Depth-First Search (DFS)

Depth-First Search, or DFS for short, is a way to explore all parts of a tree or graph. You can do it in two main ways: using recursion or iteration.

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Recursive Method

1. Base Case: First, check if the node is empty. If it is, just stop here.
2. Process the Node: Do what you need to do with this node, like printing its value.
3. Recursive Call: Keep going deeper by looking at each child of the node using DFS.

How long does it take? The time it takes is $O(V + E)$. Here, $V$ stands for the number of vertices (or points), and $E$ is the number of edges (or connections).
How much space does it use? The space needed is $O(h)$, where $h$ is how tall the tree is.

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Iterative Method

1. Use a Stack: Start by making a stack and add the root node to it.
2. Loop: As long as the stack isn’t empty:
   • Take one node off the stack, do your work with it, and then add its children to the stack.

How long does it take? Just like the recursive method, it takes $O(V + E)$.
How much space does it use? In the worst case, it could use $O(V)$ space.

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And that’s how Depth-First Search works! Whether you choose to do it recursively or iteratively, it’s a helpful way to explore trees and graphs.