In today's lesson, we examine the specifics of a crucial tree traversal algorithm: Depth-first Search (DFS). So far in this course, we have emphasized the importance of tree structures in computer science and analyzed the underlying complexities of both binary and non-binary trees. We are now ready to explore an essential tree traversal strategy — the DFS algorithm on trees.
Before moving forward, let's set a clear roadmap for our journey. By the end of this lesson, you will have a thorough understanding of the mechanics of DFS and its application to trees. We will guide you through vivid examples and step-by-step Python code, transforming your theoretical knowledge of DFS into practical skills. Eventually, in our hands-on section, you will put your skills to the test on the CodeSignal IDE, solidifying your growing mastery over the DFS algorithm.
Let's delve into this exciting realm of algorithmic exploration!
How would you explore an uncharted forest? Where would you begin? Would you inspect each pathway at ground level before climbing a tree, or would you ascend the first tree you encounter, climbing as high as possible before descending? The latter approach mirrors the strategy that the Depth-first Search (DFS) algorithm uses when exploring trees or graphs.
Essentially, DFS is a tree traversal technique that seeks to explore as far down a pathway (or to as great a depth) as possible before returning (or backtracking). Instead of splitting its focus over multiple pathways concurrently, DFS concentrates on exploring one pathway as thoroughly as possible before retreating to explore other pathways. Here's another real-world analogy for DFS: consider how you might navigate a labyrinth; you'd follow a twisting, turning path to its end before backtracking to explore another path. This principle lies at the heart of DFS — explore the depth before the breadth!
A journey of a thousand miles begins with a single step. For DFS, that first step is the root node of the tree (or an arbitrary node chosen as the root when dealing with a graph). Let's closely examine the stages involved in conducting a DFS:
