题目
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.."]
]
解析
// add 51. N-Queens
class Solution_51 {
public:
bool isValid(vector<string> &vec,int i,int j)
{
//判断当前放置位置（i，j）是否合理
for (int row = 0; row < i;row++) //判断同一列列
{
if (vec[row][j]=='Q') // vec[i][j]
{
return false;
}
}
//判断对角线45°
for (int row = i-1, col = j-1; row >= 0 && col>=0;row--,col--)
{
if (vec[row][col] == 'Q')
{
return false;
}
}
//判断对角线135%
for (int row = i-1, col = j + 1; row >= 0 && col < vec.size();row--,col++) //写法： row >= 0, col < vec.size() 错误
{
if (vec[row][col] == 'Q')
{
return false;
}
}
return true;
}
void solveNQueensHelp(vector<vector<string>> &vecs,vector<string> &vec,int row,int n)
{
if (row==n)
{
vecs.push_back(vec);
return;
}
for (int col = 0; col < n;col++)
{
if (isValid(vec,row,col))
{
vec[row][col] = 'Q';
solveNQueensHelp(vecs, vec, row + 1, n);
vec[row][col] = '.';
}
}
return;
}
vector<vector<string>> solveNQueens(int n) {
vector<string> vec(n,string(n,'.'));
vector<vector<string> > vecs; //所有解
solveNQueensHelp(vecs,vec,0,n);
return vecs;
}
};
题目来源
