When it comes to graph traversal, there are two popular algorithms used by computer scientists and software engineers: Breadth-First Search (BFS) and Depth-First Search (DFS). Both BFS and DFS are used to visit all nodes in a graph, but they differ in their approach and behavior. While moving further in this article, we will see the difference between BFS and DFS along with examples of each.
Breadth-First Search (BFS)
Breadth-First Search (BFS) is an algorithm used to visit all nodes in a graph or tree. The BFS algorithm starts at a root node and before moving to a new node in the next depth, it will traverse all the nodes at the current depth. BFS visits all the nodes at a particular depth before moving to the nodes at the next depth.
There are many advantages of BFS, but one of the most useful advantages is that it guarantees the user that it will find the shortest path from the root node to any other node. The reason is simple, BFS explores all the nodes at the current depth before moving to the nodes at the next depth. The algorithm also keeps track of the visited nodes, ensuring that each node is visited exactly once.
Example of BFS
Here’s an example of the BFS Algorithm applied to a simple graph.
Input:
Output:
A, B, C, D, E, FExplanation:
Starting from the root node A, BFS visits nodes B and C at the first depth, and nodes D, E, and F at the second depth.
To learn more, please refer to this article – Breadth-First Search.
Depth-First Search (DFS)
Depth-First Search (DFS) is another algorithm used to visit all nodes in a graph or tree. The algorithm starts at the root node and explores as far as possible along each branch before backtracking. DFS explores all the nodes in a branch before moving to the next branch.
Among all the advantages, one of the major advantages that differ from DFS is that comparatively, it uses less memory than BFS because there is no need to keep track of all the nodes at a particular depth. Instead, it keeps track of the visited nodes and explores each branch to its deepest level before backtracking. DFS also has the advantage of being easy to implement recursively.
Example of DFS
Here’s an example of the DFS Algorithm applied to a simple graph.
Input:
Output:
A -> B -> D -> C -> E -> FExplanation:
Starting from the root node A, DFS visits nodes B and D in the first branch, then backtracks to visit node C in the second branch, and finally visits nodes E and F in the third branch.
Refer to this Article for more info – Depth-First Search.
Difference Between BFS and DFS
The given tables shows the Difference between BFS and DFS.
| BFS (Breadth First Search) | DFS (Depth First Search) |
|---|---|
| BFS is a graph traversal algorithm that visits all the vertices of a graph in breadth-first order, i.e., it visits all the vertices at the same level before moving to the next level. | DFS is a graph traversal algorithm that visits all the vertices of a graph in depth-first order, i.e., it visits the deepest vertices first and then backtracks to visit the remaining vertices. |
| BFS uses a queue data structure to keep track of the visited vertices and the vertices yet to be visited. | DFS uses a stack data structure to keep track of the visited vertices and the vertices yet to be visited. |
| BFS is better suited for finding the shortest path in an unweighted graph. | DFS is better suited for finding the connected components of a graph and for detecting cycles in a graph. |
| BFS has a higher memory requirement than DFS, as it needs to store all the vertices at the current level in the queue. | DFS has a lower memory requirement than BFS, as it only needs to store the vertices on the current path in the stack. |
| BFS has a time complexity of O(V + E), where V is the number of vertices and E is the number of edges in the graph. | DFS has a time complexity of O(V + E), where V is the number of vertices and E is the number of edges in the graph. |
Which Algorithm to Use?
The choice of algorithm depends on the specific problem you’re trying to solve. If you’re looking for the shortest path in a graph, BFS is the way to go. BFS guarantees to find the shortest path from the root node to any other node in the graph, making it ideal for applications such as GPS navigation or maze solving.
If you’re looking for any path in a graph, DFS is the way to go. DFS explores each branch to its deepest level before backtracking, making it more suited to applications such as cycle detection or topological sorting.
In some cases, a hybrid approach using both BFS and DFS may be necessary. For example, if you’re trying to find the shortest path in a graph with weighted edges, you can use BFS to find the shortest path to the target node but use DFS to explore the neighboring nodes to determine the weight of each edge.
Conclusion
BFS and DFS are two popular algorithms used for graph traversal. They differ in their approach and behavior, with BFS exploring all the nodes at a particular depth before moving to the next depth, while DFS explores each branch to its deepest level before backtracking. The choice of algorithm depends on the specific problem you’re trying to solve, with BFS being ideal for finding the shortest path and DFS being more suited to applications such as cycle detection or topological sorting. In some cases, a hybrid approach using both BFS and DFS may be necessary.
Frequently Asked Questions (FAQs)
Here are some Frequently Asked Questions related to the Difference Between BFS and DFS.
Ques 1. Which algorithm is used in finding the strongly connected components of a graph?
Ans. Tarjan’s algorithm, which is based on DFS, is commonly used to find the strongly connected components of a graph.
Ques 2. Which algorithm is used to find the minimum spanning tree of a graph?
Ans. Prim’s algorithm and Kruskal’s algorithm are commonly used to find the minimum spanning tree of a graph. Neither BFS nor DFS is used directly for this purpose
Ques 3. Which algorithm is faster BFS or DFS?
Ans. Both BFS and DFS have a time complexity of O(V + E), where V is the number of vertices and E is the number of edges in the graph. Therefore, the performance of BFS and DFS is generally comparable in terms of time complexity.
Ques 4. Which algorithm uses more memory BFS or DFS?
Ans. BFS has a higher memory requirement than DFS, as it needs to store all the vertices at the current level in the queue. DFS has a lower memory requirement than BFS, as it only needs to store the vertices on the current path in the stack.
Ques 5. Which algorithm is used to traverse a binary tree?
Ans. Both BFS and DFS can be used to traverse a binary tree.