leetcode---N-Queens---回溯

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 {
public:
vector<vector<string>> ans;

bool ok(int depth, int col, int n, vector<string> &tmp)
{
int sum = col + depth;
int c = 0;
for(int i=0; i<depth; i++)
{
c = depth - i;
if(tmp[i][col] == 'Q' || tmp[i][sum-i] == 'Q' || tmp[i][col-c] == 'Q')
return false;
}
return true;
}

void dfs(int depth, vector<string> &tmp, int n)
{
if(depth >= n)
{
ans.push_back(tmp);
return;
}
for(int j=0; j<n; j++)
{
tmp[depth][j] = 'Q';
if(ok(depth, j, n, tmp))
dfs(depth+1, tmp, n);
tmp[depth][j] = '.';
}
}

vector<vector<string>> solveNQueens(int n)
{
vector<string> tmp;
for(int i=0; i<n; i++)
{
string s = "";
for(int j=0; j<n; j++)
s += '.';
tmp.push_back(s);
}
dfs(0, tmp, n);
return ans;
}
};