> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/graphs-bfs-and-dfs/snakes-and-ladders.md).

# Snakes and Ladders

On an N x N `board`, the numbers from `1` to `N*N` are written *boustrophedonically* **starting from the bottom left of the board**, and alternating direction each row.  For example, for a 6 x 6 board, the numbers are written as follows:

![](/files/-M97iTkTxNHOBIqvtpoD)

You start on square `1` of the board (which is always in the last row and first column).  Each move, starting from square `x`, consists of the following:

* You choose a destination square `S` with number `x+1`, `x+2`, `x+3`, `x+4`, `x+5`, or `x+6`, provided this number is `<= N*N`.
  * (This choice simulates the result of a standard 6-sided die roll: ie., there are always **at most 6 destinations, regardless of the size of the board**.)
* If `S` has a snake or ladder, you move to the destination of that snake or ladder.  Otherwise, you move to `S`.

A board square on row `r` and column `c` has a "snake or ladder" if `board[r][c] != -1`.  The destination of that snake or ladder is `board[r][c]`.

Note that you only take a snake or ladder at most once per move: if the destination to a snake or ladder is the start of another snake or ladder, you do **not** continue moving.  (For example, if the board is \`\[\[4,-1],\[-1,3]]\`, and on the first move your destination square is \`2\`, then you finish your first move at \`3\`, because you do **not** continue moving to \`4\`.)

Return the least number of moves required to reach square N\*N.  If it is not possible, return `-1`.

**Example 1:**

```
Input: [
[-1,-1,-1,-1,-1,-1],
[-1,-1,-1,-1,-1,-1],
[-1,-1,-1,-1,-1,-1],
[-1,35,-1,-1,13,-1],
[-1,-1,-1,-1,-1,-1],
[-1,15,-1,-1,-1,-1]]
Output: 4
Explanation: 
At the beginning, you start at square 1 [at row 5, column 0].
You decide to move to square 2, and must take the ladder to square 15.
You then decide to move to square 17 (row 3, column 5), and must take the snake to square 13.
You then decide to move to square 14, and must take the ladder to square 35.
You then decide to move to square 36, ending the game.
It can be shown that you need at least 4 moves to reach the N*N-th square, so the answer is 4.
```

**Note:**

1. `2 <= board.length = board[0].length <= 20`
2. `board[i][j]` is between `1` and `N*N` or is equal to `-1`.
3. The board square with number `1` has no snake or ladder.
4. The board square with number `N*N` has no snake or ladder.

```java
class Solution {
    int n;

    public int snakesAndLadders(int[][] board) {
        n = board.length;
        boolean[] visited = new boolean[n * n + 1];
        Queue<Integer> queue = new LinkedList<>();
        queue.offer(1);
        visited[1] = true;
        int step = 1;
        while (!queue.isEmpty()) {
            int size = queue.size();
            for (int k = 0; k < size; k++) {
                int cur = queue.poll();
                for (int i = 1; i <= 6; i++) {
                    int next = cur + i;
                    int[] pos = numToPos(next);
                    if (board[pos[0]][pos[1]] > 0) {
                        next = board[pos[0]][pos[1]];
                    }
                    if (next == n * n) {
                        return step;
                    }
                    if (!visited[next]) {
                        queue.offer(next);
                        visited[next] = true;
                    }
                }
            }
            step++;
        }
        return -1;
    }

    private int[] numToPos(int target) {
        int row = (target - 1) / n, col = (target - 1) % n;
        int x = n - 1 - row, y = row % 2 == 0 ? col : n - 1 - col;
        return new int[] { x, y };
    }
}
```


---

# 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/graphs-bfs-and-dfs/snakes-and-ladders.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.