Introduction to Depth First Search In a Graph

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Welcome to the world of graphs! Graphs are data structures used to represent connections between things, like friendships between different people on social media, road networks connecting cities, or links between web pages. Often, we need ways to explore these connections systematically and Depth First Search (DFS) is one of the fundamental methods for doing just that. It’s a powerful technique used in many computing problems, and understanding it opens the door to solving complex challenges involving connected data. This article will introduce you to the basic idea behind Depth First Search in a simple, easy-to-understand way.

Tip

If you’re new to graphs, think of them simply as a collection of points (called nodes or vertices) connected by lines (called edges). You can learn more about graphs here: Introduction to Graph Data Structure. Exploring a graph means visiting these nodes in an organized way. You can learn more about the fundamentals in Understanding Graph Traversal: The Basics.

Depth First Search, or DFS for short, is an algorithm for exploring or searching a graph. Imagine you’re exploring a large cave system or a maze. The DFS strategy is like choosing one path and following it as deep as possible until you hit a dead end or a place you’ve already been. Only then do you backtrack (go back) to the last junction where you had a choice and try a different unexplored path.

Key ideas behind DFS:

  • Go Deep First: DFS always tries to explore further along a single path before trying other paths that might be closer to the starting point. It dives “deep” into the graph first.
  • Backtrack When Necessary: When you can’t go any deeper down the current path (because you hit a dead end or a node you’ve already seen on this path), you go back (backtrack) to the last node where you had other options and explore one of those.
  • Keep Track of Visits: To avoid going in circles forever or exploring the same section multiple times, DFS needs to remember which nodes it has already visited. Usually, we mark a node as “visited” as soon as we reach it.

Steps in the DFS Algorithm

While the detailed steps in Depth first search algorithm along with visualization and code are covered in the next articles (Step-by-Step Explanation of DFS, Visualization of DFS), let’s look at the high-level steps:

  1. Start: Pick a starting node in the graph. Mark it as visited.
  2. Explore Neighbors: Look at the neighbors (nodes directly connected) of your current node.
  3. Go Deeper: If you find an unvisited neighbor, move to that neighbor. Mark it as visited and repeat Step 2 from this new node. This is the “go deep” part.
  4. Backtrack: If all neighbors of your current node have already been visited, you’re stuck on this path. Go back to the node you came from (backtrack). From that previous node, look for other unvisited neighbors (Step 2 again).
  5. Repeat: Continue this process of going deeper whenever possible and backtracking when necessary.
  6. Finish: The search stops when you have backtracked all the way to the starting node and there are no more unvisited neighbors to explore from it. If the graph has disconnected parts, you might need to restart the DFS from an unvisited node in another part.

This systematic process ensures that every reachable node from the starting point is eventually visited. For a more visual and detailed walkthrough, see How Depth First Search Works: Step-by-Step.

A Simple Example: Exploring Friendships

Let’s imagine a tiny graph representing friendships:

  • Alice is friends with Bob and Carol.
  • Bob is friends with David.

Below is how the graph representation of these friendships look like:

Below is the sequence of all the steps we performed:

  1. Start at Alice. Mark Alice as visited.
  2. Go Deeper: Pick an unvisited friend of Alice, say Bob. Move to Bob.
  3. Visit Bob. Mark Bob as visited.
  4. Go Deeper: Pick an unvisited friend of Bob, David. Move to David.
  5. Visit David. Mark David as visited. David has no unvisited friends.
  6. Backtrack: Go back to Bob. Bob has no other unvisited friends.
  7. Backtrack: Go back to Alice. Alice has another unvisited friend, Carol.
  8. Go Deeper: Move to Carol.
  9. Visit Carol. Mark Carol as visited. Carol has no unvisited friends.
  10. Backtrack: Go back to Alice. Alice has no more unvisited friends.
  11. Finish: We have visited all reachable nodes (Alice, Bob, David, Carol).

Notice how we went deep (Alice -> Bob -> David) before backtracking to explore other options which are directly under Alice (Carol). This step-by-step process on how we perform this programmatically is detailed further in how DFS works.

Another Visual Example Showcasing DFS

Below is another example which showcases the visiting pattern Depth First Search will follow while traversing a graph:

Why is DFS Useful?

DFS isn’t just a way to travel through a graph; it’s a building block for solving many problems:

  • Finding Paths: Can you get from point A to point B? DFS can find a path if one exists.
  • Detecting Cycles: Does the graph contain loops? DFS can easily detect if you revisit a node during the exploration of a single path.
  • Connectivity: Are all parts of the graph connected? You can use DFS to find out which nodes are reachable from a starting point.
  • Topological Sorting: For graphs representing dependencies (like tasks where some must be done before others), DFS helps order them correctly.
  • Solving Puzzles: Games like mazes or puzzles involving finding solutions can often be modeled as graphs and solved using DFS.

Understanding DFS is crucial because it’s a fundamental algorithm that appears in various forms across computer science. You can learn more about its specific uses in the Applications of Depth First Search article.

What’s Next?

Now that you have a basic idea of what Depth First Search is, you can dive deeper into various aspects of the algorithm:

By exploring these topics, you’ll gain a solid understanding of Depth First Search and how to apply it effectively.