Final answer:
Depth first tree search without loop checking is used to find all possible paths in a graph.
Step-by-step explanation:
The purpose of depth first tree search without loop checking is neither to find the shortest path in a graph nor to find the optimal path. It is primarily used to explore as far as possible along each branch before backtracking. Hence, when depth-first search (DFS) is used without loop checking, the algorithm might go into an infinite loop if the graph has cycles.
Regarding the options provided:
- To find the shortest path in a graph - This is typically achieved using other algorithms like Dijkstra's or Bellman-Ford, which are designed to find the shortest path efficiently.
- To find the longest path in a graph - DFS could potentially be used for this purpose, but without loop checking, DFS cannot guarantee to find the longest path since it may enter a cycle.
- To find all possible paths in a graph - DFS can help in finding all paths, but in the presence of cycles and without loop checking, it will not terminate on some graphs.
- To find the optimal path in a graph - The term 'optimal' implies the best solution based on a certain criterion which DFS alone, without additional considerations such as costs or distances, is not guaranteed to find.
In summary, the main use of DFS without loop checking is to exhaustively explore all paths from a source to various destinations within a tree or acyclic graph where the concern of loops does not arise.