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

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 issues in algorithm design and analysis. Forexample, this collection of sorting algorithms shows multiple approaches to usingdivide-and-conquer. In particular, there are multiple ways to do the dividing:Mergesort divides a list in half; Quicksort divides a list into big values and smallvalues; and Radix Sort divides the problem by working on one digit of the key ata time. Sorting algorithms can also illustrate a wide variety of analysis techniques.We’ll find that it is possible for an algorithm to have an average case whose growthrate is significantly smaller than its worse case (Quicksort). We’ll see how it ispossible to speed up sorting algorithms (both Shellsort and Quicksort) by takingadvantage of the best case behavior of another algorithm (Insertion sort). We’ll seeseveral examples of how we can tune an algorithm for better performance. We’llsee that special case behavior by some algorithms makes them a good solution for223