Graph Theory Questions Medium
The depth-first search (DFS) algorithm is a graph traversal technique that explores as far as possible along each branch before backtracking. It starts at a given vertex and explores as far as possible along each branch before backtracking.
The algorithm works by maintaining a stack to keep track of the vertices that need to be visited. It starts by pushing the initial vertex onto the stack. Then, while the stack is not empty, it pops a vertex from the stack and marks it as visited. It then explores all the adjacent vertices of the current vertex that have not been visited yet. For each unvisited adjacent vertex, it pushes it onto the stack and continues the process.
DFS is often implemented using recursion, where the recursive function visits a vertex and recursively calls itself for each unvisited adjacent vertex. This allows the algorithm to explore the graph in a depth-first manner.
DFS is useful for various graph-related problems, such as finding connected components, detecting cycles, and solving maze-like puzzles. It can also be used to generate a topological ordering of a directed acyclic graph.
Overall, the depth-first search algorithm is a powerful tool for traversing and exploring graphs in a systematic and efficient manner.