Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes, and we show that the obtained codes are not too far from being optimal. Moreover, we exploit our results on alphabetic codes to provide new bounds on the average cost of optimal binary search trees. Our results improve on the best-known bounds on the average cost of optimal binary search trees present in the literature.