A Practical Introduction to Data Structures and Algorithm Analysis

9SearchingOrganizing and retrieving information is at the heart of most computer applications,and searching is surely the most frequently performed of all computing tasks.Search can be viewed abstractly as a process to determine if an element with a particularvalue is a member of a particular set. The more common view of searchingis an attempt to find the record within a collection of records that has a particularkey value, or those records in a collection whose key values meet some criterionsuch as falling within a range of values.We can define searching formally as follows. Suppose k 1 , k 2 , ... k n are distinctkeys, and that we have a collection L of n records of the form(k 1 , I 1 ), (k 2 , I 2 ), ..., (k n , I n )where I j is information associated with key k j for 1 ≤ j ≤ n. Given a particularkey value K, the search problem is to locate the record (k j , I j ) in L such thatk j = K (if one exists). Searching is a systematic method for locating the record(or records) with key value k j = K.A successful search is one in which a record with key k j = K is found. Anunsuccessful search is one in which no record with k j = K is found (and no suchrecord exists).An exact-match query is a search for the record whose key value matches aspecified key value. A range query is a search for all records whose key value fallswithin a specified range of key values.We can categorize search algorithms into three general approaches:1. Sequential and list methods.2. Direct access by key value (hashing).3. Tree indexing methods.317