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In which problem does the search tree greatly exceed the state space?

  • A.A tree structured problem with a unique path to each state
  • B.A problem in which every action is irreversible
  • C.A problem with only one applicable action per state
  • D.A rectangular grid where each cell has several neighbours

Answer: D

In a grid a state at distance d can be reached by very many routes, so the tree has exponentially many nodes over a merely quadratic state space. Where the space is already a tree the two coincide, and irreversible or single action problems produce no redundancy either. Recognising in advance whether a space contains many alternative routes decides whether graph search is essential or merely tidy.

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