Discussion
Why does the deepest level dominate the node count of an exponential tree?
Answer: A
For a branching factor above two the bottom level exceeds the sum of all the others, so any analysis of an exponential tree is dominated by its last level. That is why iterative deepening's repeated work is cheap and why any pruning near the bottom is worth far more than pruning near the top. Memory per node, goal testing and generation cost are uniform. A structural fact about exponentials that determines several algorithmic conclusions is worth internalising rather than rederiving.
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