Chapter 6 Arrays

Spring 2013

Chapter 6 Arrays

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807

MotivationsOften you will have to store a large number of values during the execution of a program. Suppose, for instance, that you need to read one hundred numbers, compute their average, and find out how many numbers are above the average. Your program first reads the numbers and computes their average, and then compares each number with the average to determine whether it is above the average. The numbers must all be stored in variables in order to accomplish this task. You have to declare one hundred variables and repeatedly write almost identical code one hundred times. From the standpoint of practicality, it is impossible to write a program this way. So, how do you solve this problem?

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Objectives To describe why arrays are necessary in programming (§6.1). To learn the steps involved in using arrays: declaring array reference variables and

creating arrays (§§6.2.1-6.2.2). To initialize the values in an array (§6.2.3). To access array elements using indexed variables (§6.2.4). To simplify programming using the JDK 1.5 foreach loops (§6.2.5). To declare, create, and initialize an array using an array initializer (§6.2.6). To copy contents from one array to another (§6.3). To develop and invoke methods with array arguments and return value (§6.4-6.5). To declare a method with variable-length argument list (§6.6). To search elements using the linear (§6.7.1) or binary (§6.7.2) search algorithm. To sort an array using the selection sort (§6.8.1) To sort an array using the insertion sort algorithm (§6.8.2). To use the methods in the Arrays class (§6.9). To declare and create two-dimensional arrays to solve interesting problems such as

Sudoku (§6.10). To declare and create multidimensional arrays (§6.11).

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Introducing Arrays

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Array is a data structure that represents a collection of the same types of data.

5.6

4.5

3.3

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45.45

99.993

11123

double[] myList = new double[10];

myList reference myList[0]

myList[1]

myList[2]

myList[3]

myList[4]

myList[5]

myList[6]

myList[7]

myList[8]

myList[9]

Element value

Array reference variable

Array element at index 5


Declaring Array Variables

datatype[] arrayRefVar;

Example:

double[] myList;

datatype arrayRefVar[]; // This style is allowed, but not preferred

Example:

double myList[];

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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.

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Declaring and Creating in One Step

datatype[] arrayRefVar = new datatype[arraySize];

double[] myList = new double[10];

datatype arrayRefVar[] = new datatype[arraySize];

double myList[] = new double[10];

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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

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Default ValuesWhen an array is created, its elements are assigned the default value of

– 0 for the numeric primitive data types short, int, long, float, double

– '\u0000' for char types– false for boolean types.

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Indexed VariablesThe array elements are accessed through the index. The array indices are 0-based, i.e., it starts from 0 to arrayRefVar.length-1. For example:

double[] myList = new double[10]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];

myList[0], myList[1], myList[2], myList[3], myList[4], myList[5], myList[6], myList[7], myList[8], myList[9]

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Default Valuesint[] myInt = new int[5]Is initialized to:myInt[0] = 0myInt[1] = 0myInt[2] = 0myInt[3] = 0myInt[4] = 0

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double[] mydouble = new double[5]Is initialized to:mydouble[0] = 0.0mydouble[1] = 0.0 mydouble[2] = 0.0mydouble[3] = 0.0mydouble[4] = 0.0

boolean[] myBool = new boolean[5]]Is initialized to:myBool[0] = falsemyBool[1] = falsemyBool[2] = falsemyBool[3] = falsemyBool[4] = false


Using Indexed VariablesAfter 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[0] = 5.0;myList[1] = 2.4;myList[2] = myList[0] + myList[1];

Will set MyList[2] = 7.4

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Array Initializers

Declaring, creating, initializing in one step:double[] myList = {1.9, 2.9, 3.4, 3.5};

This shorthand syntax must be in one statement.

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Declaring, creating, initializing Using the Shorthand Notation

double[] myList = {1.9, 2.9, 3.4, 3.5};

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;

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CAUTION

Using the shorthand notation, you have to declare, create, and initialize the array all in one statement. Splitting it would cause a syntax error. For example, the following is wrong:

double[] myList;

myList = {1.9, 2.9, 3.4, 3.5};

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Trace Program with Arrays

public class Test { public static void main(String[] args) { int[] values = new int[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; }}

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Declare array variable values, create an array, and assign its reference to values

After the array is created

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i becomes 1


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i1




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i (=1) is less than 5


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public class Test { public static void main(String[] args) { int[] values = new int[5]; for (int i = 1; i < 5; i++) { values[i] = i + values[i-1]; } values[0] = values[1] + values[4]; }}

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After this line is executed, value[1] is 1

After the first iteration

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i1

values[1] = 1 + values[0]Values[1 = 1 + 0





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After i++, i becomes 2

animation

i2


Trace Program with Arrayspublic class Test { public static void main(String[] args) { int[] values = new int[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; }}


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i (= 2) is less than 5

animation

i2




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After this line is executed, values[2] is 3 (2 + 1)

After the second iteration

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values[2] = 2 + values[1]Values[2] = 2 + 1

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After this, i becomes 3.


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i (=3) is still less than 5.


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i3




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After this line, values[3] becomes 6 (3 + 3)

After the third iteration

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i3





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After this, i becomes 4


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i4




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i (=4) is still less than 5


0

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i4




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After this, values[4] becomes 10 (4 + 6)

After the fourth iteration

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10

animation

i4



Trace Program with Arrayspublic class Test { public static void main(String[] args) { int[] values = new int[5]; for (int i = 1; i < 5; i++) { values[i] = i + values[i-1]; } values[0] = values[1] + values[4]; }}


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After i++, i becomes 5

animation

i5





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i ( =5) < 5 is false. Exit the loop

animation

i5




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After this line, values[0] is 11 (1 + 10)

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10

animation

values[0] = 1 + 10


Processing Arrays

See the examples in the text.1. (Initializing arrays)

2. (Printing arrays)

3. (Summing all elements)

4. (Finding the largest element)

5. (Finding the smallest index of the largest element)

6. (Shifting elements)

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Initializing Arrays

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Initializing arrays with random values: The following loop initializes the array myList with random values between 0.0 and 100.0, but less than 100.0.

for ( int i = 0; i < myList. length; i++) { myList[ i] = Math. random() * 100; }


Printing Arrays

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To print an array, you have to print each element in the array using a loop like the following:

for ( int i = 0; i < myList. length; i++) { System. out. print( myList[ i] + " "); }

For an array of the char[] type, it can be printed using one print statement. For example, the following code displays Dallas: char[] city = {' D', ' a', ' l', ' l', ' a', ' s'}; System.out.println( city);


Summing all elements

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Use a variable named total to store the sum. Initially total is 0. Add each element in the array to total using a loop like this:

double total = 0; for ( int i = 0; i < myList. length; i++) { total += myList[ i]; }


Finding the largest element

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Use a variable named max to store the largest element. Initially max is myList[ 0]. To find the largest element in the array myList, compare each element in myList with max, and update max if the element is greater than max.

double max = myList[ 0]; for ( int i = 1; i < myList. length; i++) { if ( myList[ i] > max) max = myList[ i]; }


Finding the smallest index of the largest element

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Often you need to locate the largest element in an array. If an array has more than one largest element, find the smallest index of such an element. Suppose the array myList is 1, 5, 3, 4, 5, 5 The largest element is 5 and the smallest index for 5 is 1. Use a variable named max to store the largest element and a variable named indexOfMax to denote the index of the largest element. Initially max is myList[ 0], and indexOfMax is 0. Compare each element in myList with max, and update max and indexOfMax if the element is greater than max.

double max = myList[ 0]; int indexOfMax = 0; for ( int i = 1; i < myList. length; i++) { if (myList[i] > max) { max = myList[ i]; indexOfMax = i; } }

What is the consequence if ( myList[ i] > max) is replaced by ( myList[ i] >= max)?


Shifting elements

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Sometimes you need to shift the elements left or right. Here is an example to shift the elements one position to the left and fill the last element with the first element:

double temp = myList[ 0]; // Retain the first element // Shift elements left for ( int i = 1; i < myList. length; i++) { myList[ i - 1] = myList[ i]; } // Move the first element to fill in the last position myList[ myList. length - 1] = temp;


Enhanced for Loop (for-each 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.

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Example: Analyzing Array Elements

Objective: The program receives 6 numbers from the user, finds the largest number and counts the occurrence of the largest number entered.

Suppose you entered 3, 5, 2, 5, 5, and 5, the largest number is 5 and its occurrence count is 4.

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TestArray.java

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import java.util.Scanner; public class TestArray { /** Main method */ public static void main(String[] args) { final int TOTAL_NUMBERS = 6; int[] numbers = new int[TOTAL_NUMBERS]; // Create a Scanner Scanner input = new Scanner(System.in); // Read all numbers for (int i = 0; i < numbers.length; i++) { System.out.print("Enter a number: "); // Convert string into integer numbers[i] = input.nextInt(); }


TestArray.java

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// 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++; }


TestArray.java

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// 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); } }


Problem: Assigning Grades Objective: read student scores (int), get the best score, and

then assign grades based on the following scheme:– Grade is A if score is >= best–10;– Grade is B if score is >= best–20;– Grade is C if score is >= best–30;– Grade is D if score is >= best–40;– Grade is F otherwise.

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AssignGrade.java

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import java.util.Scanner; public class AssignGrade { /** Main method */ public static void main(String[] args) { // Create a Scanner Scanner input = new Scanner(System.in); // Get number of students System.out.print("Please enter number of students: "); int numberOfStudents = input.nextInt(); int[] scores = new int[numberOfStudents]; // Array scores int best = 0; // The best score char grade; // The grade // Read scores and find the best score for (int i = 0; i < scores.length; i++) { System.out.print("Please enter a score: "); scores[i] = input.nextInt(); if (scores[i] > best) best = scores[i]; }


AssignGrade.java

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// Declare and initialize output string String output = ""; // Assign and display grades for (int i = 0; i < scores.length; i++) { if (scores[i] >= best - 10) grade = 'A'; else if (scores[i] >= best - 20) grade = 'B'; else if (scores[i] >= best - 30) grade = 'C'; else if (scores[i] >= best - 40) grade = 'D'; else grade = 'F'; output += "Student " + i + " score is " + scores[i] + " and grade is " + grade + "\n"; } // Display the result System.out.println(output); } }


Copying ArraysOften, in a program, you need to duplicate an array or a part of an array. In such cases you could attempt to use the assignment statement (=), as follows: list2 = list1;

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Contents of list1

list1

Contents of list2

list2

Before the assignment list2 = list1;

Contents of list1

list1

Contents of list2

list2

After the assignment list2 = list1;

Garbage


Copying Arrays

Using a loop:int[] sourceArray = {2, 3, 1, 5, 10};int[] targetArray = new int[sourceArray.length];

for (int i = 0; i < sourceArrays.length; i++) targetArray[i] = sourceArray[i];

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The arraycopy Utility

arraycopy(sourceArray, src_pos, targetArray, tar_pos, length);

Example:System.arraycopy(sourceArray, 0, targetArray,

0, sourceArray.length);

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Passing Arrays to Methodspublic static void printArray(int[] array) { for (int i = 0; i < array.length; i++) { System.out.print(array[i] + " "); }}

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Invoke the method

int[] list = {3, 1, 2, 6, 4, 2};printArray(list);

Invoke the methodprintArray(new int[]{3, 1, 2, 6, 4, 2});

Anonymous array


Anonymous Array

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.

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Pass By Value

Java uses pass by value to pass arguments 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.

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Simple Examplepublic 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] }}

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Call Stack

When invoking m(x, y), the values of x and y are passed to number and numbers. Since y contains the reference value to the array, numbers now contains the same reference value to the same array.

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Space required for the main method int[] y: int x: 1

Stack Space required for method m int[] numbers: int number: 1

reference

5555 0 0

The arrays are stored in a heap.

Heap

reference

Array of ten int values is stored here


Heap

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.

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Space required for the main method int[] y: int x: 1

Stack Space required for xMethod int[] numbers: int number: 1

reference

Array of ten int values are stored here

The arrays are stored in a heap.

Heap

reference


Passing Arrays as Arguments

Objective: Demonstrate differences of passing primitive data type variables and array variables.

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TestPassArray.java

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public class TestPassArray { /** Main method */ 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] + "}"); }


TestPassArray.java

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/** 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; } }


Returning an Array from a Method

int[] list1 = new int[]{1, 2, 3, 4, 5, 6};int[] list2 = reverse(list1);

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public static int[] reverse(int[] list) { int[] result = new int[list.length]; for (int i = 0, j = result.length - 1; i < list.length; i++, j--) { result[j] = list[i]; } return result;}

list

result


Trace the reverse Methodint[] list1 = new int[]{1, 2, 3, 4, 5, 6};int[] list2 = reverse(list1);

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list

result

1 2 3 4 5 6

0 0 0 0 0 0

Declare result and create array

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Trace the reverse Method, cont.int[] list1 = new int[]{1, 2, 3, 4, 5, 6};int[] list2 = reverse(list1);

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list

result

1 2 3 4 5 6

0 0 0 0 0 0

i = 0 and j = 5

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list

result

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0 0 0 0 0 0

i (= 0) is less than 6

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list

result

1 2 3 4 5 6

0 0 0 0 0 1

i = 0 and j = 5 Assign list[0] to result[5]

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list

result

1 2 3 4 5 6

0 0 0 0 0 1

After this, i becomes 1 and j becomes 4

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list

result

1 2 3 4 5 6

0 0 0 0 0 1

i (=1) is less than 6

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list

result

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0 0 0 0 2 1

i = 1 and j = 4 Assign list[1] to result[4]

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list

result

1 2 3 4 5 6

0 0 0 0 2 1


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list

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0 0 0 0 2 1


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list

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1 2 3 4 5 6

0 0 0 3 2 1

i = 2 and j = 3 Assign list[i] to result[j]

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list

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1 2 3 4 5 6

0 0 0 3 2 1


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list

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0 0 0 3 2 1


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list

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1 2 3 4 5 6

0 0 4 3 2 1


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list

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1 2 3 4 5 6

0 0 4 3 2 1


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list

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1 2 3 4 5 6

0 0 4 3 2 1


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list

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1 2 3 4 5 6

0 5 4 3 2 1


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list

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1 2 3 4 5 6

0 5 4 3 2 1


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list

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1 2 3 4 5 6

0 5 4 3 2 1


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list

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1 2 3 4 5 6

6 5 4 3 2 1


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list

result

1 2 3 4 5 6

6 5 4 3 2 1

After this, i becomes 6 and j becomes -1

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list

result

1 2 3 4 5 6

6 5 4 3 2 1

i (=6) < 6 is false. So exit the loop.

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list

result

1 2 3 4 5 6

6 5 4 3 2 1

Return result

list2

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Problem: Counting Occurrence of Each Letter

Generate 100 lowercase letters randomly and assign to an array of characters.

Count the occurrence of each letter in the array.

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(a) Executing createArray in Line 6

Space required for the main method

char[] chars: ref

Heap

Array of 100 characters

Space required for the createArray method

char[] chars: ref

(b) After exiting createArray in Line 6

Space required for the main method

char[] chars: ref

Heap

Array of 100 characters

Stack Stack


CountLettersInArray.java

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public class CountLettersInArray { /** Main method */ public static void main(String args[]) { // Declare and create an array char[] chars = createArray(); // Display the array System.out.println("The lowercase letters are:"); displayArray(chars); // Count the occurrences of each letter int[] counts = countLetters(chars); // Display counts System.out.println(); System.out.println("The occurrences of each letter are:"); displayCounts(counts); }



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/** Create an array of characters */ public static char[] createArray() { // Declare an array of characters and create it char[] chars = new char[100]; // Create lowercase letters randomly and assign // them to the array for (int i = 0; i < chars.length; i++) chars[i] = RandomCharacter.getRandomLowerCaseLetter(); // Return the array return chars; } /** Display the array of characters */ public static void displayArray(char[] chars) { // Display the characters in the array 20 on each line for (int i = 0; i < chars.length; i++) { if ((i + 1) % 20 == 0) System.out.println(chars[i] + " "); else System.out.print(chars[i] + " "); } }



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/** Count the occurrences of each letter */ public static int[] countLetters(char[] chars) { // Declare and create an array of 26 int int[] counts = new int[26]; // For each lowercase letter in the array, count it for (int i = 0; i < chars.length; i++) counts[chars[i] - 'a']++; return counts; } /** Display counts */ public static void displayCounts(int[] counts) { for (int i = 0; i < counts.length; i++) { if ((i + 1) % 10 == 0) System.out.println(counts[i] + " " + (char)(i + 'a')); else System.out.print(counts[i] + " " + (char)(i + 'a') + " "); } } }


Searching ArraysSearching 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.

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public class LinearSearch { /** The method for finding a key in the list */ public static int linearSearch(int[] list, int key) { for (int i = 0; i < list.length; i++) if (key == list[i]) return i; return -1; } }

list

key Compare key with list[i] for i = 0, 1, …

[0] [1] [2] …


Linear SearchThe 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.

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Linear Search Animation

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6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

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Key List


From Idea to Solution/** The method for finding a key in the list */public static int linearSearch(int[] list, int key) { for (int i = 0; i < list.length; i++) if (key == list[i]) return i; return -1;}

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int[] list = {1, 4, 4, 2, 5, -3, 6, 2};int i = linearSearch(list, 4); // returns 1int j = linearSearch(list, -4); // returns -1int k = linearSearch(list, -3); // returns 5

Trace the method


LinearSearch.java

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public class LinearSearch { /** The method for finding a key in the list */ public static int linearSearch(int[] list, int key) { for (int i = 0; i < list.length; i++) { if (key == list[i]) return i; } return -1; } }


LinearSearchTest.java

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public class LinearSearchTest {/** * @param args */public static void main(String[] args) {

int[] list = {1, 4, 4, 2, 5, -3, 6, 2};int i = linearSearch(list, 4); // returns 1int j = linearSearch(list, -4); // returns -1int k = linearSearch(list, -3); // returns 5System.out.println("Index i is " + i);System.out.println("Index j is " + j);System.out.println("Index k is " + k);

}/** The method for finding a key in the list */public static int linearSearch(int[] list, int key) { for (int i = 0; i < list.length; i++) if (key == list[i]) return i; return -1;}

}


Binary Search

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.

92


Binary Search, cont.

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.

93

Consider the following three cases:


Binary Search

94

1 2 3 4 6 7 8 9

1 2 3 4 6 7 8 9

1 2 3 4 6 7 8 9

8

8

8

Key List

animation



95

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] 2 4 7 10 11 45 50 59 60 66 69 70 79

key is 11

key < 50 list

mid

[0] [1] [2] [3] [4] [5] key > 7

key == 11

high low

mid high low

list

[3] [4] [5]

mid high low

list

2 4 7 10 11 45

10 11 45



96

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] 2 4 7 10 11 45 50 59 60 66 69 70 79

key is 54

key > 50 list

mid

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] key < 66

key < 59

high low

mid high low

list

[7] [8]

mid high low

list

59 60 66 69 70 79

59 60

[6] [7] [8]

high low

59 60


Binary Search, cont.The binarySearch method returns the index of the element in the list that matches 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.

97


From Idea to Soluton/** 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;}

98


BinarySearch.java

99

public class BinarySearch { /** 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 -low - 1; // Now high < low } }


BinarySearchTest.java

100

public class BinarySearchTest { public static void main(String[] args) { int[] list = {2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79}; int i = binarySearch(list, 11); // returns 1 int j = binarySearch(list, 54); // returns -8 int k = binarySearch(list, -3); // returns -1 System.out.println("Index i is " + i); System.out.println("Index j is " + j); System.out.println("Index k is " + k); }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 -low - 1; // Now high < low } }


The Arrays.binarySearch MethodSince 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)); char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'};System.out.println("Index is " + java.util.Arrays.binarySearch(chars, 't'));

For the binarySearch method to work, the array must be pre-sorted in increasing order.

101

Return is 4

Return is –4 (insertion point is 3, so return is -3-1)


BinarySearchArrayTest.java

102

public class BinarySearchArrayTest { public static void main(String[] args) { 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)); char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'}; System.out.println("Index is " + java.util.Arrays.binarySearch(chars, 't')); }}


Sorting Arrays

Sorting, like searching, is also a common task in computer programming. It would be used, for instance, if you wanted to display the grades from Listing 6.2, “Assigning Grades,” in alphabetical order. Many different algorithms have been developed for sorting. This section introduces two simple, intuitive sorting algorithms: selection sort and insertion sort.

103


Selection SortSelection 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. Figure 6.17 shows how to sort the list {2, 9, 5, 4, 8, 1, 6} using selection sort.

104

2 9 5 4 8 1 6

swap

Select 9 (the largest) and swap it with 6 (the last) in the list

2 6 5 4 8 1 9

swap

The number 9 is now in the correct position and thus no longer needs to be considered.

2 6 5 4 1 8 9

swap

2 1 5 4 6 8 9

swap

Select 8 (the largest) and swap it with 1 (the last) in the remaining list




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

swap


1 2 4 5 6 8 9



Since there is only one number remaining in the list, sort is completed




Selection Sort

int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted

105

2 9 5 4 8 1 6

2 6 5 4 8 1 9

2 6 5 4 1 8 9

2 1 4 5 6 8 9

2 1 4 5 6 8 9

2 1 5 4 6 8 9

1 2 4 5 6 8 9

animation


From Idea to Solution

106

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]}

list[0] list[1] list[2] list[3] ... list[10]




list[0]

...


Expand

107


// 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; } }


Expand

108


// 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; } }


Expand

109


// Swap list[i] with list[currentMaxIndex] if necessary;if (currentMaxIndex != i) { list[currentMaxIndex] = list[i]; list[i] = currentMax;}


Wrap it in a Method

110

/** 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; } }}

Invoke it

selectionSort(yourList)


SelectionSort.java

111

public class SelectionSort { /** 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; } } } }


SelectionSortTest.java

112

public class SelectionSortTest { public static void main(String[] args) { int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted SelectionSort.selectionSort(myList); for(int i = 0; i < myList.length; i++) { System.out.print(myList[i]); if(i!= myList.length – 1) System.out.printf(“, “); } }}


Insertion Sortint[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted

113

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.

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.

2 9 5 4 8 1 6

Step2: The sorted sublist is {2, 9}. Insert 5 to the sublist.

2 5 9 4 8 1 6

Step 3: The sorted sublist is {2, 5, 9}. Insert 4 to the sublist.

2 4 5 9 8 1 6

Step 4: The sorted sublist is {2, 4, 5, 9}. Insert 8 to the sublist.

2 4 5 8 9 1 6

Step 5: The sorted sublist is {2, 4, 5, 8, 9}. Insert 1 to the sublist.

1 2 4 5 8 9 6

Step 6: The sorted sublist is {1, 2, 4, 5, 8, 9}. Insert 6 to the sublist.

1 2 4 5 6 8 9

Step 7: The entire list is now sorted


Insertion Sort

int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted

114

2 9 5 4 8 1 62 9 5 4 8 1 6

2 5 9 4 8 1 6

2 4 5 8 9 1 61 2 4 5 8 9 6

2 4 5 9 8 1 6

1 2 4 5 6 8 9

animation


How to Insert?

115

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.

[0] [1] [2] [3] [4] [5] [6]

2 5 9 4 list Step 1: Save 4 to a temporary variable currentElement

[0] [1] [2] [3] [4] [5] [6]

2 5 9 list Step 2: Move list[2] to list[3]

[0] [1] [2] [3] [4] [5] [6]

2 5 9 list Step 3: Move list[1] to list[2]

[0] [1] [2] [3] [4] [5] [6]

2 4 5 9 list Step 4: Assign currentElement to list[1]


From Idea to Solution

116

for (int i = 1; 1; i < list,length; i++) { insert list[i] into a sorted sublist list[0..i-1] so that list[0..i] is sorted}

list[0]

list[0] list[1]

list[0] list[1] list[2]

list[0] list[1] list[2] list[3]

list[0] list[1] list[2] list[3] ...


InsertionSort.java

117

public class InsertionSort { /** The method for sorting the numbers */ public static void insertionSort(double[] list) { for (int i = 1; i < list.length; i++) { /** insert list[i] into a sorted sublist list[0..i-1] so that list[0..i] is sorted. */ double currentElement = list[i]; int k; for (k = i - 1; k >= 0 && list[k] > currentElement; k--) { list[k + 1] = list[k]; } // Insert the current element into list[k+1] list[k + 1] = currentElement; } } }


InsertionSortTest.java

118

public class InsertionSortTest {public static void main(String[] args) { double[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted InsertionSort.insertionSort(myList); for(int i = 0; i < myList.length; i++) { System.out.print(myList[i]); if(i!= (myList.length - 1)) System.out.printf(", "); }/* System.out.println(); int[] myInts = {2, 9, 5, 4, 8, 1, 6}; // Unsorted InsertionSort.insertionSort(myInts); for(int i = 0; i < myInts.length; i++) { System.out.print(myInts[i]); if(i!= (myInts.length - 1)) System.out.printf(", ");} */ }


The Arrays.sort Method

119

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 ArraysThus far, you have used one-dimensional arrays to model linear collections of elements. You can use a two-dimensional array to represent a matrix or a table. For example, the following table that describes the distances between the cities can be represented using a two-dimensional array.

120

Chicago

Boston

New York

Atlanta

Miami

Dallas

Houston

Distance Table (in miles)

Chicago Boston New York Atlanta Miami Dallas Houston

0 983 787 714 1375 967 1087

983 0 214 1102 1763 1723 1842

787 214 0 888 1549 1548 1627

714 1102 888 0 661 781 810

1375 1763 1549 661 0 1426 1187

967 1723 1548 781 1426 0 239

1087 1842 1627 810 1187 239 0

1723 1548 781 1426 0 239


Declare/Create Two-dimensional Arrays

// Declare array ref vardataType[][] refVar;

// Create array and assign its reference to variablerefVar = new dataType[10][10];

// Combine declaration and creation in one statementdataType[][] refVar = new dataType[10][10];

// Alternative syntaxdataType refVar[][] = new dataType[10][10];

121


Declaring Variables of Two-dimensional Arrays and Creating Two-dimensional Arrays

int[][] matrix = new int[10][10]; orint matrix[][] = new int[10][10];//assign the value 3 to element [0][0]matrix[0][0] = 3;

//store random numbers in 2-dimensional array matrixfor (int i = 0; i < matrix.length; i++) for (int j = 0; j < matrix[i].length; j++) matrix[i][j] = (int)(Math.random() * 1000);

double[][] x;

122


Two-dimensional Array Illustration

123

0 1 2 3 4 0

7

0 1 2 3 4

1 2 3 4

0 1 2 3 4 matrix[2][1] = 7;

matrix = new int[5][5];

3

7

0 1 2 0 1 2

int[][] array = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12} };

1

2

3

4

5

6

8

9

10

11

12

array.length? 4

array[0].length? 3

matrix.length? 5

matrix[0].length? 5

array[0][0] array[0][2]

array[3][1]


Declaring, Creating, and Initializing Using Shorthand Notations

You can also use an array initializer to declare, create and initialize a two-dimensional array. For example,

124

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[][] array = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}};

Same as


Lengths of Two-dimensional Arraysint[][] x = new int[3][4];

125

x

x[0]

x[1]

x[2]

x[0][0] x[0][1] x[0][2] x[0][3] x[1][0] x[1][1] x[1][2] x[1][3] x[2][0] x[2][1] x[2][2] x[2][3]

x.length is 3

x[0].length is 4

x[1].length is 4

x[2].length is 4


Lengths of Two-dimensional Arrays, cont.

int[][] array = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}};

126

array.lengtharray[0].lengtharray[1].lengtharray[2].lengtharray[3].length

array[4].length ArrayIndexOutOfBoundsException


Ragged ArraysEach 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}};

127

matrix.length is 5matrix[0].length is 5matrix[1].length is 4matrix[2].length is 3matrix[3].length is 2matrix[4].length is 1


Ragged Arrays, cont.

128

1 2 3 4 5

int[][] triangleArray = { {1, 2, 3, 4, 5}, {2, 3, 4, 5}, {3, 4, 5}, {4, 5}, {5} };

2 3 4 5 3 4 5 4 5 5


Problem: Grading Multiple-Choice Test

Objective: write a program that grades multiple-choice test.

129

A B A C C D E E A D D B A B C A E E A D E D D A C B E E A D C B A E D C E E A D A B D C C D E E A D B B E C C D E E A D B B A C C D E E A D E B E C C D E E A D

0 1 2 3 4 5 6 7 8 9

Student 0 Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7

Students’ Answers to the Questions:

D B D C C D A E A D

0 1 2 3 4 5 6 7 8 9

Key

Key to the Questions:


GradeExam.java

130

public class GradeExam { /** Main method */ public static void main(String args[]) { // Students' answers to the questions char[][] answers = { {'A', 'B', 'A', 'C', 'C', 'D', 'E', 'E', 'A', 'D'}, {'D', 'B', 'A', 'B', 'C', 'A', 'E', 'E', 'A', 'D'}, {'E', 'D', 'D', 'A', 'C', 'B', 'E', 'E', 'A', 'D'}, {'C', 'B', 'A', 'E', 'D', 'C', 'E', 'E', 'A', 'D'}, {'A', 'B', 'D', 'C', 'C', 'D', 'E', 'E', 'A', 'D'}, {'B', 'B', 'E', 'C', 'C', 'D', 'E', 'E', 'A', 'D'}, {'B', 'B', 'A', 'C', 'C', 'D', 'E', 'E', 'A', 'D'}, {'E', 'B', 'E', 'C', 'C', 'D', 'E', 'E', 'A', 'D'} };


GradeExam.java

131

// Key to the questions char[] keys = {'D', 'B', 'D', 'C', 'C', 'D', 'A', 'E', 'A', 'D'}; // Grade all answers for (int i = 0; i < answers.length; i++) { // Grade one student int correctCount = 0; for (int j = 0; j < answers[i].length; j++) { if (answers[i][j] == keys[j]) correctCount++; } System.out.println("Student " + i + "'s correct count is " + correctCount); } } }


Problem: Finding Two Points Nearest to Each Other

132

(1, 1)

(-1, -1)

(-1, 3)

(2, 0.5)

(3, 3)

(4, 2)

(2, -1)

(4, -0.5)

-1 3 -1 -1 1 1 2 0.5 2 -1 3 3 4 2 4 -0.5

x y 0 1 2 3 4 5 6 7


FindNearestPoints.java

133

public class FindNearestPoints { public static void main(String[] args) { // Each row in points represents a point double[][] points = {{-1, 3}, {-1, -1}, {1, 1}, {2, 0.5}, {2, -1}, {3, 3}, {4, 2}, {4, -0.5}}; // p1 and p2 are the indices in the points array int p1 = 0, p2 = 1; // Initial two points double shortestDistances = distance(points[p1][0], points[p1][1], points[p2][0], points[p2][1]); // Initialize shortestDistances // Compute distance for every two points for (int i = 0; i < points.length; i++) { for (int j = i + 1; j < points.length; j++) { double distance = distance(points[i][0], points[i][1], points[j][0], points[j][1]);


FindNearestPoints.java

134

// Find distance if (shortestDistances > distance) { p1 = i; // Update p1 p2 = j; // Update p2 shortestDistances = distance; // Update shortestDistances } } } // Display result System.out.println("The closest two points are " + "(" + points[p1][0] + ", " + points[p1][1] + ") and (" + points[p2][0] + ", " + points[p2][1] + ")"); } /** Compute the distance between two points */ public static double distance( double x1, double y1, double x2, double y2) { return Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); } }


Case Study: Sudoku

135

5 3 7 6 1 9 5 9 8 6 8 6 3

4 8 3 1

7 2 6 6

4 1 9 5

8 7 9

5 3 4 6 7 8 9 1 2 6 7 2 1 9 5 3 4 8 1 9 8 3 4 2 5 6 7

8 5 9 7 6 1 4 2 3

4 2 6 8 5 3 7 9 1

7 1 3 9 2 4 8 5 6 9 6 1 5 3 7 2 8 4

2 8 7 4 1 9 6 3 5

3 4 5 2 8 6 1 7 9

The objective is to fill the grid (see Figure 6.14(a)) so that every row, every column, and every 3×3 box contain the numbers 1 to 9, as shown in Figure 6.14(b).


Case Study: Sudoku

136

Sudoku Run

int[][] grid = {{5, 3, 0, 0, 7, 0, 0, 0, 0}, {6, 0, 0, 1, 9, 5, 0, 0, 0}, {0, 9, 8, 0, 0, 0, 0, 6, 0}, {8, 0, 0, 0, 6, 0, 0, 0, 3}, {4, 0, 0, 8, 0, 3, 0, 0, 1}, {7, 0, 0, 0, 2, 0, 0, 0, 6}, {0, 6, 0, 0, 0, 0, 2, 8, 0}, {0, 0, 0, 4, 1, 9, 0, 0, 5}, {0, 0, 0, 0, 8, 0, 0, 7, 9} };

int[][] freeCellList = {{0, 2}, {0, 3}, {0, 5}, {0, 6}, {0, 7}, {0, 8}, {1, 1}, {1, 2}, {1, 6}, {1, 7}, {1, 8}, {2, 0}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 8}, {3, 1}, {3, 2}, {3, 3}, {3, 5}, {3, 6}, {3, 7}, {4, 1}, {4, 2}, {4, 4}, {4, 6}, {4, 7}, {5, 1}, {5, 2}, {5, 3}, {5, 5}, {5, 6}, {5, 7}, {6, 0}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 8}, {7, 0}, {7, 1}, {7, 2}, {7, 6}, {7, 7}, {8, 0}, {8, 1}, {8, 2}, {8, 3}, {8, 5}, {8, 6} };

Run with prepared input


Multidimensional ArraysOccasionally, 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];

137


Problem: Calculating Total Scores

Objective: 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 i’s student on the j’s exam. Your program displays the total score for each student.

138

TotalScore Run


Refine the table

139

6000 12000 6000 10000

27950 46700 23350 37450

67700 112850 56425 96745

141250 171950 85975 156600

307050 307050 153525 307050

10%

15%

27%

30%

35%

38.6%

Exercise 6.30


Reorganize the table

140

6000 27950 67700 141250 307050

12000 46700 112850 171950 307050

6000 23350 56425 85975 153525

10000 37450 96745 156600 307050

Rotate

Single filer

Married jointly

Married separatelyHead of household

6000 12000 6000 10000

27950 46700 23350 37450

67700 112850 56425 96745

141250 171950 85975 156600

307050 307050 153525 307050


Declare Two Arrays

141

int[][] brackets = { {6000, 27950, 67700, 141250, 307050}, // Single filer {12000, 46700, 112850, 171950, 307050}, // Married jointly {6000, 23350, 56425, 85975, 153525}, // Married separately {10000, 37450, 96700, 156600, 307050} // Head of household};

10%

15%

27%

30%

35%

38.6%double[] rates = {0.10, 0.15, 0.27, 0.30, 0.35, 0.386};

6000 27950 67700 141250 307050

12000 46700 112850 171950 307050

6000 23350 56425 85975 153525

10000 37450 96745 156600 307050

Single filer

Married jointly

Married separatelyHead of household

Documents

Chapter 6 Arrays