Time and Space Complexity of DFS and BFS Algorithm

The time complexity of both Depth-First Search (DFS) and Breadth-First Search (BFS) algorithms is O(V + E), where V is the number of vertices and E is the number of edges in the graph. The space complexity of DFS is O(V), where V represents the number of vertices in the graph, and for BFS, it is O(V), where V represents the number of vertices in the graph.

Time Complexity of BFS and DFS:

Breadth-first search (BFS) and depth-first search (DFS) are fundamental graph traversal algorithms used to explore and search graph structures. While both algorithms serve similar purposes, their time complexities differ, impacting their suitability for various graph problems.

Time Complexity of DFS:

The time complexity of DFS is O(V + E), where V is the number of vertices and E is the number of edges in the graph. This is because every vertex and every edge will be explored in the worst-case scenario.

Time Complexity of BFS:

The time complexity of BFS is also O(V + E), where V is the number of vertices and E is the number of edges in the graph. This is because every vertex and every edge will be explored in the worst-case scenario.

Auxiliary Space of BFS and DFS:

Auxiliary space refers to the additional memory space required by an algorithm beyond the input data. Understanding the auxiliary space of algorithms like breadth-first search (BFS) and depth-first search (DFS) is crucial for analyzing their memory usage and scalability in solving graph problems.

Auxiliary Space of DFS:

The auxiliary space of Depth-First Search (DFS) algorithm is O(V), where V is the number of vertices in the graph, this is due to the recursion stack or visited array. In a skewed tree, the recursive stack will have all the nodes in it.

Auxiliary Space of BFS:

The auxiliary space of Breadth-First Search algorithm is O(V), where V is the number of vertices in the graph. This is due to the queue used to store all the nodes at a particular level in a sequential manner. In a complete graph, the queue will have all the nodes in the queue.