A Practical Introduction to Data Structures and Algorithm Analysis

7Internal SortingWe sort many things in our everyday lives: A handful of cards when playing Bridge;bills and other piles of paper; jars of spices; and so on. And we have many intuitivestrategies that we can use to do the sorting, depending on how many objects wehave to sort and how hard they are to move around. Sorting is also one of the mostfrequently performed computing tasks. We might sort the records in a databaseso that we can search the collection efficiently. We might sort the records by zipcode so that we can print and mail them more cheaply. We might use sorting as anintrinsic part of an algorithm to solve some other problem, such as when computingthe minimum-cost spanning tree (see Section 11.5).Because sorting is so important, naturally it has been studied intensively andmany algorithms have been devised. Some of these algorithms are straightforwardadaptations of schemes we use in everyday life. Others are totally alien to how humansdo things, having been invented to sort thousands or even millions of recordsstored on the computer. After years of study, there are still unsolved problemsrelated to sorting. New algorithms are still being developed and refined for specialpurposeapplications.While introducing this central problem in computer science, this chapter hasa secondary purpose of illustrating many important issues in algorithm design andanalysis. The collection of sorting algorithms presented will illustrate that divideand-conqueris a powerful approach to solving a problem, and that there are multipleways to do the dividing. Mergesort divides a list in half. Quicksort divides a listinto big values and small values. And Radix Sort divides the problem by workingon one digit of the key at a time.Sorting algorithms will be used to illustrate a wide variety of analysis techniquesin this chapter. We’ll find that it is possible for an algorithm to have anaverage case whose growth rate is significantly smaller than its worse case (Quicksort).We’ll see how it is possible to speed up sorting algorithms (both Shellsort235