> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# N-Queens II Python Solution with Tests

> Tested Python solution for LeetCode 52 with 11 pytest cases. Generate a practice environment with lcpy.

LeetCode 52, Hard. Topics: Backtracking. [View on LeetCode](https://leetcode.com/problems/n-queens-ii/description/).

Generate this problem as a practice environment: tested reference solution, 11 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 52   # by problem number
lcpy gen -s n_queens_ii   # by problem name
```

## Problem

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 *the number of distinct solutions to the **n-queens puzzle***.

### Examples

```
Input: n = 4
Output: 2

Explanation: There are two distinct solutions to the 4-queens puzzle as shown.
```

```
Input: n = 1
Output: 1
```

### Constraints

* `1 <= n <= 9`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/n_queens_ii/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/n_queens_ii/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n!)
    # Space: O(n)
    def total_n_queens(self, n: int) -> int:
        cols: set[int] = set()
        diag1: set[int] = set()
        diag2: set[int] = set()

        def backtrack(row: int) -> int:
            if row == n:
                return 1
            count = 0
            for col in range(n):
                if col in cols or (row - col) in diag1 or (row + col) in diag2:
                    continue
                cols.add(col)
                diag1.add(row - col)
                diag2.add(row + col)
                count += backtrack(row + 1)
                cols.remove(col)
                diag1.remove(row - col)
                diag2.remove(row + col)
            return count

        return backtrack(0)
```

## Complexity

| Time  | Space |
| ----- | ----- |
| O(n!) | O(n)  |

## Tags

[NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).