
{
//列
for(int i = 0; i < row; i++)
if(cur[i][col] == 'Q')return false;
//右对角线
for(int i = row-1, j=col-1; i >= 0 && j >= 0; i--,j--)
if(cur[i][j] == 'Q')return false;
//左对角线
for(int i = row-1, j=col+1; i >= 0 && j < cur.size(); i--,j++)
if(cur[i][j] == 'Q')return false;
return true;
}
};