# N-Queens II

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

![](https://assets.leetcode.com/uploads/2018/10/12/8-queens.png)

Given an integer *n*, return the number of distinct solutions to the *n*-queens puzzle.

**Example:**

```
Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
```

```java
public class Solution {
    int count = 0;

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

    public void backtracking(int row, boolean[] columnMarker, boolean[] d1marker, boolean[] d2marker, int n) {
        if (row == n)
            count++;

        for (int col = 0; col < n; col++) {
            int id1 = col - row + n;
            int id2 = col + row;
            if (columnMarker[col] || d1marker[id1] || d2marker[id2])
                continue;

            columnMarker[col] = true;
            d1marker[id1] = true;
            d2marker[id2] = true;
            backtracking(row + 1, columnMarker, d1marker, d2marker, n);
            columnMarker[col] = false;
            d1marker[id1] = false;
            d2marker[id2] = false;
        }
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/recursion-and-backtracking/n-queens-ii.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.