Snakes and Ladders

Snakes and Ladders

What is this problem about?

The "Snakes and Ladders" problem is a popular graph-traversal challenge that models the classic board game. You are given an $N \times N$ grid where some cells have "ladders" that take you to a higher-numbered cell and some have "snakes" that drop you to a lower-numbered one. The board is numbered in a "Boustrophedon" (snake-like) fashion, starting from the bottom-left and winding back and forth up to the top.

The goal is to find the minimum number of die rolls (each roll being 1 to 6) required to reach the last cell ($N^2$). This is essentially a shortest-path problem on an unweighted graph, where each cell is a node and each possible die roll is an edge to another node.

Why is this asked in interviews?

This question is a staple at companies like Apple, Microsoft, and Amazon because it evaluates a candidate's ability to model a real-world scenario as a graph problem. It requires careful mapping of the board's 1D numbers to 2D grid coordinates, which is notoriously tricky due to the winding "snake" pattern of the numbering. Furthermore, it tests proficiency with Breadth-First Search (BFS), the standard algorithm for finding the shortest path in an unweighted graph.

Algorithmic pattern used

The core algorithmic pattern is Breadth-First Search (BFS). BFS is ideal here because it explores all possible positions reachable in one move, then all positions reachable in two moves, and so on. The first time we reach the destination cell, we are guaranteed to have found the shortest path (minimum number of rolls). We also use a "visited" set to avoid redundant processing of the same board position.

Example explanation

Imagine a $6 \times 6$ board. You start at cell 1.

1. From cell 1, you can roll a die and land on cells 2 through 7.
2. If cell 4 has a ladder to cell 14, landing on 4 immediately moves you to 14.
3. In your BFS queue, you store (current_cell, moves). Initially, it's (1, 0).
4. In the first step, you explore all outcomes of one roll. One outcome is landing on 4, which jumps you to 14. Your queue now has (14, 1).
5. You continue this process until a tuple contains the destination cell (36).

Common mistakes candidates make

The most common mistake is failing to correctly map the 1D cell number to the 2D row and column, especially given the "Boustrophedon" numbering. Another error is not handling the "jump" correctly—if you land on a snake or ladder, you must take it, but you don't roll again from the intermediate landing spot in the same turn. Candidates also sometimes forget to use a visited array, leading to infinite loops if there's a cycle of snakes and ladders.

Interview preparation tip

To solve the "Snakes and Ladders interview question," focus on your BFS implementation. Practice mapping 1D indices to 2D grid coordinates for different types of board layouts. A good strategy is to write a helper function getCoords(num) to isolate this complexity. This makes your main BFS logic much cleaner and easier to debug during the interview.