What is BFS ?                         


Breadth-First Search (BFS) is a graph traversal algorithm that systematically explores a graph's vertices level by level. Starting from a chosen node, BFS visits its neighbors before moving on to the next level of nodes. It utilizes a queue data structure to maintain the order of exploration, ensuring that nodes at the same level are visited before moving deeper. BFS is employed in various applications, such as finding the shortest path in unweighted graphs, network broadcasting, and web crawling. Its guarantee of discovering the shortest path makes it particularly suitable for scenarios where optimality and completeness are crucial.

                          What is DFS ?                         

Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along one branch before backtracking. Starting at the initial node, DFS recursively visits adjacent nodes, marking them as visited and backtracks when no unvisited neighbors remain. It uses a stack or recursion for tracking the exploration path. DFS is versatile, applicable to various graph-related problems such as topological sorting, connected component identification, and maze solving. While it may not guarantee the shortest path, DFS is memory-efficient and well-suited for scenarios where exhaustive exploration of possibilities along a branch is beneficial.

      Difference between BFS vs DFS ?      

Basis

BFS

DFS

1. Nature   -

Explores level by level, i.e., it explores all the neighbor nodes at the current depth before moving on to nodes at the next depth.

 

Explores as far as possible along one branch before backtracking.

2. Data Structure:

Uses a queue data structure to keep track of the nodes to be explored.

Uses a stack (or recursion) to keep track of nodes to be explored.

3. Memory Usage:

Generally requires more memory because it needs to store all nodes at the current level.

Typically uses less memory as it only needs to store a stack of nodes corresponding to the current branch.

4. Implementation:

Iterative implementation is usually preferred using a queue.

Recursive implementation is common, but it can also be implemented using a stack.

5. Completeness

Guaranteed to find the shortest path in an unweighted graph.

Does not guarantee the shortest path.

6. Time Complexity:

Generally has higher time complexity compared to DFS.

Usually has a lower time complexity.

 

7. Use Cases :

Useful in finding the shortest path, puzzle solving, and scenarios where you want to explore all possibilities level by level.

Useful in topological sorting, finding connected components, and scenarios where you want to explore as far as possible along each branch.

 

8. Path vs. Space

May not be practical for dense graphs due to its space complexity.

Typically more memory-efficient, especially for sparse graphs.

 

9. Applications :

 

Web crawling, shortest path problems, network broadcasting.

Topological sorting, solving mazes, finding connected components.

 

10. Order of Visitation

Nodes are visited in the order they are discovered, level by level.

  

 

Nodes are visited in a depthward motion until a dead end is reached, and then the algorithm backtracks.