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Why does breadth first search's time bound use the solution depth?

  • A.It expands nodes in order of increasing path cost from the start
  • B.It stores the entire frontier so cannot go deeper than memory allows
  • C.It applies the goal test to every node before expanding any of them
  • D.It never expands a node deeper than the shallowest solution

Answer: D

Because it completes each level before starting the next, breadth first never touches a node below the level containing the goal, so its work is bounded by the solution depth. Depth first has no such guarantee. Cost ordering belongs to uniform cost, memory is a consequence rather than a cause, and goal testing order is a detail. The parameter appearing in a complexity bound follows directly from the order in which the algorithm works, which is why the two bounds differ.

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