Grid Traversal Basics

Why is called BFS or DFS when you traverse a grid? I am having difficulty understanding this concept.

Breadth-first search (BFS) and depth-first search (DFS) are not only applicable to trees or graphs but can also be applied to grids. When we apply these traversal techniques to grids, we typically think of each cell in the grid as a node, and the neighboring cells as connected nodes, which forms an implicit graph.

Let’s look at both methods in more detail:

  1. BFS: In breadth-first search, we start at a certain point (often referred to as the ‘source’) and then explore all the neighboring cells at the current ‘depth’ before moving on to cells at the next depth level. In a grid, the neighboring cells are typically those that are horizontally and vertically adjacent. This method can be used to find the shortest path in a grid from a source to a target, because it explores all possible paths in order of increasing length.

  2. DFS: In depth-first search, we start at the source and explore as far into the grid as possible along each branch before backtracking. This can be visualized as going down a straight path in the grid until you can’t go any further, and then you go back to the nearest point where you can choose a new path. DFS can be used to explore all possible paths through the grid, or to find a path from a source to a target without necessarily guaranteeing it will be the shortest path.

For example, consider a 2D grid used in a maze-solving algorithm. Each cell in the grid can be seen as a node. If the cell is open, we can travel from it to its adjacent cells. The adjacent cells (or ’nodes’) are usually to the north, south, east, and west of the current cell, assuming we can only move up, down, left, or right.

Overall, while grids are not explicitly graphs, we can treat them as such, which allows us to apply powerful graph traversal algorithms like BFS and DFS to solve a variety of problems.