# 51. N-Queens

#### Hard

***

The **n-queens** puzzle is the problem of placing `n` queens on an `n x n` chessboard such that no two queens attack each other.

Given an integer `n`, return *all distinct solutions to the **n-queens puzzle***. You may return the answer in **any order**.

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

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/11/13/queens.jpg)

```
Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
```

**Example 2:**

```
Input: n = 1
Output: [["Q"]]
```

 

**Constraints:**

* `1 <= n <= 9`

```python
class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        col = set()
        posDia = set()
        negDia = set()
        res = []
        board = [["."]*n for _ in range(n)]
        def backtrack(r):
            if r == n:
                copy = ["".join(row) for row in board]
                res.append(copy)
                return
            for c in range(n):
                if c in col or (r+c) in posDia or (r-c) in negDia:
                    continue
                # Found The Place for Queen
                col.add(c)
                posDia.add(r+c)
                negDia.add(r-c)
                board[r][c] = "Q"
                backtrack(r+1) # Do the backtrack for next row
                # Bactrack previous row Queen Position
                col.remove(c)
                posDia.remove(r+c)
                negDia.remove(r-c)
                board[r][c] = "."
        backtrack(0)
        return res
```