# 0052. N-Queens II

https://leetcode.com/problems/n-queens-ii

## Description

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**_.

**Example 1:**

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

```
**Input:** n = 4
**Output:** 2
**Explanation:** There are two distinct solutions to the 4-queens puzzle as shown.
```

**Example 2:**

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

**Constraints:**

* `1 <= n <= 9`

## ac

[https://leetcode.com/problems/n-queens-ii/discuss/20048/Easiest-Java-Solution-(1ms-98.22](https://leetcode.com/problems/n-queens-ii/discuss/20048/Easiest-Java-Solution-\(1ms-98.22))

```java
public class Solution {
    int count = 0;
    public int totalNQueens(int n) {
        boolean[] cols = new boolean[n];     // columns   |
        boolean[] d1 = new boolean[2 * n];   // diagonals \
        boolean[] d2 = new boolean[2 * n];   // diagonals /
        backtracking(0, cols, d1, d2, n);
        return count;
    }

    public void backtracking(int row, boolean[] cols, boolean[] d1, boolean []d2, int n) {
        if(row == n) count++;

        for(int col = 0; col < n; col++) {
            int id1 = col - row + n;
            int id2 = col + row;
            if(cols[col] || d1[id1] || d2[id2]) continue;

            cols[col] = true; d1[id1] = true; d2[id2] = true;
            backtracking(row + 1, cols, d1, d2, n);
            cols[col] = false; d1[id1] = false; d2[id2] = false;
        }
    }
}
```
