Depth-First Search (DFS) is a search algorithm that recursively explores the interconnected vertices of a graph in a depth-first manner. The algorithm follows a single branch until the end is reached, and then backtracks to previous vertices if necessary to explore other branches.
To implement DFS, a stack data structure is typically used to keep track of vertices being explored. The algorithm starts at a designated start vertex and pushes it onto the stack. Then, it visits the first adjacent vertex that has not yet been visited and pushes it onto the stack. The algorithm continues with this process, visiting the first adjacent vertex of the last vertex added to the stack until it reaches a vertex with no adjacent unvisited vertices. The algorithm then pops this vertex off the stack and starts exploring the previous vertex.
An example of DFS is the following:
Consider a graph with vertices labeled A, B, C, D, E, and F, and edges connecting them as follows:
A - B
| |
C - D - E
|
F
Starting from vertex A, DFS would visit vertex B since it is the first adjacent vertex of A. It would then visit vertex D since it is the first adjacent vertex of B that has not yet been visited. From D, DFS would visit E since it is the first adjacent vertex of D that has not yet been visited. Since E has no unvisited adjacent vertices, DFS would backtrack to D and then visit F, which is the only unvisited adjacent vertex of D. Finally, DFS would backtrack to A and then visit vertex C, which is the only unvisited adjacent vertex. The output of the DFS traversal would be: A, B, D, E, F, C.
DFS is a graph traversal technique that visits all the nodes of a graph in a depthward motion until there is no more node left to visit.
This algorithm starts the visit from the root node and explores as far as possible along each branch before backtracking to the previous node.
In DFS, nodes are marked as visited when they are being explored.
If a node has multiple unvisited neighbors, the algorithm proceeds with any one of them.
The algorithm maintains a stack to keep track of the visited nodes during the search.
The time complexity of the DFS algorithm is O(V+E) where V is the number of vertices and E is the number of edges.
DFS can be used to detect cycles in a graph and to solve problems such as topological sorting and strongly connected components.
DFS is typically implemented using recursion, but it can also be implemented using a stack data structure.
What is the time complexity of Depth-First Search in the worst case scenario?
Answer: The time complexity of Depth-First Search in the worst case scenario is O(|V| + |E|), where |V| is the number of vertices and |E| is the number of edges in the graph.
What data structure is used in Depth-First Search to keep track of visited vertices?
Answer: A boolean array or hash set is used in Depth-First Search to keep track of visited vertices.
How does Depth-First Search differentiate between a tree edge and a back edge?
Answer: A tree edge is an edge that is visited for the first time during traversal, while a back edge is an edge that leads from a child node to an ancestor node in the traversal tree.
Is Depth-First Search an optimal algorithm for finding shortest path in a weighted graph?
Answer: No, Depth-First Search is not an optimal algorithm for finding shortest path in a weighted graph as it does not take into account the weights of the edges.
When does Depth-First Search encounter a cycle in a graph?
Answer: Depth-First Search encounters a cycle in a graph when it encounters a back edge during traversal.