Difference Between BFS and DFS

BFS and DFS are the basic yet important traversal algorithms in computer science that are used while working with trees and graphs. Both algorithms are used in solving problems in data structures based on pathfinding, connectivity, shortest paths, and many other categories. Although both BFS and DFS are used to traverse nodes in a graph or tree, they also have differences. In this article, we will discuss what BFS and DFS are, their features, advantages and disadvantages, time and space complexity, and the difference between BFS and DFS based on multiple aspects.

Table of Contents:

• What is BFS?
• What is DFS?
• Differences Between BFS and DFS
  • Traversal Orders
  • Data Structure Used
  • Shortest Path Finding
  • Memory Usage
  • Completeness
  • Preferred Scenarios
• BFS and DFS Time Complexity
• BFS vs DFS: Which is Faster?
• BFS vs DFS: Which is Better for Shortest Path?
• BFS and DFS Applications
• Conclusion

What is BFS?

BFS is a graph traversal algorithm that visits the nodes on a level-by-level basis. It will first visit all of its neighbors before visiting any that have unvisited neighbors. BFS works by starting at a source node and traversing outwards from there, and using a queue data structure to keep track of the next node. BFS stands for Breadth-First Search.

Example: 

The final output for this graph using the BFS traversal algorithm is: 

A B C D E F G H I J

Step-by-Step BFS Traversal Explanation:

1. Start at ‘A’ -> enqueue its neighbors: [‘B’, ‘C’, ‘D’]
2. Visit ‘B’ -> Add its neighbors: [‘E’, ‘F’]
3. Visit ‘C’ -> No neighbors
4. Visit ‘D’ -> Add ‘G’
5. Visit ‘E’ -> Add ‘H’
6. Visit ‘F’ -> No neighbors
7. Visit ‘G’ -> Add ‘I’ and ‘J’
8. Visit ‘H’ -> No neighbors
9. Visit ‘I’ -> No neighbors
10. Visit ‘J’ -> No neighbors

Features of BFS

• BFS goes to all the nodes on the current depth level before moving on to the next depth.
• It works on a FIFO (First-In-First-Out) queue.
• It is optimal when we are looking for the shortest paths in an unweighted graph.
• BFS is great for level-order traversal in trees.

Advantages of BFS

• BFS helps to search for the shortest path in unweighted graphs easily.
• It is simple and easy to implement.
• It is efficient in cases where the solution is close to the source node.

Disadvantages of BFS

• It can take a lot of memory as it stores all child nodes.
• BFS is less efficient in very deep or infinite graphs.
• Queue operations can be slower for large graphs in BFS.

What is DFS?

DFS is also a graph traversal algorithm that recursively visits nodes on a branch until there are no unvisited adjacent nodes, then backtracks, and moves up or down one level as needed to get to the next unvisited node. It uses a stack structure when traversing through the graph, and creates a stack data structure using recursion.

Example:

The final output for this graph using the DFS traversal algorithm is:

A B E H F C D G I J

Step-by-Step DFS Traversal Explanation:

• Start at ‘A’
• Go to ‘B’, then ‘E’, then ‘H’
• Backtrack to ‘E’ -> No more neighbors -> Backtrack to ‘B’ -> Visit ‘F’
• Backtrack to ‘A’ -> Visit ‘C’
• Backtrack to ‘A’ -> Visit ‘D’ -> Go to ‘G’ -> Visit ‘I’, then ‘J’

Features of DFS

• DFS traverses the nodes first in depth instead of breadth. 
• It uses a LIFO (Last-In First-Out) stack or recursion. 
• It is ideal for solving puzzles and maze problems. 
• DFS is used for topological sort, cycle detection, and more advanced cases of pathfinding algorithms.

Advantages of DFS

• DFS takes less memory to store and traverse the nodes as compared to BFS.
• It is more efficient in graphs with high depth.
• It helps in finding connected components easily.

Disadvantages of DFS

• It may not find the shortest path because it traverses the nodes in depth.
• DFS can go into infinite loops without proper checks.
• Recursive DFS may lead to a stack overflow when it is used in very deep graphs.

Differences Between BFS and DFS

Here are a few differences between BFS and DFS that are explained briefly to help you understand in an efficient manner.

1. Traversal Orders

BFS traverses the graph from level to level. It starts with the root or source node, and then it searches through all of the neighboring nodes first before turning to the next level of neighbors. 

And, the DFS traverses as deep as possible on one path before the search backtracks. It starts with the root node and follows the path down to the leaf (or the end) before backtracking and trying a different path. 

2. Data Structure Used

BFS uses a queue data structure, which is based on FIFO (First-In First-Out). The nodes that are added to the back of the queue and are popped from the front will be processed by BFS in the order in which the nodes were added to the queue. 

DFS uses a stack data structure that works on the LIFO (Last-In First-Out) principle or recursion, which utilizes the call stack. DFS will always traverse in depth before revisiting previous nodes.

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3. Shortest Path Finding

BFS finds the shortest path in unweighted graphs because it explores nodes in increasing distance order. And, as soon as the destination node is found, the path is guaranteed to be the shortest. 

While the DFS algorithm does not guarantee the shortest path, it will traverse a longer path first, and miss the shortest one entirely unless all paths are compared manually.

4. Memory Usage

BFS stores all nodes at the current level in memory. Memory usage can grow quickly, especially in wide or infinite graphs, and thus, space complexity is O(V) in the worst case.

DFS stores only the current path from the root to the node(or leaf being explored). It is memory-efficient in wide graphs but can still be deep. Thus, the space complexity is O(h), where h is the depth of the tree or graph.

5. Completeness

BFS is a complete search strategy because it will find a solution if one exists (in finite graphs). It is systematic and comprehensive for finding paths or connected components.

Depth-First Search (DFS) is not complete in general, particularly in infinite graphs or those without loop detection mechanisms. Without constraints, DFS can follow an infinite path and miss existing solutions entirely. However, if loop checks (visited set) or a depth limit are implemented, DFS becomes complete for finite graphs, as these mechanisms prevent endless traversal and ensure all reachable nodes are eventually examined.

6. Preferred Scenarios

You can use BFS when you need to find the shortest path, and the graph is shallow or has limited depth. You can also use BFS when you’re dealing with level-based problems (e.g., social networks, tree level-order traversal).

You can use DFS when you need to explore all possible paths, the graph is deep, or memory is limited, and you’re solving puzzles, doing backtracking, or topological sorting.

Here is a table that shows the difference between BFS and DFS:

BFS and DFS Time Complexity

Here is the time and space complexity of BFS and DFS:

Time Complexity of BFS and DFS

For both BFS and DFS, the time complexity is O(V + E), 

where, 

• V is the number of vertices (nodes)
• E is the number of edges

Because both algorithms visit each node once, and each edge is also considered once in undirected graphs, an edge is seen twice, but this still results in O(E). Therefore, the total number of operations is proportional to the number of nodes and edges taken together.

Space Complexity of BFS and DFS

• BFS has a space complexity of O(V) because it stores all nodes at a level in a queue and tracks visited nodes. 
• DFS (recursive) uses O(h) space, where h is the depth of the graph, due to the call stack. 
• DFS (iterative) uses O(V) space for the explicit stack and visited set.

Here is a table that shows the time and space complexity in a precise manner:

BFS vs DFS: Which is Faster? 

• Neither BFS nor DFS can be considered faster, because it totally depends on the problem and the graph structure. 
• BFS is generally faster when there is a need for searching the shortest path, or when the target node is near the root, because it will search all paths level by level.
• DFS can be faster if the target node is at depth in the graph and lies on the first traversed path.
• And in terms of worst-case time complexity, they are both O(V + E), so their theoretical speed is the same.

BFS vs DFS: Which is Better for Shortest Path?

BFS is a better algorithm for finding the shortest path in an unweighted graph because it visits nodes level by level and ensures that when it arrives at a node for the first time, it has done so with the shortest route (fewest edges). Meanwhile, DFS visits each path in-depth before moving on to the other. It might get to the target node through a longer path. Thus, DFS guarantees to find a path, but it can’t guarantee that it will find the shortest unless it exhaustively explores all paths and manually compares.

Use BFS when:

• The graph is unweighted.
• You need the shortest path by the number of edges.

For weighted graphs, use Dijkstra’s algorithm or A* instead.

BFS and DFS Applications

Both BFS and DFS are fundamental graph traversal algorithms used in many real-world and computational problems. Here are a few applications of BFS and DFS:

BFS Applications

• BFS is used to find the shortest path in undirected graphs between two nodes efficiently.
• To find people at a certain distance, such as mutual friends or other connections, BFS is used.
• BFS is also used in crawling web pages layer by layer from a source page.
• BFS makes sure that all nodes receive a message level by level.
• In undirected graphs, BFS helps to find the groups of connected nodes.

DFS Applications

• DFS is used in topological sorting to sort nodes in a directed acyclic graph (DAG) based on dependencies.
• It is also used to detect cycles in both directed and undirected graphs.
• It traverses deep paths and is useful for backtracking-based problems, such as maze and puzzle problems.
• DFS is used to traverse all possible paths for decision-making in games.
• Also, the algorithms like Tarjan’s and Kosaraju’s use DFS to find the strongly connected components in directed graphs.

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Conclusion

BFS and DFS are basic graph traversal algorithms that are used to solve problems in data structures. BFS is most effective for finding the shortest path in unweighted graphs and performs level-by-level exploration using a queue. DFS traverses the nodes in depth using a stack or recursion and is good for problems such as backtracking, topological sorting, and cycle detection. You can choose between BFS and DFS based on the structure of the graph and the problem requirements. Understanding their differences in traversing, complexity, and memory usage will help you apply them efficiently in real-world applications.

Difference Between BFS and DFS – FAQs