Sorting and Searching

Transcription

1 CHAPTER 13 Sorting and Searching The exercises in this chapter are a framework for comparing algorithms empirically. This approach provides students with a means for understanding the finer details of each sorting and search algorithm, and enables them to discover why one sorting or searching algorithm is more appropriate than another. Exercises 13-6 what happens when multiple values occur in the list to be sorted using: a) Selection sort b) Insertion sort Not Provided Trace the steps when sorting the following list: 23, 48, 49, 69, 12, 85, 20, 37, 51, 69, 23 using: a) Selection sort b) Insertion sort Java Software Solutions: Foundations of Program Design 408

2 Trace the steps when sorting the following list: 70, 60, 50, 40, 30, 20, 10 using: a) Selection sort b) Insertion sort Java Software Solutions: Foundations of Program Design 409

3 Trace the steps when sorting the following list: 11, 22, 33, 44, 55, 66, 77, 88, 99 using: a) Selection sort b) Insertion sort Java Software Solutions: Foundations of Program Design 410

4 Compare the different executions of each sort with the lists in Problem 13-2 and Problem How many comparisons are made in each? Not Provided What optimization can be performed during a linear search if the data is sorted? Once a search processes an element of the data that is greater than the key, the rest of the elements in the sorted data will be greater than the key. Therefore, the search can be terminated without processing all data elements What would happen if the list used in a binary search is not sorted? The algorithm will not work correctly. The execution of the program may not even terminate. An assumption of the binary search is that all data elements to the left of the element being examined are lesser values and all data elements to the right are greater values. If this assumption is not true, then the algorithm (assuming an incorrect ordering) will jump around erratically Why are three assignment statement necessary to exchange two values, as seen in the selection sort? What is the role of the temp variable in the selection sort example? Not Provided. Programming Projects 13-8 Modify the linear search method to optimize the search if you assume the list is sorted. In other words, don t examine any more values than you need to in order to assert that the target value is not present. ******************************************************************* Linear_Search_Test.java In Text Application Authors: Lewis and Loftus Classes: Linear_Search_Test Linear_Search ******************************************************************* Class Linear_Search_Test contains the driver of a program that searches a list of numbers using a linear search algorithm. Methods: Java Software Solutions: Foundations of Program Design 411

5 public static void main (String[] args) public class Linear_Search_Test { =========================================================== Creates an array of integers, then searches for a particular value. =========================================================== public static void main (String[] args) { int numbers[] = {7, -3, 7, 2, 8, -1, 3, 2, 5, 6, 7; System.out.println ("The index of 6 is " + Linear_Search.search (numbers, 6)); method main class Linear_Search_Test Class Linear_Search contains a static method that searches an array of integers. Methods: public static int search (int[] numbers, int target) class Linear_Search { =========================================================== Searches the specified array for target using a linear search, but assume the list is sorted in ascending order, and optimize the searching. =========================================================== public static int search (int[] numbers, int target) { int index = 0; Java Software Solutions: Foundations of Program Design 412

6 while (index < numbers.length) { if (target == numbers[index]) return index; target found else if (target > numbers[index]) return -1; index++; return -1; target not found method search class Linear_Search 13-9 Each of the sorting algorithms presented in this chapter arrange lists of number in ascending order. Rewrite the sort algorithms to arrange a list in descending order. ******************************************************************* Insertion_Sort_Test.java In Text Application Authors: Lewis and Loftus Classes: Insertion_Sort_Test Insertion_Sort ******************************************************************* Class Insertion_Sort_Test contains the driver of a program that sorts a list of numbers (descending order) using the insertion sort algorithm. Methods: public static void main (String[] args) public class Insertion_Sort_Test { =========================================================== Java Software Solutions: Foundations of Program Design 413

7 Creates an array of integers, sorts them, then prints them out. =========================================================== public static void main (String[] args) { int[] numbers = {3, 9, 6, 1, 2; Insertion_Sort.sort (numbers); for (int index = 0; index < numbers.length; index++) System.out.print (numbers[index] + " "); System.out.println (); method main class Insertion_Sort_Test Class Insertion_Sort contains a static method that sorts an array of integers in descending order. Methods: public static void sort (int[] numbers) class Insertion_Sort { =========================================================== Sorts the specified array (descending order) using insertion sort. =========================================================== public static void sort (int[] numbers) { for (int index = 1; index < numbers.length; index++) { int key = numbers[index]; int position = index; shift larger values to the left while (position > 0 && numbers[position-1] < key) { numbers[position] = numbers[position-1]; position--; Java Software Solutions: Foundations of Program Design 414

8 numbers[position] = key; method sort class Insertion_Sort ******************************************************************* Selection_Sort_Test.java In Text Application Authors: Lewis and Loftus Classes: Selection_Sort_Test Selection_Sort ******************************************************************* Class Selection_Sort_Test contains the driver of a program that sorts a list of numbers (descending order) using the selection sort algorithm. Methods: public static void main (String[] args) public class Selection_Sort_Test { =========================================================== Creates an array of integers, sorts them, then prints them out. =========================================================== public static void main (String[] args) { int[] numbers = {3, 9, 6, 1, 2; Selection_Sort.sort (numbers); Java Software Solutions: Foundations of Program Design 415

9 for (int index = 0; index < numbers.length; index++) System.out.print (numbers[index] + " "); System.out.println(); method main class Selection_Sort_Test Class Selection_Sort contains a static method that sorts an array of integers (descending order). Methods: public static void sort (int[] numbers) class Selection_Sort { =========================================================== Sorts the specified array (descending order) using selection sort. =========================================================== public static void sort (int[] numbers) { int min, temp; for (int index = 0; index < numbers.length-1; index++) { min = index; for (int scan = index+1; scan < numbers.length; scan++) if (numbers[scan] > numbers[min]) min = scan; swap the values temp = numbers[min]; numbers[min] = numbers[index]; numbers[index] = temp; for (int index1 = 0; index1 < numbers.length; index1++) System.out.print (numbers[index1] + " "); System.out.println(); Java Software Solutions: Foundations of Program Design 416

10 method sort class Selection_Sort ******************************************************************* Object_Sort_Test.java In Text Application Authors: Lewis and Loftus Classes: Object_Sort_Test Object_Sort Search_Engines Interfaces: Sortable ******************************************************************* import java.net.*; Class Object_Sort_Test contains the driver of a program that creates a sortable object (a URL list) and sorts it. Methods: public static void main (String[] args) throws MalformedURLException { public class Object_Sort_Test { =========================================================== Creates a Search_Engines object, then sorts them using the object sort method. =========================================================== public static void main (String[] args) throws MalformedURLException { Search_Engines engines = new Search_Engines(); Object_Sort.sort (engines); Java Software Solutions: Foundations of Program Design 417

11 for (int index = 0; index < engines.length(); index++) System.out.println (engines.value_at(index)); method main class Object_Sort_Test Interface Sortable lists the methods needed to sort any list of objects. Methods: boolean compare (Object left, Object right) Object value_at (int position) void set_value (Object value, int position) int length() interface Sortable { =========================================================== Should be implemented to return true if left > right. =========================================================== boolean compare (Object left, Object right); =========================================================== Should be implemented to return the object at the specified location. =========================================================== Object value_at (int position); =========================================================== Should be implemented to set the value of the specified location. =========================================================== void set_value (Object value, int position); =========================================================== Should be implemented to return the number of items in the list. Java Software Solutions: Foundations of Program Design 418

12 =========================================================== int length(); interface Sortable Class Object_Sort contains a static method that sorts any object that implements the Sortable interface. Methods: public static void sort (Sortable items) class Object_Sort { =========================================================== Sorts the specified items into descending order using an insertion sort that relys on the Sortable methods. =========================================================== public static void sort (Sortable items) { for (int index = 1; index < items.length(); index++) { Object key = items.value_at (index); int position = index; while (position > 0 &&!items.compare (items.value_at (position-1), key)) { items.set_value (items.value_at (position-1), position); position--; items.set_value (key, position); method sort class Object_Sort Class Search_Engines represents a set of URLs that can be used for web searching. The class implements the Sortable interface Java Software Solutions: Foundations of Program Design 419

13 so that the list of URLs can be sorted by host name. Constructors: public Search_Engines() throws MalformedURLException Methods: public boolean compare (Object left, Object right) public Object value_at (int index) public void set_value (Object value, int index) public int length() class Search_Engines implements Sortable { private URL[] sites = new URL[5]; =========================================================== Sets up the list of search engines. =========================================================== public Search_Engines() throws MalformedURLException { sites[0] = new URL (" sites[1] = new URL (" sites[2] = new URL (" sites[3] = new URL (" sites[4] = new URL (" constructor Search_Engines =========================================================== Returns true if the host of left is alphabetically after the host of right. =========================================================== public boolean compare (Object left, Object right) { URL site1 = (URL) left; URL site2 = (URL) right; String host1 = site1.gethost(); String host2 = site2.gethost(); Java Software Solutions: Foundations of Program Design 420

14 if (host1.compareto(host2) > 0) return true; else return false; method compare =========================================================== Returns the URL object at the specified index. =========================================================== public Object value_at (int index) { return (sites[index]); method value_at =========================================================== Sets the URL object at the specified index. =========================================================== public void set_value (Object value, int index) { sites[index] = (URL)value; method set_value =========================================================== Returns the number of URLs stored in the object. =========================================================== public int length() { return (sites.length); method length class Search_Engines Design and implement a program which reads every word of a paragraph of text and counts the occurrences of each word. Use hashing as part of the solution. ******************************************************************* Paragraph_HashTest.java In Text Applet Authors: Lewis and Loftus Classes: Paragraph_Hash_Test Paragraph_Hash Word_Object Java Software Solutions: Foundations of Program Design 421

15 ******************************************************************* import java.io.*; import java.util.*; Class Paragraph_Hash_Test contains the driver of a program that obtains a paragraph of text, places in a hash table and prints the frequency of the words contained in the paragraph. Methods: public static void main (String[] args) public class Paragraph_Hash_Test { public static void main (String [] args) throws IOException { BufferedReader stdin = new BufferedReader (new InputStreamReader(System.in)); Get the paragraph from the user and send it to the hasher System.out.println("Enter a paragraph of text: "); Paragraph_Hash.hasher (stdin.readline()); method main class Paragraph_Hash_Test Class Paragraph_Hash contains the hashing routine which accepts a String of text, places each unique word found in a Word_Object and inserts it into the hash table. Repeated words have their frequency counters incremented. When all words from the paragraph have been handled, a summary of word frequencies is printed. Methods: public static void hasher (String inputstring) Java Software Solutions: Foundations of Program Design 422

16 class Paragraph_Hash { public static void hasher(string inputstring) throws NoSuchElementException { Create a hash table to store the words Hashtable table = new Hashtable(10); Create a string tokenizer to parse the paragraph words StringTokenizer tokenizer = new StringTokenizer(inputString); while(tokenizer.hasmoretokens()) { Get the next word from the paragraph String element = tokenizer.nexttoken(); Check to see if this word is in the hash table already if (!table.containskey(element)) table.put(element, new Word_Object (element)); else ((Word_Object) table.get(element)).incrementcount(); while loop Get the enumeration of the hash table for printing Enumeration enum = table.elements(); while (enum.hasmoreelements()) System.out.println(enum.nextElement().toString()); method main class Paragraph_Hash Class Word_Object represents the data type inserted into the hash table. It will maintain the text of the hashed word and the current frequency of the word. Methods are provided for the printing of the object, incrementing the frequency counter. Methods: public Word_Object (String str) public void incrementcount () public String tostring() Java Software Solutions: Foundations of Program Design 423

17 class Word_Object { private String word; private int count; public Word_Object (String str) { word = str; count = 1; constructor Word_Object public void incrementcount () { count++; method incrementcount public String tostring () { return ("Word = " + word + " method tostring frequency = " + count); class Word_Object Design and implement a program which sorts a list of People objects, each of which contains a name, age, and salary. Allow the list to be sorted by any of these values, depending on the sort method invoked. ******************************************************************* People_Sort_Test.java In Text Application Authors: Lewis and Loftus Classes: People_Sort_Test People People_Sort ******************************************************************* Class People_Sort_Test contains the driver of a program that sorts a list of people using the insertion sort algorithm. Methods: Java Software Solutions: Foundations of Program Design 424

18 public static void main (String[] args) public class People_Sort_Test { =========================================================== Creates an array of People, sorts them, then prints them out. =========================================================== public static void main (String[] args) { People[] my_friends = { new People ("Pete DePasquale", 29, 31000), new People ("Sam Perugini", 20, 15000), new People ("Thomas Standish", 35, 45000), new People ("Grady Booch", 19, 30000), new People ("Fred Brooks", 45, ) ; System.out.println("\n\nPeople sorted by names:"); System.out.println("==============================="); People_Sort.sort_By_Name (my_friends); for (int index = 0; index < my_friends.length; index++) System.out.println (my_friends[index].tostring()); System.out.println("\n\nPeople sorted by age:"); System.out.println("==============================="); People_Sort.sort_By_Age (my_friends); for (int index = 0; index < my_friends.length; index++) System.out.println (my_friends[index].tostring()); System.out.println("\n\nPeople sorted by salary:"); System.out.println("==============================="); People_Sort.sort_By_Salary (my_friends); for (int index = 0; index < my_friends.length; index++) System.out.println (my_friends[index].tostring()); method main Java Software Solutions: Foundations of Program Design 425

19 class People_Sort_Test Class People contains a person's name, age and salary information. Access methods to obtain the name, age and salary are provided as well as a tostring method to print the contents all on one line. Methods: public People(String nm, int ag, int sal) public String tostring() public String getname() public int getage() public int getsalary() class People { private String name; private int age; private int salary; public People(String nm, int ag, int sal) { name = nm; age = ag; salary = sal; People constructor public String tostring() { return (name + " " + age + " $" + salary); method tostring public String getname() { return name; method getname Java Software Solutions: Foundations of Program Design 426

20 public int getage() { return age; method getage public int getsalary() { return salary; method getsalary class People Class People_Sort contains a static method that sorts an array of People. Methods: public static void sort_by_name (People[] friends) public static void sort_by_age (People[] friends) public static void sort_by_salary (People[] friends) class People_Sort { =========================================================== Sorts the specified array (by person's name) using insertion sort. =========================================================== public static void sort_by_name (People[] friends) { for (int index = 1; index < friends.length; index++) { People key = friends[index]; int position = index; shift larger values to the right while (position > 0 && friends[position-1].getname(). compareto(key.getname()) > 0) { friends[position] = friends[position-1]; position--; Java Software Solutions: Foundations of Program Design 427

21 friends[position] = key; method sort_by_name =========================================================== Sorts the specified array (by person's age) using insertion sort. =========================================================== public static void sort_by_age (People[] friends) { for (int index = 1; index < friends.length; index++) { People key = friends[index]; int position = index; shift larger values to the right while (position > 0 && friends[position-1].getage() > key.getage()) { friends[position] = friends[position-1]; position--; friends[position] = key; method sort_by_age =========================================================== Sorts the specified array (by person's salary) using insertion sort. =========================================================== public static void sort_by_salary (People[] friends) { for (int index = 1; index < friends.length; index++) { People key = friends[index]; int position = index; shift larger values to the right while (position > 0 && friends[position-1].getsalary() > key.getsalary()) { Java Software Solutions: Foundations of Program Design 428

22 friends[position] = friends[position-1]; position--; friends[position] = key; method sort_by_salary class People_Sort Design and implement a generic binary search algorithm. Exercise the class by storing a list of employees, and searching for individuals by name. ******************************************************************* Employee_Search_Test.java In Text Application Authors: Lewis and Loftus Classes: Employee_Search_Test Employee Object_Binary_Search ******************************************************************* import java.io.*; Class Employee_Sort_Test contains the driver of a program that searches a list of employees for a particular employee and prints that person's information. Methods: public static void main (String[] args) public class Employee_Search_Test { Java Software Solutions: Foundations of Program Design 429

23 =========================================================== Creates an array of Employees, and then searches for a specific individual. =========================================================== public static void main (String[] args) throws IOException { BufferedReader stdin = new BufferedReader (new InputStreamReader (System.in)); Employee[] subordinates = { new Employee ("Fred Brooks", 45, ), new Employee ("Grady Booch", 19, 30000), new Employee ("Pete DePasquale", 29, 31000), new Employee ("Sam Perugini", 20, 15000), new Employee ("Thomas Standish", 35, 45000) ; System.out.print ("Enter the name of the person to seach for: "); int result = Object_Binary_Search.search(subordinates, stdin.read- Line()); if (result == -1) System.out.println("\nSearch failed."); else System.out.println("\n" + subordinates[result].tostring()); method main class Employee_Search_Test Interface Searchable lists the method needed to compare any list of objects during a search operation Methods: boolean compare (Object left, Object right) interface Searchable { Java Software Solutions: Foundations of Program Design 430

24 =========================================================== Should be implemented to return 0 if this = target, 1 if this > target and -1 if this < target =========================================================== int compare (Object target); interface Searchable Class Employee contains a person's name, age and salary information. Access methods to obtain the name, age and salary are provided as well as a tostring method to print the contents all on one line and a comparison method. Methods: public Employee (String nm, int ag, int sal) public String tostring () public String getname () public int getage () public int getsalary () public boolean compare (Object obj) class Employee implements Searchable { private String name; private int age; private int salary; public Employee(String nm, int ag, int sal) { name = nm; age = ag; salary = sal; People constructor =========================================================== Returns the string representation of this object =========================================================== Java Software Solutions: Foundations of Program Design 431

25 public String tostring () { return (name + " " + age + " $" + salary); method tostring =========================================================== Returns the name of the employee =========================================================== public String getname () { return name; method getname =========================================================== Returns the age of the employee =========================================================== public int getage () { return age; method getage =========================================================== Returns the salary of the employee =========================================================== public int getsalary () { return salary; method getsalary =========================================================== Returns 0 if this = target, 1 if this > target and -1 if this < target =========================================================== public int compare (Object obj) { int comparison_result; if (obj instanceof String) comparison_result = name.compareto((string) obj); else comparison_result = 0; if (comparison_result > 0) return 1; else Java Software Solutions: Foundations of Program Design 432

26 return -1; method compare =========================================================== Returns true if this Employee's name is equal to target =========================================================== public boolean equals(object target) { if (this.name.equals((string) target)) return true; else return false; class Employee Class Object_Binary_Search contains a static method that searches an array of Objects. Methods: public static int search (Object[] numbers, Object target) class Object_Binary_Search { =========================================================== Searches the specified array for target using a binary search. =========================================================== public static int search (Searchable[] items, Object target) { int index; int left = 0, right = items.length - 1; while (left <= right) { index = (left + right) / 2; if (items[index].equals(target)) return index; target found Java Software Solutions: Foundations of Program Design 433

27 if (items[index].compare(target) < 0) left = index + 1; else right = index - 1; return -1; target not found method search class Object_Binary_Search Modify the algorithms for the selection sort and the insertion sort to count the: Number of comparisons Number of exchanges Number of times each loop is executed ******************************************************************* Insertion_Sort_Test2.java In Text Application Authors: Lewis and Loftus Classes: Insertion_Sort_Test Insertion_Sort ******************************************************************* Class Insertion_Sort_Test2 contains the driver of a program that sorts a list of numbers using the insertion sort algorithm. Methods: public static void main (String[] args) public class Insertion_Sort_Test2 { Java Software Solutions: Foundations of Program Design 434

28 =========================================================== Creates an array of integers, sorts them, then prints them out. =========================================================== public static void main (String[] args) { int[] numbers = new int[4000]; for (int index = 0; index < numbers.length; index++) { numbers[index] = (int)(math.random()*100000); Insertion_Sort2.sort (numbers); for (int index = 0; index < numbers.length; index++) System.out.println (numbers[index]); Insertion_Sort2.printSummary(); method main class Insertion_Sort_Test Class Insertion_Sort contains a static method that sorts an array of integers. Methods: public static void sort (int[] numbers) public static void printsummary () class Insertion_Sort2 { public static int numberofcomparisons; public static int numberofexchanges; public static int numberofloopexecutions; =========================================================== Sorts the specified array using insertion sort. =========================================================== Java Software Solutions: Foundations of Program Design 435

29 public static void sort (int[] numbers) { numberofcomparisons = numberofexchanges = numberofloopexecutions = 0; for (int index = 1; index < numbers.length; index++) { int key = numbers[index]; int position = index; shift larger values to the right while (position > 0 && numbers[position-1] > key) { numbers[position] = numbers[position-1]; position--; numberofcomparisons++; numberofexchanges++; numberofloopexecutions++; numbers[position] = key; numberofexchanges++; method sort =========================================================== Prints the statistics of the sort. =========================================================== public static void printsummary () { System.out.println("The total number of comparisons was: " + numberofcomparisons); System.out.println("The total number of exchanges was: " + numberofexchanges); System.out.println("The total number of loop executions was: " + numberofloopexecutions); method printsummary class Insertion_Sort ******************************************************************* Selection_Sort_Test2.java In Text Application Java Software Solutions: Foundations of Program Design 436

30 Authors: Lewis and Loftus Classes: Selection_Sort_Test Selection_Sort ******************************************************************* Class Selection_Sort_Test2 contains the driver of a program that sorts a list of numbers using the selection sort algorithm. Methods: public static void main (String[] args) public class Selection_Sort_Test2 { =========================================================== Creates an array of integers, sorts them, then prints them out. =========================================================== public static void main (String[] args) { int[] numbers = new int[4000]; for (int index = 0; index < numbers.length; index++) { numbers[index] = (int)(math.random()*100); long start = System.currentTimeMillis(); Selection_Sort2.sort (numbers); long stop = System.currentTimeMillis(); System.out.println ("Time is " + (stop - start)); for (int index = 0; index < numbers.length; index++) System.out.println (numbers[index]); Selection_Sort2.printSummary(); method main Java Software Solutions: Foundations of Program Design 437

31 class Selection_Sort_Test Class Selection_Sort contains a static method that sorts an array of integers. Methods: public static void sort (int[] numbers) public static void printsummary () class Selection_Sort2 { public static int numberofcomparisons; public static int numberofexchanges; public static int numberofloopexecutions; =========================================================== Sorts the specified array using selection sort. =========================================================== public static void sort (int[] numbers) { int min, temp; numberofcomparisons = numberofexchanges = numberofloopexecutions = 0; for (int index = 0; index < numbers.length-1; index++) { numberofloopexecutions++; min = index; for (int scan = index+1; scan < numbers.length; scan++) { numberofcomparisons++; if (numbers[scan] < numbers[min]) { min = scan; swap the values temp = numbers[min]; numbers[min] = numbers[index]; Java Software Solutions: Foundations of Program Design 438

32 numbers[index] = temp; numberofexchanges++; method sort =========================================================== Prints the statistics of the sort. =========================================================== public static void printsummary () { System.out.println("The total number of comparisons was: " + numberofcomparisons); System.out.println("The total number of exchanges was: " + numberofexchanges); System.out.println("The total number of loop executions was: " + numberofloopexecutions); method printsummary class Selection_Sort Java Software Solutions: Foundations of Program Design 439