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.."]
]

Solution:

class Solution {
private:
vector<vector<string> > res;
vector<int> vi;

public:
bool isValued(int k)
{
for(int i = 0; i < k; ++i)
{
if(vi[i] == vi[k] || abs(vi[i] - vi[k]) == abs(i - k))
{
return false;
}
}

return true;
}

void dfs(int depth, int n)
{
if(depth == n)
{
vector<string> vs(n);
for(int i = 0; i < n; ++i)
{
string str(n, '.');
str[vi[i]] = 'Q';
vs[i] = str;
}
res.push_back(vs);
}
else
{
for(int i = 0; i < n; ++i)
{
vi[depth] = i;
if(isValued(depth)) dfs(depth + 1, n);
}
}
}

vector<vector<string>> solveNQueens(int n) {
vi.resize(n);
res.clear();
dfs(0, n);

return res;
}
};