Which traversal algorithm is typically implemented using a stack data structure?

Question

Prepp Team · Accepted Answer

Let's understand which common graph traversal algorithm typically uses a stack data structure. We have two main algorithms for traversing graphs and trees: Depth First Search (DFS) and Breadth First Search (BFS).

Understanding Graph Traversal

Graph traversal is the process of visiting every node in a graph. This is important for many graph algorithms, such as finding a path between two nodes, finding connected components, or topological sorting.

Depth First Search (DFS) Explained

Depth First Search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root (or an arbitrary node) and explores as far as possible along each branch before backtracking. It goes deep first before going wide.

Think of DFS like exploring a maze. You go down one path as far as you can. If you hit a dead end, you back up (backtrack) and try another path. This process of going deep and then backtracking aligns perfectly with how a stack data structure works.

How DFS Uses a Stack

The Depth First Search (DFS) algorithm is naturally implemented using a stack. When you visit a node, you push its unvisited neighbors onto a stack. Then, you pop a node from the stack and visit it, repeating the process. Because a stack is Last-In, First-Out (LIFO), the algorithm explores the most recently added (and thus deepest) neighbor first before returning to explore siblings.

Here's a simple idea of the DFS process using a stack:

Start at a source node, mark it as visited, and push it onto the stack.
While the stack is not empty:
Pop a node from the stack.
For each neighbor of the popped node:
If the neighbor has not been visited:
Mark the neighbor as visited.
Push the neighbor onto the stack.

This stack data structure keeps track of the nodes that need to be visited next, prioritizing the nodes encountered deeper in the traversal path before backtracking.

Breadth First Search (BFS) Explained

In contrast to DFS, Breadth First Search (BFS) is an algorithm for traversing or searching tree or graph data structures that starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a 'search key') and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. BFS explores the graph level by level.

BFS is typically implemented using a queue data structure. When a node is visited, its unvisited neighbors are added to the back of the queue. Because a queue is First-In, First-Out (FIFO), the algorithm explores nodes in the order they were added, which means exploring all nodes at the current level before moving to the next level.