Data Structures and Algorithm Analysis - Computer Science at ...

302 Chap. 9 Searchingintroduced in Section 4.4. However, each has different performance characteristicsthat make it the method of choice in particular circumstances.The current chapter considers methods for searching data stored in lists. List inthis context means any list implementation including a linked list or an array. Mostof these methods are appropriate for sequences (i.e., duplicate key values are allowed),although special techniques applicable to sets are discussed in Section 9.3.The techniques from the first three sections of this chapter are most appropriate forsearching a collection of records stored in RAM. Section 9.4 discusses hashing,a technique for organizing data in an array such that the location of each recordwithin the array is a function of its key value. Hashing is appropriate when recordsare stored either in RAM or on disk.Chapter 10 discusses tree-based methods for organizing information on disk,including a commonly used file structure called the B-tree. Nearly all programs thatmust organize large collections of records stored on disk use some variant of eitherhashing or the B-tree. Hashing is practical for only certain access functions (exactmatchqueries) and is generally appropriate only when duplicate key values arenot allowed. B-trees are the method of choice for dynamic disk-based applicationsanytime hashing is not appropriate.9.1 Searching Unsorted and Sorted ArraysThe simplest form of search has already been presented in Example 3.1: the sequentialsearch algorithm. Sequential search on an unsorted list requires Θ(n) timein the worst case.How many comparisons does linear search do on average? A major considerationis whether K is in list L at all. We can simplify our analysis by ignoringeverything about the input except the position of K if it is found in L. Thus, we haven + 1 distinct possible events: That K is in one of positions 0 to n − 1 in L (eachposition having its own probability), or that it is not in L at all. We can express theprobability that K is not in L asP(K /∈ L) = 1 −n∑P(K = L[i])where P(x) is the probability of event x.Let p i be the probability that K is in position i of L (indexed from 0 to n − 1.For any position i in the list, we must look at i + 1 records to reach it. So we saythat the cost when K is in position i is i + 1. When K is not in L, sequential searchwill require n comparisons. Let p n be the probability that K is not in L. Then theaverage cost T(n) will bei=1