Breadth First Search vs Depth First Search

BFS Vs. DFS: An Overview

Breadth First Search and Depth First Search are the two techniques of Graph Traversal. The breadth-first search (BFS) algorithm explores all the vertices of a graph in a breadthwise order. Whereas in the case of depth-first search, the algorithm works by starting from an arbitrary node of the graph and exploring as far as possible before backtracking.

We have seen their detailed work in the tutorial, Breadth First Traversal and Depth First Traversal. If you haven't seen that tutorial, go back and refer to it. In this DSA tutorial, we will take a look at the differentiating factors between them. For further insights, consider enrolling in the Data Structures and Algorithms Certification Course.

What is Breadth First Search?

Breadth-First Search (BFS) is a graph traversal algorithm that explores all the vertices of a graph in a breadthwise order. It means it starts at a given vertex or node and visits all the vertices at the same level before moving to the next level. It is a recursive algorithm for searching all the vertices of a graph or tree data structure. It uses a queue data structure to keep track of the vertices to visit.

Breadth-First Search (BFS) Example

What is Depth First Search?

The depth-first search algorithm works by starting from an arbitrary node of the graph and exploring as far as possible before backtracking i.e. moving to an adjacent node until there is no unvisited adjacent node. After backtracking, it repeats the same process for all the remaining vertices which have not been visited till now. It is a recursive algorithm for searching all the vertices of a graph or tree data structure. It uses a stack data structure to keep track of the vertices to visit.

Depth-First Search (DFS) Example

Differences between BFS and DFS

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Considerations for Choosing Between BFS and DFS

1. Problem Requirements: Figure out whether the problem involves finding the shortest path, detecting cycles, or searching for a feasible solution.
2. Graph Characteristics: BFS is generally more suitable for sparse graphs or graphs with many short paths, while DFS is often used for dense graphs or graphs with deep paths.
3. Space Complexity: BFS requires more memory to maintain the queue for storing nodes at each level, while DFS uses less memory as it traverses deeply before backtracking.
4. Time Complexity: BFS has a higher time complexity than DFS, especially for large graphs, due to its breadth-first nature and the need to explore all neighboring nodes at each level.
5. Optimality: BFS guarantees the shortest path in unweighted graphs while DFS does not guarantee optimality.
6. Search Space: BFS explores all possible nodes at each level before moving to the next level, making it suitable for problems where the solution lies close to the starting node. DFS explores deeply into the search space and is suitable for problems with deep paths or where backtracking is necessary.
7. Implementation Complexity: BFS is relatively straightforward to implement using a queue data structure, while DFS may require recursion or maintaining a stack explicitly.
8. Cycle Detection: DFS is commonly used for cycle detection in graphs due to its ability to backtrack and explore deeply into the graph.

Summary

In this tutorial, we saw the differences between BFS and DFS. Understanding these two types of graph traversal methods is essential to understanding the graph data structure. To test your practical understanding of these two techniques, enroll in our Best Data Structures And Algorithms Course.