Searching a balanced binary search tree of 1023 nodes takes at most 10 comparisons; scanning a list of the same values takes up to 1023. Why does the tree save so much, and what does the saving depend on?

B. From discarding half the remaining candidates at every comparison.

One comparison at the root discards half the tree entirely — not examined and rejected, never visited — so the candidate set halves each step: 1023, 511, 255, down to 1 in ten. Cost tracks height, and a balanced tree's height is about log₂ n. Sorted order alone is not the mechanism: a sorted list scanned linearly still takes n steps, and the halving is what saves the work.