ࡱ> ~uVg IbjbjVV *r<r<]@6@ll$$$8888pd8`j-!-!-!jjjjjjj,modj$-!N-!-!-!jllOj777-! l<$j7-!j776[U|Wxi,. ;Vi0j0`jWVBp35DBp8WWBp$i-!-!7-!-!-!-!-!jjw7X-!-!-!`j-!-!-!-!Bp-!-!-!-!-!-!-!-!-! 2: Reference For Chapter 7 Arrays Array is a data structure that represents a collection of the same types of data.  Declaring Array Variables datatype[] arrayRefVar; Example: double[] myList; datatype arrayRefVar[]; // This style is allowed, but not preferred Example: double myList[]; Creating Arrays arrayRefVar = new datatype[arraySize]; Example: myList = new double[10]; myList[0] references the first element in the array. myList[9] references the last element in the array. Declaring and creating arrays in one step datatype[] arrayRefVar = new datatype[arraySize]; Example: double[] myList = new double[10]; datatype arrayRefVar[] = new datatype[arraySize]; Example: double myList[] = new double[10]; The length of an array Once an array is created, its size is fixed. It cannot be changed. You can find its size using arrayRefVar.length For example, myList.length returns 10 // field, instance variable Default Values When an array is created, its elements are assigned the default value of 0 for the numeric primitive data types, '\u0000' for char types, and false for boolean types. Indexed variables The array elements are accessed through the index. The array indices are 0-based, i.e., it starts from 0 to arrayRefVar.length-1. In the previous example, myList holds ten double values and the indices are from 0 to 9. Each element in the array is represented using the following syntax, known as an indexed variable: arrayRefVar[index]; After an array is created, an indexed variable can be used in the same way as a regular variable. For example, the following code adds the value in myList[0] and myList[1] to myList[2]. myList[2] = myList[0] + myList[1]; Declaring, creating, initializing in one step: double[] myList = {1.9, 2.9, 3.4, 3.5}; This shorthand syntax must be in one statement. This shorthand notation is equivalent to the following statements: double[] myList = new double[4]; myList[0] = 1.9; myList[1] = 2.9; myList[2] = 3.4; myList[3] = 3.5; Example Program import javax.swing.JOptionPane; public class TestArray { public static void main(String[] args) { final int TOTAL_NUMBERS = 6; int[] numbers = new int[TOTAL_NUMBERS]; // Read all numbers for (int i = 0; i < numbers.length; i++) { String numString = JOptionPane.showInputDialog( "Enter a number:"); // Convert string into integer numbers[i] = Integer.parseInt(numString); } // Find the largest int max = numbers[0]; for (int i = 1; i < numbers.length; i++) { if (max < numbers[i]) max = numbers[i]; } // Find the occurrence of the largest number int count = 0; for (int i = 0; i < numbers.length; i++) { if (numbers[i] == max) count++; } // Prepare the result String output = "The array is "; for (int i = 0; i < numbers.length; i++) { output += numbers[i] + " "; } output += "\nThe largest number is " + max; output += "\nThe occurrence count of the largest number " + "is " + count; // Display the result System.out.println(output); } } Example A program that calls a method with an array as an argument/parameter. public class TestPassArray { public static void main(String[] args) { int[] a = {1, 2}; // Swap elements using the swap method System.out.println("Before invoking swap"); System.out.println("array is {" + a[0] + ", " + a[1] + "}"); swap(a[0], a[1]); System.out.println("After invoking swap"); System.out.println("array is {" + a[0] + ", " + a[1] + "}"); // Swap elements using the swapFirstTwoInArray method System.out.println("Before invoking swapFirstTwoInArray"); System.out.println("array is {" + a[0] + ", " + a[1] + "}"); swapFirstTwoInArray(a); System.out.println("After invoking swapFirstTwoInArray"); System.out.println("array is {" + a[0] + ", " + a[1] + "}"); } /** Swap two variables */ public static void swap(int n1, int n2) { int temp = n1; n1 = n2; n2 = temp; } /** Swap the first two elements in the array */ public static void swapFirstTwoInArray(int[] array) { int temp = array[0]; array[0] = array[1]; array[1] = temp; } } Passing Arrays to Methods public static void printArray(int[] array) { for (int i = 0; i < array.length; i++) { System.out.print(array[i] + " "); } } Invoke the method int[] list = {3, 1, 2, 6, 4, 2}; printArray(list); Invoke the method printArray(new int[]{3, 1, 2, 6, 4, 2}); The statement printArray(new int[]{3, 1, 2, 6, 4, 2}); creates an array using the following syntax: new dataType[]{literal0, literal1, ..., literalk}; There is no explicit reference variable for the array. Such array is called an anonymous array. Java uses pass by value to pass parameters to a method. There are important differences between passing a value of variables of primitive data types and passing arrays. For a parameter of a primitive type value, the actual value is passed. Changing the value of the local parameter inside the method does not affect the value of the variable outside the method. For a parameter of an array type, the value of the parameter contains a reference to an array; this reference is passed to the method. Any changes to the array that occur inside the method body will affect the original array that was passed as the argument. Another Simple Example public class Test { public static void main(String[] args) { int x = 1; // x represents an int value int[] y = new int[10]; // y represents an array of int values m(x, y); // Invoke m with arguments x and y System.out.println("x is " + x); System.out.println("y[0] is " + y[0]); } public static void m(int number, int[] numbers) { number = 1001; // Assign a new value to number numbers[0] = 5555; // Assign a new value to numbers[0] } } Runtime Stack  The JVM stores the array in an area of memory, called heap, which is used for dynamic memory allocation where blocks of memory are allocated and freed in an arbitrary order. Enhanced for loop JDK 1.5 introduced a new for loop that enables you to traverse the complete array sequentially without using an index variable. For example, the following code displays all elements in the array myList: for (double value: myList) System.out.println(value); In general, the syntax is for (elementType value: arrayRefVar) { // Process the value } You still have to use an index variable if you wish to traverse the array in a different order or change the elements in the array. Searching Arrays Searching is the process of looking for a specific element in an array; for example, discovering whether a certain score is included in a list of scores. Searching is a common task in computer programming. There are many algorithms and data structures devoted to searching. In this section, two commonly used approaches are discussed, linear search and binary search.  The linear search approach compares the key element, key, sequentially with each element in the array list. The method continues to do so until the key matches an element in the list or the list is exhausted without a match being found. If a match is made, the linear search returns the index of the element in the array that matches the key. If no match is found, the search returns -1. Example: int[] list = {1, 4, 4, 2, 5, -3, 6, 2}; int i = linearSearch(list, 4); // returns 1 int j = linearSearch(list, -4); // returns -1 int k = linearSearch(list, -3); // returns 5 For binary search to work, the elements in the array must already be ordered. Without loss of generality, assume that the array is in ascending order. e.g., 2 4 7 10 11 45 50 59 60 66 69 70 79 The binary search first compares the key with the element in the middle of the array. If the key is less than the middle element, you only need to search the key in the first half of the array. If the key is equal to the middle element, the search ends with a match. If the key is greater than the middle element, you only need to search the key in the second half of the array.   The binarySearch method returns the index of the search key if it is contained in the list. Otherwise, it returns insertion point - 1. The insertion point is the point at which the key would be inserted into the list. /** Use binary search to find the key in the list */ public static int binarySearch(int[] list, int key) { int low = 0; int high = list.length - 1; while (high >= low) { int mid = (low + high) / 2; if (key < list[mid]) high = mid - 1; else if (key == list[mid]) return mid; else low = mid + 1; } return -1 - low; } The Arrays.binarySearch Method Since binary search is frequently used in programming, Java provides several overloaded binarySearch methods for searching a key in an array of int, double, char, short, long, and float in the java.util.Arrays class. For example, the following code searches the keys in an array of numbers and an array of characters. int[] list = {2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79}; System.out.println("Index is " + java.util.Arrays.binarySearch(list, 11)); //returns 4 char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'}; System.out.println("Index is " + java.util.Arrays.binarySearch(chars, 't')); // returns 4 (insertion point is 3) For the binarySearch method to work, the array must be pre-sorted in increasing order. Sorting Arrays Sorting, like searching, is also a common task in computer programming. Two simple, intuitive sorting algorithms: selection sort and insertion sort. Selection sort finds the largest number in the list and places it last. It then finds the largest number remaining and places it next to last, and so on until the list contains only a single number. The following figure shows how to sort the list {2, 9, 5, 4, 8, 1, 6} using selection sort.  Psedu-code for (int i = list.length - 1; i >= 1; i--) { select the largest element in list[0..i]; swap the largest with list[i], if necessary; // list[i] is in place. The next iteration applies on list[0..i-1] } // Find the maximum in the list[0..i] double currentMax = list[0]; int currentMaxIndex = 0; for (int j = 1; j <= i; j++) { if (currentMax < list[j]) { currentMax = list[j]; currentMaxIndex = j; } } // Swap list[i] with list[currentMaxIndex] if necessary; if (currentMaxIndex != i) { list[currentMaxIndex] = list[i]; list[i] = currentMax; } /** The method for sorting the numbers */ public static void selectionSort(double[] list) { for (int i = list.length - 1; i >= 1; i--) { // Find the maximum in the list[0..i] double currentMax = list[0]; int currentMaxIndex = 0; for (int j = 1; j <= i; j++) { if (currentMax < list[j]) { currentMax = list[j]; currentMaxIndex = j; } } // Swap list[i] with list[currentMaxIndex] if necessary; if (currentMaxIndex != i) { list[currentMaxIndex] = list[i]; list[i] = currentMax; } } } The insertion sort algorithm sorts a list of values by repeatedly inserting an unsorted element into a sorted sublist until the whole list is sorted.   How to insert?? The bubble-sort algorithm makes several iterations through the array. On each iteration, successive neighboring pairs are compared. If a pair is in decreasing order, its values are swapped; otherwise, the values remain unchanged. The technique is called a bubble sort or sinking sort because the smaller values gradually "bubble" their way to the top and the larger values sink to the bottom. int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted Iteration 1: 2, 5, 4, 8, 1, 6, 9 Iteration 2: 2, 4, 5, 1, 6, 8, 9 Iteration 3: 2, 4, 1, 5, 6, 8, 9 Iteration 4: 2, 1, 4, 5, 6, 8, 9 Iteration 5: 1, 2, 4, 5, 6, 8, 9 Iteration 6: 1, 2, 4, 5, 6, 8, 9 Arrays.sort Method Since sorting is frequently used in programming, Java provides several overloaded sort methods for sorting an array of int, double, char, short, long, and float in the java.util.Arrays class. For example, the following code sorts an array of numbers and an array of characters. double[] numbers = {6.0, 4.4, 1.9, 2.9, 3.4, 3.5}; java.util.Arrays.sort(numbers); char[] chars = {'a', 'A', '4', 'F', 'D', 'P'}; java.util.Arrays.sort(chars); Two-dimensional Arrays // Declare array ref var dataType[][] refVar; // Create array and assign its reference to variable refVar = new dataType[10][10]; // Combine declaration and creation in one statement dataType[][] refVar = new dataType[10][10]; // Alternative syntax dataType refVar[][] = new dataType[10][10]; int[][] matrix = new int[10][10]; or int matrix[][] = new int[10][10]; matrix[0][0] = 3; for (int i = 0; i < matrix.length; i++) for (int j = 0; j < matrix[i].length; j++) matrix[i][j] = (int)(Math.random() * 1000);  matrix.length? 5 matrix[0].length? 5 array.length? 4 array[0].length? 3 You can also use an array initializer to declare, create and initialize a two-dimensional array. For example, int[][] array = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12} }; int[][] array = new int[4][3]; array[0][0] = 1; array[0][1] = 2; array[0][2] = 3; array[1][0] = 4; array[1][1] = 5; array[1][2] = 6; array[2][0] = 7; array[2][1] = 8; array[2][2] = 9; array[3][0] = 10; array[3][1] = 11; array[3][2] = 12; int[][] x = new int[3][4];  Ragged Array Each row in a two-dimensional array is itself an array. So, the rows can have different lengths. Such an array is known as a ragged array. For example, int[][] matrix = { {1, 2, 3, 4, 5}, {2, 3, 4, 5}, {3, 4, 5}, {4, 5}, {5} }; matrix.length is 5 matrix[0].length is 5 matrix[1].length is 4 matrix[2].length is 3 matrix[3].length is 2 matrix[4].length is 1  See GradeExam.java ComputeTax.java Multidimensional Array Occasionally, you will need to represent n-dimensional data structures. In Java, you can create n-dimensional arrays for any integer n. The way to declare two-dimensional array variables and create two-dimensional arrays can be generalized to declare n-dimensional array variables and create n-dimensional arrays for n >= 3. For example, the following syntax declares a three-dimensional array variable scores, creates an array, and assigns its reference to scores. double[][][] scores = new double[10][5][2]; Example: write a program that calculates the total score for students in a class. Suppose the scores are stored in a three-dimensional array named scores. The first index in scores refers to a student, the second refers to an exam, and the third refers to the part of the exam. Suppose there are 7 students, 5 exams, and each exam has two parts--the multiple-choice part and the programming part. So, scores[i][j][0] represents the score on the multiple-choice part for the is student on the js exam. Your program displays the total score for each student. public class TotalScore { /** Main method */ public static void main(String args[]) { double[][][] scores = { {{7.5, 20.5}, {9.0, 22.5}, {15, 33.5}, {13, 21.5}, {15, 2.5}}, {{4.5, 21.5}, {9.0, 22.5}, {15, 34.5}, {12, 20.5}, {14, 9.5}}, {{5.5, 30.5}, {9.4, 10.5}, {11, 33.5}, {11, 23.5}, {10, 2.5}}, {{6.5, 23.5}, {9.4, 32.5}, {13, 34.5}, {11, 20.5}, {16, 7.5}}, {{8.5, 25.5}, {9.4, 52.5}, {13, 36.5}, {13, 24.5}, {16, 2.5}}, {{9.5, 20.5}, {9.4, 42.5}, {13, 31.5}, {12, 20.5}, {16, 6.5}}, {{1.5, 29.5}, {6.4, 22.5}, {14, 30.5}, {10, 30.5}, {16, 5.0}}}; // Calculate and display total score for each student for (int i = 0; i < scores.length; i++) { double totalScore = 0; for (int j = 0; j < scores[i].length; j++) for (int k = 0; k < scores[i][j].length; k++) totalScore += scores[i][j][k]; System.out.println("Student " + i + "'s score is " + totalScore); } } } Student 0's score is 160.0 Student 1's score is 163.0 Student 2's score is 147.4 Student 3's score is 174.4 Student 4's score is 201.4 Student 5's score is 181.4 Student 6's score is 165.9      PAGE \* MERGEFORMAT 16  EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8   EMBED Word.Picture.8     !tu$ J Z   <  ) * R ·th\Qhh1hE=^CJaJh1hS5CJaJh1h9_>*CJaJh1h1"CJaJ(jh1h1"CJUaJmHnHuh1h9_5CJaJh1h1"5CJaJh1hCJaJh1h9_CJaJh1h5CJaJh1hSfE5CJaJ#h1hSfE5CJPJaJnHtH&h1hSfE5CJPJaJnHo(tH  !tvwxyz{|}~^gd1"gd9_ & F gd9_h`hgdSfE% 2 I J Z [     < = o { gd9_ & Fgd9_^gd1"{   u v ( ) R p gd9_ & Fgd9_ ^`gd9_R Z _ c p u z \]go{·蝑xh1h)6CJ]aJh1h)CJaJh1h 5CJaJh1h CJaJh1h9_CJOJQJaJh1hSCJaJh1hS5CJaJh1h9_6CJ]aJh1h9_5CJaJh1h9_CJaJh1h9_>*CJaJ+ y z +[\^gd9_`gd9_h^hgd9_ & F gd9_ ^`gd9_gd9_ & F gd9_89R}Hde">X^_gd9_>m6VZ\]e=ngd9_9:uSPgd9_%Pvz}~=k & Fgd6gd)^gd)gd  qrzijxyz5 6 7 8 J 6"7"G"H"#{pdXMh1hPCJaJh1h\5CJaJh1hP5CJaJh1hSCJaJh1h%P5CJaJh1h\6CJ]aJh1h\CJaJ(jh1h6CJUaJmHnHuh1h6CJOJQJaJh1h65CJaJh1hS5CJaJh1h)CJaJh1h66CJ]aJh1h6CJaJlmqr79ik(cgijxy^gd6gd) & Fgd6gd6y{|}~5 6 7 8 J K !!4!Q!S!m!o!!!!gdSgd\gd)!!6"7"H"I"#############L%M%V%~%%%&&^gdKO! & FgdKO!gdPgd)gdS#########$ $-$1$G%I%& '!'F(G(H(I(V(W(X(l(x((ǻǭǻǻǢwlWlKlh1h5>*CJaJ(jh1h5CJUaJmHnHuh1h5CJaJh1h\CJaJ(jh1h QCJUaJmHnHuh1h QCJaJh1hJCJaJh1hKO!6CJ]aJh1hKO!>*CJaJh1hKO!CJaJ(jh1hPCJUaJmHnHuh1hPCJaJh1hP6CJ]aJ&&& '!'''F(G(I(J(K(L(M(N(O(P(Q(R(S(T(U(V(W(Y(Z( & Fgd Qgd)^gdJ`gdJ & FgdJZ([(\(](^(_(`(a(b(c(d(e(f(g(h(E)F){))))))*1*G*f*x**^gd(YXgd)(((F)****,,*---.-P-----/.=.B.P.x/y/z////۵vhhSێGh1hq5CJaJ(jh1h]Y;CJUaJmHnHuh1h]Y;6CJ]aJh1h55CJaJh1h]Y;5CJaJh1h]Y;CJaJ!h1hbB*CJ^JaJphh1hbCJaJh1h(YXCJaJh1h(YX5CJaJh1hZbCJOJQJaJh1h5CJaJh1h5CJOJQJaJh1hCJaJ**********,,R,t,,,,,P-Q-S------R.gd]Y;gd)H^Hgdb^gd(YXR.S.w/x/z/{/|/}/~///////////////////// & Fgd]Y;gd)///////////////010v0x0y000001$1B1_1g1gdqgd)//2224344444444444456 666777^9u9v9w9лۦۛۛېwk`kT`h1hU)5CJaJh1hLCJaJh1hL5CJaJh1hU)CJaJh1h'y 6CJ]aJh1h'y CJaJh1h6CJaJ(jh1hwCJUaJmHnHu(jh1hnXJCJUaJmHnHuh1h]Y;CJaJh1hnXJCJaJh1hqCJOJQJaJh1hqCJaJg1m1n1111122+2]2222223;3Y3v3~33333 4&4,404gd)gdq0424344444444444444444444444444 & FgdnXJgd)gdq444444444466667$7H7l77777888^gdLgdL & FgdL^gdU)gd'y  & Fgd6Bgd)899@9^9v9w99999992:_:`:v:::::::;(;U;;  gd.lOgdLgd'y ^gdLw9;;;;;;;;P<R<<<=======ƻxixTH<h1h5CJaJh1h1s5CJaJ(jh1h%CJUaJmHnHuh1hnXJCJOJQJaJh1h%CJOJQJaJh1h%CJaJh1hnXJCJaJh1hX=CJOJQJaJh1h6BCJOJQJaJh1h'y CJaJh1hU)CJaJ(jh1h6BCJUaJmHnHuh1hLCJaJh1hLCJOJQJaJ;;;;;;;;;;;;;;;;;;;;;;;P<Q<R<d<gd%gd)gdX=h^hgd'y gd'y d<q<~<<<<<<<%=Y===================gd)gd%==C>Q>a>>???@?A?I?k?l?m???AAAA B&B;BABC-CgChCzC{CCCG諠}qqqqqbh1hCJOJQJaJh1h>*CJaJh1h'"5CJaJh1hOCJaJh1h5CJaJh1hCJaJh1hnXJCJaJ(jh1hCJUaJmHnHuh1hCJOJQJaJh1h6CJ]aJh1hCJaJh1hnXJ5CJaJ=a>x>>>>>>>>>>>?(?>???A?B?C?D?E?F?G?H?I?l?m??gd)gd??@@YAZAAAAAAAAAACCCCD7D}DD Egdh^hgd^gdOgdO<`<gdO & FgdOgd) EOEEE"F#F^FFFFG>G?G{GGGGGGGG H'HBH]H_H`Hgdv 7$8$H$gd1s 7$8$H$gdgdGGGGGGG H H&H'HAHBH\H]H^H`HaHcHdHfHgHiHjHkHlHmHnHoHpHHHHHHHHHHHHHHHHHHH{jh6Ujh1"U!j I h9_CJPJUVaJh9_jh9_UhwmHnHujhvUhb!hvh5@jh5@Uh1h6CJaJ h1hCJOJQJ^JaJ, *h1hB*CJOJQJ^JaJph/`HbHcHeHfHhHiHjHkHlHmHnHoHHHHHHHHHHHHHHHgdPgd6gd9_$a$gdvHHHHHHHHHHHHHIIIIIII I!I"I$I%IIϾϮtld`OGj3h]Y;U!jهI h]Y;CJPJUVaJh]Y;jh]Y;Uj8'h5U!jRI h5CJPJUVaJh5jh5UjUh QU!jI h QCJPJUVaJh Qjh QUjhPU!j؄I hPCJPJUVaJhPjhPUjh6Ujh6U!jӃI h6CJPJUVaJh6HII#I$I@IAI]I^IzI{IIIIIIIII 7$8$H$gd1sgdgd%gdLgd6gdnXJgd]Y;gd5gd Q>I?IAIBIYIZI[I\I]I^I_IvIwIxIyI{I|IIIIIIIIIIIIII¾¾xtc[xtSOhjhUjeh%U!jI h%CJPJUVaJh%jh%UjYh6BU!j[I hLCJPJUVaJhLjhLUjRhwU!jI h6CJPJUVaJh6jh6UhqjFhwU!jLI hnXJCJPJUVaJhnXJjhnXJUh]Y;jh]Y;UIIIIIIIh1h6CJaJh5@hjhUj!mhU!jYI hCJPJUVaJ,1h/ =!"#$% `! 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Daniel Liang Daniel Liang  FMicrosoft Word Picture MSWordDocWord.Picture.89q  FMicrosoft Office Word Picture MSWordDocWord.Picture.89qOlePres000$WordDocument(**"SummaryInformation(+3DocumentSummaryInformation8; bjbj "jj:l     .. D D D D EGGGGGG$ #`kQkD D xD D EEhXD " `xj D0t#t# SHAPE \* MERGEFORMAT  list low [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] 10 11 45 list low high key == 11 2 4 7 10 11 45 high mid low high mid key > 7 [0] [1] [2] [3] [4] [5] mid list key < 50 key is 11 2 4 7 10 11 45 50 59 60 66 69 70 79 [3] [4] [5]  79:BCGQ  &(FGKLTUbcqr5CJ\aJCJOJQJ^JaJCJaJ jUjCJUmHnHu5:BCGHIJKLMNOPQ:  &'(FGKLTUbcqr 1hN N!"~#!$6 %Oh+'0t  0 < HT\dlssY. Daniel Liang. D. DNormale Daniel Liangng2niMicrosoft Word 9.0@G@J@4-՜.+,0 hp  $Armstrong Atlantic State University7  Title_12382060340 FuiuiOle Data -/D1TableL1Dd D  3 @@"?@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontVi@V  Table Normal :V 44 la (k@(No List NON CDT ]^ CJOJQJ_HmH sH tH  PU[KQV[afgu"f PU[KQV[afgu"f     @V@IT$)/<57<ESbRj&jj&j^jjjj&j^j&jj^j4j&j^j4j4jjjjj4jjjjjj@HIMNOPQRST#$()./;<567;<DERSab00I000I00?I00?I00?I00?I00?I00?I00?0I00?0I00?0I00?0I00%0I00!0I000I000I000I0 000I000I000I000I000I000I00 ?I00 ?0I00 ?0I00 ?00I00 ?0I00?0I00?0I00?0I00?0I000I00I00 < a   %=>_8@r&(    6 "`$  t  s * "`  z  0"` z  0"` z  0"`# z  0"`! NB @ S D"z  0"` z  0"` z  0"` z  0"` NB @ S D z  0"` NB @ S Dz  0"`  NB @ S D z  0"` NB @ S Dz  0"` NB @ S Dz  0"` z  0!"` !z  0"` NB @ S Dz  0"`  NB @ S D z  0"`  NB  S Dz  0"` t  s *"` t  s * "`  z  0"` z  0 "`  z  0 "`  NB  S Dt  s * "`  NB @ S DB S  ?  !"#$ t`  t  tb  ttzt t(Z (d th d tL t$h r t t<< tD@td62tt,, thD@tn 6 tttttplt. * tV rb t6 2 ttt8 4tL L tZFBt"t8.4t ttzt@@CGIL"$')-177:?CHNV]::::::::::::::::::::::@GILT"$')-/:<57:<CEQS`b@i` %@$)w:w:w:w:w:w:w:w:w:w:w:w:w:w:w:w:w:w:w:*@ :P@UnknownGz Times New Roman5Symbol3& z Arial?5 z Courier New71 Courier"hx;&;& 7 7!>4?? 3QHX(?i`2Y. Daniel LiangY. Daniel LiangCompObj.2oObjInfoOlePres00014f.WordDocument4m._. C }  + . "System 9?" -@Times New Roman-  2 Z - ---$) ) ---- $) ) --'& @Times New Roman-n2 B & [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]%%%%%%%%%%&%%%%% 2 G  & !'--$@X X @@---- $@X X @--'V D- >2 "DV  2 4 7 10 11 45 &&&&&%&%&@Times New Roman-2 DV 50%&-82 DV  59 60 66 69 70 79&%%&&%&&%&%& 2 / DV  !'--$.jj..--- - $.jj.-- 'h2- 2 w 2h key is 54%"$&& 2 w%2h !'--$7j7j--- - $7j7j-- '4h- 2  h4 key > 50%"$*&& 2 h4 !'--$@@@--- - $@@-- 'C- 2 C list 2 qC !'--$((--- - $((-- '}&- 2 `&}mid9& 2 `&} #'-- 88nnmkkjkkmnn--' --$  --- - $  -- ' -  2   [0] [1] [2]%%%%2   [3] [4] [5] %%% 2   >2 " [6] [7] [8] [9] [10] [11] [12]%%%%&%%%%% 2 M   ! 2 %  "'--$JdJd--- - $JdJd-- 'Gb- 2 * bG key < 66%"$*&& 2 *bG !'--$jj--- - $jj-- 'h- 2 h key %"$@1Courier New- 2 h< ---2 h59&& 2 'h !'--$  S S  --- - $  S S -- 'Q - 2 e  Q high&%& 2 eD  Q !'-- 88 t       t s q p p p q s t t % --' --$&&--- - $&&-- '}$- 2 `$}low&5 2 `$} #'-- 88nnmkkjkkmnn--' --$..00.--- - $..00-- '-1- 2 11-mid9& 2 1- #'-- 88rrlrmqoponplokojmjljjklnpqrrrnl[nU[nl--' --$  0Y 0Y  --- - $  0Y 0Y -- '-W  - 2   W -high&%& 2 J  W - !'-- 88  l m o o p o o m l           l+ [  [ l--' --$??**?--- - $??**-- ''B- 2 BB'low&5 2 B' #'-- 88}}f}g|i{jyjwjviugufuuvwy{|}}}yfUy`Uyf--' --$MM--- - $MM-- 'K- 2 -K list 2 -{K !'--$N  NN--- - $N  N-- ' R- g2 =R  [7] [8] %% 2 WR  !'--$VVV--- - $VV-- 'Z- 2 ZZmid9& 2 Z #'-- 883466766433"Tw"3--' --$"""--- - $""-- '&- 2 &&high&%& 2 & !'-- 88TBCD D C B @ > =NOPRSTUUTT@,BZ#@--' --$KK--- - $KK-- 'I- 2 Ilow&5 2 >I #'-- 88P7Q9Q:Q<P=N>M>K=J<     M:WbT/<M:--' --$--- - $-- '- 2  list 2 q !'--$Id Id --- - $Id Id -- 'Fb - }2 >Lb F 59 60 66 69 70 79&&&%&&%&%&&& 2 >( b F ! 2 b F "'--$X X --- - $X X -- 'V - =2 !V  12 V  59 60 %&&& 2 5V  !'--$  --- - $  -- ' - d2 ^;  [6] [7] [8] %%% 2 ^Z  !'--$`@@``--- - $`@@`-- '>d- 2 d>high&%& 2 1d> !'--$`TT``--- - $`TT`-- 'Rd- 2 dRlow&5 2 GdR #'-- 88ZZZZYWVTSV`k8V--' --$a a --- - $a a -- '_ - b2 :_  59 60%&&& 2 >_  !'-- 886 4 3 1 0 00124N94--'-q`  bjbjqPqP 4::@   -.)))))),,,,,,,$2.h0f,))$Z)))))),,+++))x,+)),++pX+ }9)++,0-+1Q*B1+1+))))+)))))))))),,+))))))-))))))))    SHAPE \* MERGEFORMAT  list low 59 60 low high [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] 59 60 list low high key < 59 59 60 66 69 70 79 high mid low high mid key < 66 [6] [7] [8] [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] mid list key > 50 key is 54 2 4 7 10 11 45 50 59 60 66 69 70 79 [7] [8] %&=?@HIMT  # $ ( ) . / 6 8 ; <   6 7 ; < D E R S a b ʼʱʦhi`5CJ\aJhi`hi`CJaJhi`CJOJQJ^JaJhi`CJaJhi`jhi`Ujhi`CJUmHnHu"jhi`CJUmHnHtHu@@HIMNOPQRST  # $ ( ) . / ; < @ < 5 6 7 ; < D E R S a gdi`a b 21h:pi`N N!"~#!$% SummaryInformation(35DocumentSummaryInformation8_1238206425,H: FuiuiOle Oh+'0|  8 D P\dltY. Daniel Liang Normal.dotY. Daniel Liang2Microsoft Office Word@^в@@ 7՜.+,0 hp  $Armstrong Atlantic State University?  Title  FMicrosoft Office Word Picture MSWordDocWord.Picture.89q  FMicrosoft Office Word Picture MSWordDocWord.Picture.89q1Table797CompObjoObjInfo8<OlePres000I@@@ NormalCJ_HaJmH sH tH DAD Default Paragraph FontVi@V  Table Normal :V 44 la (k@(No List 6O6 T5$7$8$9DH$aJ2B@2 Body Textx4;~L!ytOVI$!"%DBA7640.)IJ4;~L!ytOVI      @V4fhmoCEJL~SUNP)+.0{}JD ^D p^p^p^pD ^D H^Hp^pD ^D ^p^pD ^D ^H^HH^H^H^H^pD ^D H^Hp^pD ^D ^D ^D ^D ^H^H4fghmnoCDEJKL~STUNOP)*+./0{|}I0hI00I0I0 !"#$I0I0@!@I0I0@!@!I0I0@!@!I0I0!I0I0 H0I0I0H0I0I0 H0I0I0H0I0I0H0I0I0aI0I0 I0I0&aKI0I0)I0)I0)I0)I0)I0)I0)I0)I0)I0)I0)I0)I0)I0) I0) I0)I0)I0)I0)I0)I0)I0)I0)I0I0HI0I0K0i#aI0I0I0}     8JK@4J^(  f  s *2 TB  c $LD1TB  c $LD0HB  C D/f  s *. f  s *- TB  @ c $LD,f  s *+ TB  c $LD*TB  c $LD)HB  C Df  s *( TB  c $LDf  s *' l  0 &  TB  c $LD%HB  C D l  0   TB @ c $LDl  0$ TB  c $LDHB  C Dl  0 TB   c $LDl ! 0 !#  l " 0 ""  TB # c $LD!l $ 0 $  l % 0% TB &@ c $LDTB ' c $LDTB ( c $LDf ) s * f . s * TB /@ c $LDf 0 s * TB 1 c $LDTB 2 c $LDHB 3 C Df 4 s * TB 5 c $LDf 6 s * l 7 07  TB ;@ c $LD l A 0A  l B 0B  l D 0D  TB F@ c $LDTB G c $LDl I 0I l J 0J B S  ?  !"#$%&'()*+,-./012t4 ` t3 T t2` (` t1 ( tJ tI ltG\\ ( tF 8 tD! <$tBh!tA Dt;\ P !t7 (!t6X<t5PP t0 t/8 t.0 t) (tT,t(l\l@th`hthLt 8 t't t ttP h Lt&8pP H thHh t%$t$L t h `@ tx | | t# l t" 0(t!T t @XTtl | l ` t T @h tT t `t  tt h4|t P$8 tt $t0htT \t\\tH H t |t 34 4hlEI::::::4fhmEJL~). 34= $4fmoDU./|@ Pp P@UnknownGz Times New Roman5Symbol3& z Arial"hMZ&MZ&--!!>433 3qHX(?= 2 AdministratorY. Daniel Liang17AI $ U  \ . "System 9U  -@Times New Roman-  2 Z b ---$~ ~|a|a ~ ---- $~ ~|a|a --'y_ @Times New Roman-U2 H1 _y2 9 5 4 8 1 6""""""" 2 H' _y - 2  _y -'--88!!""!!7--'--88      *--'--%#--'--$T<T<T<---- $T<T<--'?W- 2 {WW?swap/" 2 {W? - 2 WW? -'--$sss---- $ss--'v- @2 )v#vSelect 9 (the largest) and swap it %""!"!/"72 vvvwith 6 (the last) in the list/"!""" 2 v$v - 2 vv -'--88(@KAJCKDLEMFNEPEQCR,*('&&&'((*C /*--'--$kk---- $kk--'i- S2 U0i2 6 5 4 8 1 """"""  2 Ui9"  2 U1i - 2 i -'--88 --'--88 l--'--%--'--$NNN---- $NN--'Q- 2 Qswap/" 2 qQ - 2 Q -'--8858:;;;:875571V $7--'--$) )   ) ---- $) )   --' , - (2 , ,  The number 9 now isy("""3"""!/2 c ,   in the ""72 \, ,  correct position and thus no !"!!!"!!""!@Times New Roman--%2 , ,  longer need to bei!"!""!"- 2  ,   -2  ,  considered.!""" 2 D ,   - 2 , ,   -'--$#pp##--- - $#pp#-- 'n&- G2 b(&n2 6 5 4 1 """"" 2 b~&n8 "2 b&n 9h"  2 b6&n - 2 &n -'-- 88(()*+-.001100 . - + * )((-F-(---'--%2--' --$VhhVV--- - $VhhV-- 'fY- 2 Yfswap/" 2 TYf - 2 Yf -'-- 889TVWYZZYXW<:87666799:RB:--' --$0zz00--- - $0zz0-- 'x3- ;2 o 3x2 1 5 4 """" %2 o3x6 8 9i"""  2 o@3x - 2 3x -'-- 885--'--%h--' --$c||cc--- - $c||c-- 'zf- 2 fzswap/" 2 hfz - 2 fz -'-- 88DD('&%&'(*+H<I=J?J@JBICHDFDDDDDF@A"eN-PF@--' --$sss--- - $ss-- 'v- @2 "v#vSelect 8 (the largest) and swap it %""!"!/"@2 ov#vwith 1 (the last) in the remaining /"!"""4!"!2 vvlist 2 v - 2 &vv -'--$     --- - $    -- '  - 42 +   The number 8 now is in the ("""3"""!/""72 x   correct position and thus no !"!!!"!!""!--%2    longer need to bei!"!""!"- 2     -2    considered.!""" 2 5    - 2 /    -'-- 88        - --' --$ii  i--- - $ii  -- ' l- @2 4l#l Select 6 (the largest) and swap it %""!"!/"@2 l#l with 1 (the last) in the remaining /"!"""4!"!2 ll list 2 l  - 2 8ll  -'--$     --- - $    -- '  - 42 .   The number 6 now is in the ("""3"""!/""72 {   correct position and thus no !"!!!"!!""!--%2    longer need to bei!"!""!"- 2     -2    considere !""2    d." 2 0    - 2 2    -'-- 88!JLNOPPONM#! !!"8+"--'-- 88;0?)@*A+A-A.@/>0=0;0;0=,:[<#;=,--'-- 88hhijkmnppqqppnmkjihhmm0Tm--' --$t3 t W W3 t3 --- - $t3 t W W3 -- ' U6 w- 2 r ww6 U 2 "+2 r w6 U 1 4 "" /2 r 9w6 U 5 6 8 9"!!"  2 r w6 U - 2 ww6 U -'--$i i   i --- - $i i   -- '  l- F2 S l'l  4 is the largest and last in the list. ""!!"!")2 ll  No swap is necessary0!/"" 2 l  - 2 ll  -'-- 88 6u 8t 9u :v ;w <y ;z ;{ 9| "           9  %  --' --$~@ ~ a a@ ~@ --- - $~@ ~ a a@ -- ' _C - #2  C _ 2 1 "" ;2   C _ 4 5 6 8 9""!!"  2  C _  2 C _ - 2 7 C _ -'-- 88#          # % & ' ' ' & % # # #  E y # --'-- 88## # $ % & ( ) + + , ,# +% +& )' (' &' %& $% ## ## (# A (E  (# --'--% # --' --$s  ( (s s --- - $s  ( (s -- ' &v - 2 v & swap/" 2 v & - 2  v & -'-- 88+A          .9 0: 1; 1= 1? 0@ .A -A +A +A -= ' LJ N -= --' --$   --- - $  -- ' " - 42 9 " " The number 4 now is in the ("""3"""!/""72 " " correct position and thus no !"!!!"!!""!--%2 " " longer need to bea!"!""!"- 2 " -2  " considered.!""" 2 : " - 2 = " " -'--$M  f fM M --- - $M  f fM -- ' dP - 2 P d 1 "  2 P d G2 (P d 2 4 5 6 8 9"""!!"  2 P d - 2 P d -'-- 88/J L M O P P O N M 20.-,,,-//0H'8 0--' --$i i   i --- - $i i   -- '  l- @2 L l#l  Select 2 (the largest) and swap it %""!"!/"@2 l#l  with 1 (the last) in the remaining /"!"""4!"!2 ll  list 2 l  - 2 P ll  -'--$        --- - $      -- '    - 42 U    The number 2 now is in the ("""3"""!/""72    correct position and thus no !"!!!"!!""!--%2    longer need to bea!"!""!"- 2    -2   considered.!""" 2 +    - 2 Y    -'--$___--- - $__-- '"b- >2 ^b"b"Since there is only one number in %""!" !"""3""52 bb"the remaining list, sort is "4""!!2 b b"completed !4"" 2 xb" - 2 bbb" -'-- 88 A B D E F F E D C            .  !  --'-- 881Z          5S 6T 7U 7W 7X 6Z 4Z 3Z 1Z 1Z 3V 08 Qf e 3V --' --$sss--- - $ss-- 'v- @2 2v#vSelect 5 (the largest) and swap it %""!"!/"@2 v#vwith 4 (the last) in the remaining /"!"""4!"!2 vvlist 2 v - 2 6 vv -'--$   --- - $  -- '  - 42 6    The number 5 now is in the ("""3"""!/""72    correct position and thus no !"!!!"!!""!--%2    longer need to bea!"!""!"- 2   -2   considered.!""" 2 &   - 2 :    -'-WordDocument;=.SummaryInformation(>DocumentSummaryInformation8_1238206796C Fuiuiq`  bjbjqPqP .::4xxxTjjjj~ *41113333333$4hH7b3x1+1113 32221*x321322>:x2 ^58>j1^2330*427'2727x211211111332111*41111   d j   j  2 9 5 4 8 1 6 swap Select 9 (the largest) and swap it with 6 (the last) in the list swap 2 6 5 4 8 1 9 The number 9 now is in the correct position and thus no longer need to be considered. swap 2 1 5 4 6 8 9 Select 6 (the largest) and swap it with 1 (the last) in the remaining list swap 2 6 5 4 1 8 9 Select 8 (the largest) and swap it with 1 (the last) in the remaining list The number 8 now is in the correct position and thus no longer need to be considered. The number 6 now is in the correct position and thus no longer need to be considered. Since there is only one number in the remaining list, sort is completed The number 2 now is in the correct position and thus no longer need to be considered. Select 2 (the largest) and swap it with 1 (the last) in the remaining list 1 2 4 5 6 8 9 The number 4 now is in the correct position and thus no longer need to be considered. swap 2 1 4 5 6 8 9 4 is the largest and last in the list. No swap is necessary 2 1 4 5 6 8 9 Select 5 (the largest) and swap it with 4 (the last) in the remaining list The number 5 now is in the correct position and thus no longer need to be considered. 34fhmo6 7 C D E J L l } ~    S T U    N O P ( ) + t u  - . 0 { | } h= B*CJph h= aJ h= CJh= jh= CJUmHnHuT4fghmnoC D E J K L ~  5$7$8$9DH$4     S T U     N O P 5$7$8$9DH$ ) * + . / 0 { | } 5$7$8$9DH$} h= aJh= h= CJ,1hN N!"#!$% Oh+'0|  8 D P\dltAdministrator Normal.dotY. Daniel Liang2Microsoft Office Word@@VU/>@VU/>-՜.+,0 hp  $Armstrong Atlantic State University3  TitleOle 1Table@B)CompObjoObjInfoAE     4 !"#%&'()*+-./0123O6789:;<>?@ABCDEFGHIJKLMN[QRSTUVWXYZl]^_`abcefghijknopqrstwxyz{|}~@@@ NormalCJ_HaJmH sH tH DAD Default Paragraph FontViV  Table Normal :V 44 la (k(No List 6O6 T5$7$8$9DH$aJ2B@2 Body Textx45RKCw     nigfdb`^]mj[45RKCwz       @VQT$&oq$&hj`bD ^D  ^ v ^v D ^D  ^ D ^D  ^ D ^D  ^ D ^D  ^ D ^D  ^ D ^D QRST$%&opq$%&hij`ab00@0I00,I00,00I00WI00,I00WI00 WI00WI00 7I00WI00WI00WI0 07I0&0W0@0I0)07I0)070@0I0)070@0I0)070@0I0)07I0)07I0)07I0)070@0I0)070@0I0)0 70@0I0)070@0I0)0W0@0I0)0WI0)0W00I0E070@0I0H0W0@0I000#L  q b   8~@n ~ (  l  0 TB  c $LDl  0 l [ 0[ NB \ S LDl ] 0] l ^ 0^ l ` 0` l b 0b l d 0d l f 0f l g 0g l i 0i l j 0j l m 0m  l n 0n TB p c $LD NB r S LD NB s@ S LDTB t c $LD NB u S LD NB v@ S LDTB w c $LDNB x S LDNB y@ S LDTB z c $LDNB { S LDNB |@ S LDTB } c $LDNB ~ S LDB S  ? |h ht~ Z t} t{8  ty  tz8 8 tvB& tx|BBtw|P|4 tuz$ttzztrztpzztmdxtitf  tb0 D t^ t\t[t>>ttnVX `tjf &tg N td t`X t] (t Ptsxtry:Afm9@_f(/W^RSKLCD::::Q$q$jbA|XO}w9x @? @UnknownGz Times New Roman5Symbol3& z Arial"qhFF!>4dy 3qHX(?O}2 AdministratorY. Daniel LiangOlePres000 $WordDocumentDF4SummaryInformation(G$DocumentSummaryInformation8,  FMicrosoft Office Word Picture MSWordDocWord.Picture.89q  FMicrosoft Word Picture MSWorq`  bjbjqPqP 4::xxxx     %FFFFF"""% % % % % % %$>&h(b-%x""""-%FF B%###"*FxF%#"%##>:x#F: 1u %#@# $X%0%#)e#^)#)x#8""#"""""-%-%#"""%""""     2 9 5 4 8 1 6 Step 1: Initially, the sorted sublist contains the first element in the list. Insert 9 to the sublist. Step 7: The entire list is now sorted 1 2 4 5 8 9 6 Step 5: The sorted sublist is {2, 4, 5, 8, 9}. Insert 1 to the sublist. 2 4 5 8 9 1 6 Step 4: The sorted sublist is {2, 4, 5, 9}. Insert 8 to the sublist. 2 4 5 9 8 1 6 Step 3: The sorted sublist is {2, 5, 9}. Insert 4 to the sublist. 2 5 9 4 8 1 6 Step2: The sorted sublist is {2, 9}. Insert 5 to the sublist. 1 2 4 5 6 8 9 Step 6: The sorted sublist is {1, 2, 4, 5, 8, 9}. Insert 6 to the sublist. 2 9 5 4 8 1 6 !QT\  $ & / E F S T o p q x  $ & . D E L ȻȯȯȟȯȻȯȻȯ h9CJh9B*CJphhO}B*CJph hO}aJ hACJ hO}CJhO}hO}B*CJphhO}"jhACJUmHnHtHujhwCJUmHnHu"jhwCJUmHnHtHu8QRST$ % & o p q 5$7$8$9DH$ q $ % & h i j    ` a b 5$7$8$9DH$L M h i j q y z { | }        3 4 D E ` a b k h9CJhO}B*CJphh9B*CJphhO}hO}B*CJphhO} hO}aJ hO}CJ hACJ)b 21h:pwN N!"#!$% Oh+'0x  4 @ LX`hpAdministratorNormalY. Daniel Liang2Microsoft Office Word@F#@u@ֆ%u՜.+,0 hp  $Armstrong Atlantic State University  Title_1238206896?]L FuiuiOle !Data IK51Table="Dd D  3 @@"?@@@ NormalCJ_HaJmH sH tH DAD Default Paragraph FontViV  Table Normal :V 44 la (k(No List NON CDT ]^ CJOJQJ_HmH sH tH !*+,-./0123[s|?@AJKLMfgp       !*+,-./0123[s|?@AJKLMfgp       @V +L^)Blx  jjjNjjjj jNjjjNjj jNjj+KLTUVWXYZ[\]^()ABijkltuvwx I000I000I00I00I00I00I00I00I00I00I00I000I00%0I00!0I000I000I00I0 00I000I000I00I00I000I00 I00 I00 I00 0I00 I000I000I00I000I000I000 B   () _8@>(    6 "`  t  s * "`  z  0"` z  0"`  z  0"` t  s *"`  z  0"`  z  0"`  z  0!"` !t  s *"` z  0"` z  0"`  z  0"` t  s * "`  z  0"` z  0"` B S  ?  h 6 r tt( pt nth~ lt v t r tx @ tht ptj 2t@ tZt nt\ $tv lt>t+ +8=OSaeEIos :::::::::::+LS^)@Bhlsx + >9 +K^ w:w:w:w:w:w:w:w:w:w:w:w:w:w:@  @UnknownGz Times New Roman5Symbol3& z Arial71 Courier"qhlFmF%%!>4d** 3QHX(?>92Y. Daniel LiangY. Daniel LiangCompObjJN"oObjInfo$OlePres000MP%$WordDocumentP4q`  bjbjqPqP 4::+ zzzz  ^$Lh!f(xpX 0ækz!.0^"Q"" ^   dz   z  SHAPE \* MERGEFORMAT  Step 2: Move list[2] to list[3] list [0] [1] [2] [3] [4] [5] [6] 2 4 5 9 list [0] [1] [2] [3] [4] [5] [6] Step 1: Save 4 to a temporary variable currentElement Step 3: Move list[1] to list[2] 2 5 9 [0] [1] [2] [3] [4] [5] [6] list 2 5 9 list Step 4: Assign currentElement to list[1] 2 5 9 4 [0] [1] [2] [3] [4] [5] [6] (*+KLT^  ( ) A B i l t x  ̼h>9CJaJh>9jh>9Ujh>9CJUmHnHu"jh>9CJUmHnHtHujhCJUmHnHu"jhCJUmHnHtHu(+KLTUVWXYZ[\]^   ( ) A B + B i j k l t u v w x    21h:p>9N N!"#!$ % SummaryInformation(OQ\DocumentSummaryInformation8d_1238207323V FuiuiOle &Oh+'0x  4 @ LX`hpY. Daniel LiangNormalY. 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