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246 Arrays Chapter 7 43 [STAThread] 44 static void Main() 45 { 46 Application.Run( new RollDie() ); 47 } 48 49 private void rollButton_Click( 50 object sender, System.EventArgs e ) 51 { 52 // pass the labels to a method that will 53 // randomly assign a face to each die 54 DisplayDie( dieLabel1 ); 55 DisplayDie( dieLabel2 ); 56 DisplayDie( dieLabel3 ); 57 DisplayDie( dieLabel4 ); 58 DisplayDie( dieLabel5 ); 59 DisplayDie( dieLabel6 ); 60 DisplayDie( dieLabel7 ); 61 DisplayDie( dieLabel8 ); 62 DisplayDie( dieLabel9 ); 63 DisplayDie( dieLabel10 ); 64 DisplayDie( dieLabel11 ); 65 DisplayDie( dieLabel12 ); 66 67 double total = 0; 68 69 for ( int i = 1; i < 7; i++ ) 70 total += frequency[ i ]; 71 72 displayTextBox.Text = "FacetFrequencytPercentn"; 73 74 // output frequency values 75 for ( int x = 1; x < frequency.Length; x++ ) 76 { 77 displayTextBox.Text += x + "t" + 78 frequency[ x ] + "tt" + String.Format( "{0:N}", 79 frequency[ x ] / total * 100 ) + "%n"; 80 } 81 82 } // end Main 83 84 // simulates roll, display proper 85 // image and increment frequency 86 public void DisplayDie( Label dieLabel ) 87 { 88 int face = randomNumber.Next( 1, 7 ); 89 90 dieLabel.Image = Image.FromFile( 91 Directory.GetCurrentDirectory() + 92 "\images\die" + face + ".gif" ); 93 94 frequency[ face ]++; 95 } Fig. 7.6 Using arrays to eliminate a switch structure. (Part 2 of 3.)
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Chapter 7 Arrays 245 quency to determine which element should be incremented during each iteration of the loop, replaces lines 95 115 of Fig. 6.11. The random number calculation on line 88 produces numbers 1 6 (the values for a six-sided die); thus, the frequency array must be large enough to allow subscript values of 1 6. The smallest number of elements required for an array to have these subscript values is seven elements (subscript values 0 6). In this program, we ignore element 0 of array frequency. Lines 75 80 replace lines 69 81 from Fig. 6.11. We can loop through array frequency; therefore, we do not have to enumerate each line of text to display in the Label, as we did in Fig. 6.11. 1 // Fig. 7.7: RollDie.cs 2 // Rolling 12 dice. 3 4 using System; 5 using System.Drawing; 6 using System.Collections; 7 using System.ComponentModel; 8 using System.Windows.Forms; 9 using System.Data; 10 using System.IO; 11 12 public class RollDie : System.Windows.Forms.Form 13 { 14 private System.Windows.Forms.Button rollButton; 15 16 private System.Windows.Forms.RichTextBox displayTextBox; 17 18 private System.Windows.Forms.Label dieLabel1; 19 private System.Windows.Forms.Label dieLabel2; 20 private System.Windows.Forms.Label dieLabel3; 21 private System.Windows.Forms.Label dieLabel4; 22 private System.Windows.Forms.Label dieLabel5; 23 private System.Windows.Forms.Label dieLabel6; 24 private System.Windows.Forms.Label dieLabel7; 25 private System.Windows.Forms.Label dieLabel8; 26 private System.Windows.Forms.Label dieLabel9; 27 private System.Windows.Forms.Label dieLabel10; 28 private System.Windows.Forms.Label dieLabel11; 29 private System.Windows.Forms.Label dieLabel12; 30 31 private System.ComponentModel.Container components = null; 32 33 Random randomNumber = new Random(); 34 int[] frequency = new int[ 7 ]; 35 36 public RollDie() 37 { 38 InitializeComponent(); 39 } 40 41 // Visual Studio .NET generated code 42 Fig. 7.6 Using arrays to eliminate a switch structure. (Part 1 of 3.)
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244 Arrays Chapter 7 6 7 class Histogram 8 { 9 // main entry point for application 10 static void Main( string[] args ) 11 { 12 int[] n = { 19,3,15, 7, 11, 9, 13, 5,17,1 }; 13 string output = “”; 14 15 output += “ElementtvaluetHistogramn”; 16 17 // build output 18 for ( int i = 0; i < n.Length; i++ ) 19 { 20 output += "n" + i + "t" + n[ i ] + "t"; 21 22 for ( int j = 1; j <= n[ i ]; j++ ) // print a bar 23 output += "*"; 24 } 25 26 MessageBox.Show( output, "Histogram Printing Program", 27 MessageBoxButtons.OK, MessageBoxIcon.Information ); 28 29 } // end Main 30 31 } // end class Histogram Fig. 7.5 Program that prints histograms. (Part 2 of 2.) 7.4.4 Using the Elements of an Array as Counters Sometimes programs use a series of counter variables to summarize data, such as the results of a survey. In Chapter 6, Methods, we used a series of counters in our dice-rolling program to track the number of occurrences of each side on a six-sided die as the program rolled 12 dice at a time. We also indicated that there is a more elegant method than that in Fig. 6.11 for writing the dice-rolling program. An array version of this application is shown in Fig. 7.6. The program uses the seven-element array frequency to count the occurrences of each side of the die. Line 94, which uses the random facevalue as the subscript for array fre
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Chapter 7 Arrays 243 6 7 class SumArray 8 { 9 // main entry point for application 10 static void Main( string[] args ) 11 { 12 int[] a = { 1,2, 3, 4,5,6, 7, 8,9,10 }; 13 int total = 0; 14 15 for ( int i = 0; i < a.Length; i++ ) 16 total += a[ i ]; 17 18 MessageBox.Show( "Total of array elements: " + total, 19 "Sum the elements of an array", 20 MessageBoxButtons.OK, MessageBoxIcon.Information ); 21 22 } // end Main 23 24 } // end class SumArray Fig. 7.4 Computing the sum of the elements of an array. (Part 2 of 2.) 7.4.3 Using Histograms to Display Array Data Graphically Many programs present data to users in a graphical manner. For example, numeric values often are displayed as bars in a bar chart. In such a chart, longer bars represent larger numeric values. One simple way to display numeric data graphically is with a histogram that shows each numeric value as a bar of asterisks (*). Our next application (Fig. 7.5) reads numbers from an array and graphs the information in the form of a bar chart, or histogram. The program displays each number followed by a bar consisting of a corresponding number of asterisks. The nested for loops (lines 18 24) append the bars to the string that will be displayed in the MessageBox. Note the loop continuation condition of the inner for structure on line 22 (j<=n[i]). Each time the program reaches the inner for structure, the loop counts from 1to n[i], using a value in array n to determine the final value of the control variable j and the number of asterisks to display. 1 // Fig. 7.6: Histogram.cs 2 // Using data to create a histogram. 3 4 using System; 5 using System.Windows.Forms; Fig. 7.5 Program that prints histograms. (Part 1 of 2.)
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242 Arrays Chapter 7 Line 14 declares x as a reference to an array of integers. Each element in the array is of type int. The variable x is of type int[], which denotes an array whose elements are of type int. Line 15 allocates the 10 elements of the array with new and assigns the array to reference x. Each element of this array has the default value 0. Line 20 creates another int array and initializes each element using an initializer list. In this case, the number of elements in the initializer list determines the array s size. For example, line 20 creates a 10-element array with the indices 0 9 and the values 32, 27, 64, and so on. Note that this declaration does not require the new operator to create the array object the compiler allocates memory for the object when it encounters an array declaration that includes an initializer list. On line 22, we create constant integer ARRAY_SIZE using keyword const. A constant must be initialized in the same statement where it is declared and cannot be modified thereafter. If an attempt is made to modify a const variable after it is declared, the compiler issues a syntax error. Constants also are called named constants. They often are used to make a program more readable and are usually denoted with variable names in all capital letters. Common Programming Error 7.3 Assigning a value to a constant after the variable has been initialized is a compiler error. On lines 23 and 26, we create integer array z of length 10 using the ARRAY_SIZE named constant. The for structure in lines 29 30 initializes each element in array z. The values are generated by multiplying each successive value of the loop counter by 2 and adding 2 to the product. After this initialization, array z contains the even integers 2, 4, 6, , 20. The for structure in lines 35 37 uses the values in arrays x, y and z to build an output string, which will be displayed in a MessageBox. Zero-based counting (remember, array subscripts start at 0) allows the loop to access every element of the array. The constant ARRAY_SIZE in the for structure condition (line 29) specifies the arrays lengths. 7.4.2 Totaling the Elements of an Array Often, the elements of an array represent series of values to be used in calculations. For example, if the elements of an array represent the grades for an exam in a class, the professor may wish to total the elements of an array, then calculate the class average for the exam. The application in Fig. 7.4 sums the values contained in the 10-element integer array a (declared, allocated and initialized on line 12). Line 16 in the body of the for loop performs the addition using the array element at position i during each loop iteration. Note that the values being supplied as initializers for array a normally would be read into the program. For example, in a Windows application, the user could enter the values through a TextBox, or the values could be read from a file on disk. (See Chapter 17, Files and Streams.) 1 // Fig. 7.4: SumArray.cs 2 // Computing the sum of the elements in an array. 3 4 using System; 5 using System.Windows.Forms; Fig. 7.4 Computing the sum of the elements of an array. (Part 1 of 2.)
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Chapter 7 Arrays 241 6 7 class InitArray 8 { 9 // main entry point for application 10 static void Main( string[] args ) 11 { 12 string output = “”; 13 14 int[] x; // declare reference to an array 15 x = new int[ 10 ]; // dynamically allocate array and set 16 // default values 17 18 // initializer list specifies number of elements 19 // and value of each element 20 int[] y = { 32, 27, 64, 18, 95, 14, 90, 70, 60, 37 }; 21 22 const int ARRAY_SIZE = 10; // named constant 23 int[] z; // reference to int array 24 25 // allocate array of ARRAY_SIZE (i.e., 10) elements 26 z = new int[ ARRAY_SIZE ]; 27 28 // set the values in the array 29 for ( int i = 0; i < z.Length; i++ ) 30 z[ i ] = 2 + 2 * i; 31 32 output += "SubscripttArray xtArray ytArray zn"; 33 34 // output values for each array 35 for ( int i = 0; i < ARRAY_SIZE; i++ ) 36 output += i + "t" + x[ i ] + "t" + y[ i ] + 37 "t" + z[ i ] + "n"; 38 39 MessageBox.Show( output, 40 "Initializing an array of int values", 41 MessageBoxButtons.OK, MessageBoxIcon.Information ); 42 43 } // end Main 44 45 } // end class InitArray Fig. 7.3 Initializing element arrays in three different ways. (Part 2 of 2.)
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240 Arrays Chapter 7 The declaration int[] c = new int[ 12 ]; allocates 12 elements for integer array c. The preceding statement can also be performed in two steps as follows: int[] c; // declares the array c = new int[ 12 ]; // allocates the reference to the array When arrays are allocated, the elements are initialized to zero for the numeric primitive- data-type variables, to falsefor bool variables and to null for reference types. Common Programming Error 7.2 Unlike in C or C++, in C# the number of elements in the array is never specified in the square brackets after the array name. The declaration int[ 12 ] c; causes a syntax error. Memory may be reserved for several arrays with a single declaration. The following declaration reserves 100 elements for string array b and 27 elements for stringarray x: string[] b = new string[ 100 ], x = new string[ 27 ]; Similarly, the following declaration reserves 10 elements for array1and 20 elements for array2 (both of type double): double[] array1 = new double[ 10 ], array2 = new double[ 20 ]; Arrays may be declared to contain most data types. In an array of value types, every element of the array contains one value of the declared type. For example, every element of an int array is an int value. In an array of reference types, every element of the array is a reference to an object of the data type of the array. For example, every element of a stringarray is a reference to a string. Each of these string references has the value null by default. 7.4 Examples Using Arrays This section presents several examples using arrays that demonstrate declaring arrays, allocating arrays, initializing arrays and manipulating array elements in various ways. For simplicity, the examples in this section use arrays that contain elements of type int. Please remember that a program can declare arrays of most data types. 7.4.1 Allocating an Array and Initializing Its Elements Figure 7.3 creates three integer arrays of 10 elements and displays those arrays in tabular format. The program demonstrates several techniques for declaring and initializing arrays. 1 // Fig 7.3: InitArray.cs 2 // Different ways of initializing arrays. 3 4 using System; 5 using System.Windows.Forms; Fig. 7.3 Initializing element arrays in three different ways. (Part 1 of 2.)
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Chapter 7 Arrays 239 To divide the value of the seventh element of array cby 2and assign the result to the variable x, we would write x= c[ 6] / 2; Common Programming Error 7.1 It is important to note the difference between the seventh element of the array and array element seven. Array subscripts begin at 0, thus the seventh element of the array has a subscript of 6, while array element seven has a subscript of 7 and is actually the eighth element of the array. This confusion is a source of off-by-one errors. The brackets that enclose the subscript of an array are operators. Brackets have the same level of precedence as parentheses. The chart in Fig. 7.2 shows the precedence and associativity of the operators introduced to this point in the text. They are displayed top to bottom in decreasing order of precedence, with their associativity and type. The reader should note that the ++ and — operators in the first row represent the postincrement and postdecrement operators, while the ++ and –operators in the second row represent the preincrement and predecrement operators. Also, notice that in the first row the associativity is mixed. This is because the associativity of the postincrement and postdecrement operators is right to left, while the associativity for the other operators is left to right. 7.3 Declaring and Allocating Arrays Arrays occupy space in memory. The programmer specifies the type of the elements and uses operator new to allocate dynamically the number of elements required by each array. Arrays are allocated with new because arrays are objects and all objects must be created with new. We will see an exception to this rule shortly. Operators Associativity Type () [] . ++ –left to right highest (unary postfix) ++ — + - ! (type) right to left unary (unary prefix) * / % left to right multiplicative + -left to right additive < <= > >= left to right relational == != left to right equality & left to right logical AND ^ left to right logical exclusive OR | left to right logical inclusive OR && left to right conditional AND || left to right conditional OR ?: right to left conditional = += -= *= /= %= right to left assignment Fig. 7.2 Precedence and associativity of the operators discussed so far.
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238 Arrays Chapter 7 number of the element in square brackets ([]). The first element in every array is the zeroth element. Thus, the first element of array cis referred to as c[0], the second element of array c is referred to as c[1], the seventh element of array c is referred to as c[6] and so on. The ith element of array c is referred to as c[i-1]. Array names follow the same conventions as other variable names, as discussed in Chapter 3, Introduction to C# Programming. The position number in square brackets is more formally called a subscript (or an index). A subscript must be an integer or an integer expression. If a program uses an expression as a subscript, the program evaluates the expression first to determine the subscript. For example, if variable ais equal to 5 and variable b is equal to 6, then the statement c[ a + b ] += 2; adds 2 to array element c[11]. Note that a subscripted array name is an lvalue it can be used on the left side of an assignment to place a new value into an array element. Let us examine array c in Fig. 7.1 more closely. The name of the array is c. Every array in C# knows its own length. The length of the array is determined by the expression: c.Length The array s 12 elements are referred to as c[0], c[1], c[2], , c[11]. The value of c[0] is -45, the value of c[1] is 6, the value of c[2] is 0, the value of c[7] is 62 and the value of c[11] is 78. To calculate the sum of the values contained in the first three elements of array c and to store the result in variable sum, we would write sum = c[ 0 ] + c[ 1 ] + c[ 2 ]; Name of array (Note that all elements of this array have the same name, c) Position number (index or subscript) of the element within array c c[ 0 ] c[ 1 ] c[ 2 ] c[ 3 ] c[ 4 ] c[ 5 ] c[ 6 ] c[ 7 ] c[ 8 ] c[ 9 ] c[ 10 ] c[ 11 ] -45 6 0 72 1543 -89 0 62 -3 1 6453 78 Fig. 7.1 A 12-element array.
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Chapter 7 Arrays 237 Outline 7.1 Introduction 7.2 Arrays 7.3 Declaring and Allocating Arrays 7.4 Examples Using Arrays 7.4.1 Allocating an Array and Initializing Its Elements 7.4.2 Totaling the Elements of an Array 7.4.5 Using Arrays to Analyze Survey Results 7.4.3 Using Histograms to Display Array Data Graphically 7.4.4 Using the Elements of an Array as Counters 7.4.5 Using Arrays to Analyze Survey Results 7.5 Passing Arrays to Methods 7.6 Passing Arrays by Value and by Reference 7.7 Sorting Arrays 7.8 Searching Arrays: Linear Search and Binary Search 7.8.1 Searching an Array with Linear Search 7.8.2 Searching a Sorted Array with Binary Search 7.9 Multiple-Subscripted Arrays 7.10 foreach Repetition Structure Summary Terminology Self-Review Exercises Answers to Self-Review Exercises Exercises 7.1 Introduction This chapter serves as an introduction to data structures. Arrays are data structures consisting of data items of the same type. Arrays are static entities, in that they remain the same size once they are created. We begin by learning about creating and accessing arrays, then use this knowledge to begin more complex manipulations of arrays, including powerful searching and sorting techniques. We then demonstrate creating more sophisticated arrays that have multiple dimensions. Chapter 24, Data Structures, introduces dynamic data structures such as lists, queues, stacks and trees that can grow and shrink as programs execute. We also introduce C# s predefined data structures that enable the programmer to use existing data structures for lists, queues, stacks and trees, rather than having to reinvent the wheel. 7.2 Arrays An array is a group of contiguous memory locations that all have the same name and type. To refer to a particular location or element in the array, we specify the name of the array and the position number (a value that indicates a specific location within the array) of the element to which we refer. Figure 7.1 shows an integer array called c. This array contains 12 elements. A program can refer to any element of an array by giving the name of the array followed by the position
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