As we ascend in our voyage through algorithmic mazes, we encounter a fundamental principle: abstraction. We've seen how mazes can be represented as grids, but what if our maze isn't neatly laid out on a 2D plane? What if it's a network of interconnected nodes, or a hierarchy of states? This is where the art of abstraction shines. By detaching the underlying data structure from the specific visualization or physical layout, we can create more general and powerful algorithms that can tackle a wider variety of problems.
Consider a simple maze solver algorithm, like Breadth-First Search (BFS). When we represented mazes as 2D arrays, our BFS algorithm operated on coordinates (row, column). But what if our maze is represented as a graph, where each location is a node and connections between locations are edges? The core logic of BFS – exploring level by level, keeping track of visited nodes and a queue of nodes to visit – remains the same. What changes is how we access neighbors and how we represent the 'current position'.
graph TD
A[Start Node] --> B{Check Neighbors};
B --> C[Add Unvisited Neighbors to Queue];
C --> D{Is Queue Empty?};
D -- No --> B;
D -- Yes --> E[End];
To adapt our BFS to a graph representation, we need a way to define our 'maze' abstractly. This involves thinking about what information our algorithm needs and what operations it needs to perform. At a minimum, our abstract maze should provide: 1. A way to get the starting point. 2. A way to get all valid neighbors of a given point. 3. A way to determine if a point is the goal. The underlying implementation of these can be anything – a list of adjacency lists for a graph, a set of interconnected objects, or even a function that generates neighbors dynamically.
class AbstractMaze {
getStart() {
throw new Error('getStart must be implemented');
}
getNeighbors(node) {
throw new Error('getNeighbors must be implemented');
}
isGoal(node) {
throw new Error('isGoal must be implemented');
}
}Now, let's look at a generic BFS algorithm that can work with any maze conforming to our AbstractMaze interface. The beauty here is that the bfs function itself doesn't need to know if it's solving a grid maze, a graph maze, or something entirely different. It just needs to interact with the maze through the defined abstract methods.