# 51-n-queens


Try it on <a href='https://leetcode.com/problems/51-n-queens'>leetcode</a>

## Description
<div class="description">
<div><p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens' placement, where <code>'Q'</code> and <code>'.'</code> both indicate a queen and an empty space, respectively.</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;">
<pre><strong>Input:</strong> n = 4
<strong>Output:</strong> [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

<p><strong>Example 2:</strong></p>

<pre><strong>Input:</strong> n = 1
<strong>Output:</strong> [["Q"]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>
</div>
</div>

## Solution(Python)
```Python
class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        res = []
        for solution in self.queens(n, 0, [], [], []):
            board = [
                "".join("Q" if i == j else "." for i in range(len(solution)))
                for j in solution
            ]
            res.append(board)
        return res

    def queens(self, n, i, a, b, c):
        if i < n:
            for j in range(n):
                if j not in a and i + j not in b and i - j not in c:
                    yield from self.queens(n, i + 1, a + [j], b + [i + j], c + [i - j])
        else:
            yield a

```