Key Concepts: Economic Computation, Part II

In this section we will talk about some simple algorithms for looking up items in a sorted list. Broadly speaking, an algorithm is a group of instructions that completely characterize the process of converting a set of inputs into desired outputs. To illustrate this concept, we shall solve a basic search problem. Let L = {l1, l2, . . . , lK} denote a set of ordered objects, where lk precedes lk+1 in the ordering for all k. For example, the list L can be a list of alphabetized words or a set of real numbers ordered from least to greatest. Let l∗ denote a single object similar to those in the list L. Our objective is to find the correct placement for l∗ in the list L. In other words, we wish to devise an algorithm that accepts inputs L and l∗, and produces an output k∗ ∈ N such that the list L∗ = {l1, . . . , lk∗−1, l∗, lk∗ , . . . , lK} is an ordered list.