Discussion
A problem has branching factor 3 and solution depth 5. How many nodes does breadth first generate?
Answer: D
Summing the levels from the root to the solution depth gives:
\[ 1 + 3 + 9 + 27 + 81 + 243 = 364 \]
so about 364 nodes. The bottom level alone accounts for 243 of them, which is the observation that makes iterative deepening cheap. Noticing that the last level dominates the sum is the single most useful fact about exponential trees and it explains several results at once.
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