Final answer:
The order of node visitation in a state space search differs by the algorithm used. In breadth-first search, all nodes are visited level by level until the goal is reached. In contrast, depth-limited and iterative deepening searches involve probing to a certain depth, with the latter expanding its limit incrementally until the goal state is found.
Step-by-step explanation:
The student's question pertains to exploring different search algorithms within a state space where each state k can generate two successors, 2k and 2k+1. Given the start state of 1 and considering the goal state is 11, the order in which nodes will be visited can vary greatly depending on the search algorithm used.
In breadth-first search, the algorithm explores all the neighbor nodes at the present depth prior to moving on to nodes at the next depth level. The visitation order for reaching the goal state of 11 would be: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Depth-limited search with a limit of 3 implies that the search will go only three levels deep. The node visitation order up to limit 3 would be: 1, 2, 4, 8, 9, 5, 10, 11 (goal state reached within depth limit).
Iterative deepening search combines the benefits of depth-first and breadth-first searches by repeatedly executing depth-limited searches with increasing depth limits until the goal is found. The nodes are visited in the following sequence: [Depth 0]: 1 [Depth 1]: 1, 2, 3 [Depth 2]: 1, 2, 4, 5, 3, 6, 7 [Depth 3]: 1, 2, 4, 8, 9, 5, 10, 11 (goal). Eventually, the goal of 11 is reached at the third level.