N-Queens.txt

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.."]
]
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bool check(int row, int *place)
{
	for(int i = 0; i < row; ++i)
	{
		int diff = abs(place[i] - place[row]);
		if(diff == 0 || diff == row - i)
			return false;
	}
	return true;
}

void placeQueens(int row, int n, int *place, vector<vector<string> > &ret)
{
	if(row == n)
	{
		vector<string> tmp;
		for(int i = 0; i < row; ++i)
		{
			string s(n, '.');
			s[place[i]] = 'Q';
			tmp.push_back(s);
		}
		ret.push_back(tmp);
		return;
	}
	for(int i = 0; i < n; ++i)
	{
		place[row] = i;
		if(check(row, place))
			placeQueens(row + 1, n, place, ret);
	}
}

vector<vector<string> > solveNQueens(int n)
{
	vector<vector<string> > ret;
	int *place = new int[n];
	placeQueens(0, n, place, ret);
	return ret;
}