The algorithm that a person should use to visit every vertex starting from one vertex, exploring as far as possible along each branch, then backtracking to explore other vertices from the same vertex, is Depth-First Search (DFS).
Explanation:
- DFS starts from a given vertex and explores as deeply as possible along each branch before backtracking, which matches the described behavior of visiting all vertices, finishing from one vertex, then backtracking to explore others
- This approach uses a stack (often implicitly via recursion) to remember the path and backtrack when no further progress is possible.
- DFS is commonly used for graph traversal and exploration, and it systematically visits every vertex reachable from the start vertex
- Backtracking is closely related to DFS and can be seen as DFS applied with pruning or constraints, but the core traversal mechanism described is DFS
Summary:
- Algorithm to use: Depth-First Search (DFS)
- Key features: Visit a vertex, explore as far as possible, backtrack when stuck, then explore other vertices.
- Applications: Graph traversal, puzzle solving, cycle detection, pathfinding.
This matches the exact scenario described in the query
