Khóa học algorithms

Depth-First Search (DFS) and Depth-First Traversal

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Depth-first search (DFS) is a method for exploring a tree or graph. In a DFS, you go as deep as possible down one path before backing up and trying a different one.

Depth-first search is like walking through a corn maze. You explore one path, hit a dead end, and go back and try a different one.

Here's a how a DFS would traverse this tree, starting with the root:

A 4-row binary tree represented by circles connected with lines. Our depth-first search has us start at the root node at the top of the tree.

We'd go down the first path we find until we hit a dead end:

The same binary tree with all nodes in the leftmost branch bolded after being visited.

Then we'd do the same thing again—go down a path until we hit a dead end:

Then we do the same thing again: head down the next leftmost path until we reach a dead end.

And again:

And again.

And again:

Until we've visited every node in the tree.

Until we reach the end.

Depth-first search is often compared with breadth-first search.


  • Depth-first search on a binary tree generally requires less memory than breadth-first.
  • Depth-first search can be easily implemented with recursion.


  • A DFS doesn't necessarily find the shortest path to a node, while breadth-first search does.
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