ch07-arrays.ppt

Building Java Programs
Chapter 7
Arrays
Copyright (c) Pearson 2013.
All rights reserved.

2
Can we solve this problem?
• Consider the following program (input underlined):
How many days' temperatures? 7
Day 1's high temp: 45
Average temp = 44.6
4 days were above average.

3
Why the problem is hard
• We need each input value twice:
– to compute the average (a cumulative sum)
– to count how many were above average
• We could read each value into a variable... but we:
– don't know how many days are needed until the program runs
– don't know how many variables to declare
• We need a way to declare many variables in one step.

4
Arrays
• array: object that stores many values of the same type.
– element: One value in an array.
– index: A 0-based integer to access an element from an array.
index 0 1 2 3 4 5 6 7 8 9
value 12 49 -2 26 5 17 -6 84 72 3
element 0 element 4 element 9

5
Array declaration
type[] name = new type[length];
– Example:
int[] numbers = new int[10];
index 0 1 2 3 4 5 6 7 8 9
value 0 0 0 0 0 0 0 0 0 0

6
Array declaration, cont.
• The length can be any integer expression.
int x = 2 * 3 + 1;
int[] data = new int[x % 5 + 2];
• Each element initially gets a "zero-equivalent" value.
Type Default value
int 0
double 0.0
boolean false
String
or other object
null
(means, "no object")

7
Accessing elements
name[index] // access
name[index] = value; // modify
– Example:
numbers[0] = 27;
numbers[3] = -6;
System.out.println(numbers[0]);
if (numbers[3] < 0) {
System.out.println("Element 3 is negative.");
}
index 0 1 2 3 4 5 6 7 8 9
value 0 0 0 0 0 0 0 0 0 0
index 0 1 2 3 4 5 6 7 8 9
value 27 0 0 -6 0 0 0 0 0 0

8
Arrays of other types
double[] results = new double[5];
results[2] = 3.4;
results[4] = -0.5;
boolean[] tests = new boolean[6];
tests[3] = true;
index 0 1 2 3 4
value 0.0 0.0 3.4 0.0 -0.5
index 0 1 2 3 4 5
value false false false true false false

9
Out-of-bounds
• Legal indexes: between 0 and the array's length - 1.
– Reading or writing any index outside this range will throw an
ArrayIndexOutOfBoundsException.
• Example:
int[] data = new int[10];
System.out.println(data[0]); // okay
System.out.println(data[9]); // okay
System.out.println(data[-1]); // exception
System.out.println(data[10]); // exception
index 0 1 2 3 4 5 6 7 8 9
value 0 0 0 0 0 0 0 0 0 0

10
Accessing array elements
int[] numbers = new int[8];
numbers[1] = 3;
numbers[4] = 99;
numbers[6] = 2;
int x = numbers[1];
numbers[x] = 42;
numbers[numbers[6]] = 11; // use numbers[6] as index
x
numbers
x 3
index 0 1 2 3 4 5 6 7
value
index 0 1 2 3 4 5 6 7
value 0 4 11 42 99 0 2 0

11
Arrays and for loops
• It is common to use for loops to access array elements.
for (int i = 0; i < 8; i++) {
System.out.print(numbers[i] + " ");
}
System.out.println(); // output: 0 4 11 0 44 0 0 2
• Sometimes we assign each element a value in a loop.
for (int i = 0; i < 8; i++) {
numbers[i] = 2 * i;
}
index 0 1 2 3 4 5 6 7
value 0 2 4 6 8 10 12 14

12
The length field
• An array's length field stores its number of elements.
name.length
for (int i = 0; i < numbers.length; i++) {
System.out.print(numbers[i] + " ");
}
// output: 0 2 4 6 8 10 12 14
– It does not use parentheses like a String's .length().
• What expressions refer to:
– The last element of any array?
– The middle element?

13
Weather question
• Use an array to solve the weather problem:
Average temp = 44.6

14
Weather answer
// Reads temperatures from the user, computes average and # days above average.
import java.util.*;
public class Weather {
public static void main(String[] args) {
Scanner console = new Scanner(System.in);
System.out.print("How many days' temperatures? ");
int days = console.nextInt();
int[] temps = new int[days]; // array to store days' temperatures
int sum = 0;
for (int i = 0; i < days; i++) { // read/store each day's temperature
System.out.print("Day " + (i + 1) + "'s high temp: ");
temps[i] = console.nextInt();
sum += temps[i];
}
double average = (double) sum / days;
int count = 0; // see if each day is above average
for (int i = 0; i < days; i++) {
if (temps[i] > average) {
count++;
}
}
// report results
System.out.printf("Average temp = %.1fn", average);
System.out.println(count + " days above average");
}
}

15
Quick array initialization
type[] name = {value, value, … value};
– Example:
int[] numbers = {12, 49, -2, 26, 5, 17, -6};
– Useful when you know what the array's elements will be
– The compiler figures out the size by counting the values
index 0 1 2 3 4 5 6
value 12 49 -2 26 5 17 -6

16
"Array mystery" problem
• traversal: An examination of each element of an array.
• What element values are stored in the following array?
int[] a = {1, 7, 5, 6, 4, 14, 11};
for (int i = 0; i < a.length - 1; i++) {
if (a[i] > a[i + 1]) {
a[i + 1] = a[i + 1] * 2;
}
}
index 0 1 2 3 4 5 6
value
index 0 1 2 3 4 5 6
value 1 7 10 12 8 14 22

17
Limitations of arrays
• You cannot resize an existing array:
int[] a = new int[4];
a.length = 10; // error
• You cannot compare arrays with == or equals:
int[] a1 = {42, -7, 1, 15};
int[] a2 = {42, -7, 1, 15};
if (a1 == a2) { ... } // false!
if (a1.equals(a2)) { ... } // false!
• An array does not know how to print itself:
int[] a1 = {42, -7, 1, 15};
System.out.println(a1); // [I@98f8c4]

18
The Arrays class
• Class Arrays in package java.util has useful static
methods for manipulating arrays:
• Syntax: Arrays.methodName(parameters)
Method name Description
binarySearch(array, value) returns the index of the given value in a sorted
array (or < 0 if not found)
copyOf(array, length) returns a new copy of an array
equals(array1, array2) returns true if the two arrays contain same
elements in the same order
fill(array, value) sets every element to the given value
sort(array) arranges the elements into sorted order
toString(array) returns a string representing the array, such as
"[10, 30, -25, 17]"

19
Arrays.toString
• Arrays.toString accepts an array as a parameter and
returns a String representation of its elements.
int[] e = {0, 2, 4, 6, 8};
e[1] = e[3] + e[4];
System.out.println("e is " + Arrays.toString(e));
Output:
e is [0, 14, 4, 6, 8]
– Must import java.util.*;

20
Weather question 2
• Modify the weather program to print the following output:
Average temp = 44.6
Temperatures: [45, 44, 39, 48, 37, 46, 53]
Two coldest days: 37, 39
Two hottest days: 53, 48

21
Weather answer 2
// Reads temperatures from the user, computes average and # days above average.
import java.util.*;
public class Weather2 {
...
int[] temps = new int[days]; // array to store days' temperatures
... (same as Weather program)
// report results
System.out.printf("Average temp = %.1fn", average);
System.out.println(count + " days above average");
System.out.println("Temperatures: " + Arrays.toString(temps));
Arrays.sort(temps);
System.out.println("Two coldest days: " + temps[0] + ", " + temps[1]);
System.out.println("Two hottest days: " + temps[temps.length - 1] +
", " + temps[temps.length - 2]);
}
}

23
Swapping values
int a = 7;
int b = 35;
// swap a with b?
a = b;
b = a;
System.out.println(a + " " + b);
}
– What is wrong with this code? What is its output?
• The red code should be replaced with:
int temp = a;
a = b;
b = temp;

24
Array reversal question
• Write code that reverses the elements of an array.
– For example, if the array initially stores:
[11, 42, -5, 27, 0, 89]
– Then after your reversal code, it should store:
[89, 0, 27, -5, 42, 11]
• The code should work for an array of any size.
• Hint: think about swapping various elements...

25
Algorithm idea
• Swap pairs of elements from the edges; work inwards:
index 0 1 2 3 4 5
value 11 42 -5 27 0 89
index 0 1 2 3 4 5
value 89 42 -5 27 0 11
index 0 1 2 3 4 5
value 89 0 -5 27 42 11
index 0 1 2 3 4 5
value 89 0 27 -5 42 11

26
Flawed algorithm
• What's wrong with this code?
int[] numbers = [11, 42, -5, 27, 0, 89];
// reverse the array
int temp = numbers[i];
numbers[i] = numbers[numbers.length - 1 - i];
numbers[numbers.length - 1 - i] = temp;
}
• The loop goes too far and un-reverses the array! Fixed version:
for (int i = 0; i < numbers.length / 2; i++) {
}

27
Array reverse question 2
• Turn your array reversal code into a reverse method.
– Accept the array of integers to reverse as a parameter.
int[] numbers = {11, 42, -5, 27, 0, 89};
reverse(numbers);
– How do we write methods that accept arrays as parameters?
– Will we need to return the new array contents after reversal?
...

28
Array parameter (declare)
public static type methodName(type[] name) {
• Example:
// Returns the average of the given array of numbers.
public static double average(int[] numbers) {
int sum = 0;
sum += numbers[i];
}
return (double) sum / numbers.length;
}
– You don't specify the array's length (but you can examine it).

29
Array parameter (call)
methodName(arrayName);
• Example:
public class MyProgram {
// figure out the average TA IQ
int[] iq = {126, 84, 149, 167, 95};
double avg = average(iq);
System.out.println("Average IQ = " + avg);
}
...
– Notice that you don't write the [] when passing the array.

30
Array return (declare)
public static type[] methodName(parameters) {
• Example:
// Returns a new array with two copies of each value.
// Example: [1, 4, 0, 7] -> [1, 1, 4, 4, 0, 0, 7, 7]
public static int[] stutter(int[] numbers) {
int[] result = new int[2 * numbers.length];
result[2 * i] = numbers[i];
result[2 * i + 1] = numbers[i];
}
return result;
}

31
Array return (call)
type[] name = methodName(parameters);
• Example:
public class MyProgram {
int[] iq = {126, 84, 149, 167, 95};
int[] stuttered = stutter(iq);
System.out.println(Arrays.toString(stuttered));
}
...
• Output:
[126, 126, 84, 84, 149, 149, 167, 167, 95, 95]

33
A swap method?
• Does the following swap method work? Why or why not?
int a = 7;
int b = 35;
// swap a with b?
swap(a, b);
System.out.println(a + " " + b);
}
public static void swap(int a, int b) {
int temp = a;
a = b;
b = temp;
}

34
Value semantics
• value semantics: Behavior where values are copied when
assigned, passed as parameters, or returned.
– All primitive types in Java use value semantics.
– When one variable is assigned to another, its value is copied.
– Modifying the value of one variable does not affect others.
int x = 5;
int y = x; // x = 5, y = 5
y = 17; // x = 5, y = 17
x = 8; // x = 8, y = 17

35
Reference semantics (objects)
• reference semantics: Behavior where variables actually store
the address of an object in memory.
– When one variable is assigned to another, the object is
not copied; both variables refer to the same object.
– Modifying the value of one variable will affect others.
int[] a1 = {4, 15, 8};
int[] a2 = a1; // refer to same array as a1
a2[0] = 7;
System.out.println(Arrays.toString(a1)); // [7, 15, 8]
index 0 1 2
value 4 15 8
index 0 1 2
value 7 15 8
a1 a2

36
References and objects
• Arrays and objects use reference semantics. Why?
– efficiency. Copying large objects slows down a program.
– sharing. It's useful to share an object's data among methods.
DrawingPanel panel1 = new DrawingPanel(80, 50);
DrawingPanel panel2 = panel1; // same window
panel2.setBackground(Color.CYAN);
panel1
panel2

37
Objects as parameters
• When an object is passed as a parameter, the object is not
copied. The parameter refers to the same object.
– If the parameter is modified, it will affect the original object.
DrawingPanel window = new DrawingPanel(80, 50);
window.setBackground(Color.YELLOW);
example(window);
}
public static void example(DrawingPanel panel) {
panel.setBackground(Color.CYAN);
...
} panel
window

38
Arrays pass by reference
• Arrays are passed as parameters by reference.
– Changes made in the method are also seen by the caller.
int[] iq = {126, 167, 95};
increase(iq);
System.out.println(Arrays.toString(iq));
}
public static void increase(int[] a) {
for (int i = 0; i < a.length; i++) {
a[i] = a[i] * 2;
}
}
– Output:
[252, 334, 190]
index 0 1 2
value 126 167 95
index 0 1 2
value 252 334 190
iq
a

39
Array reverse question 2
• Turn your array reversal code into a reverse method.
– Accept the array of integers to reverse as a parameter.
int[] numbers = {11, 42, -5, 27, 0, 89};
reverse(numbers);
• Solution:
public static void reverse(int[] numbers) {
for (int i = 0; i < numbers.length / 2; i++) {
}
}

40
Array parameter questions
• Write a method swap that accepts an arrays of integers and
two indexes and swaps the elements at those indexes.
int[] a1 = {12, 34, 56};
swap(a1, 1, 2);
• Write a method swapAll that accepts two arrays of integers
as parameters and swaps their entire contents.
– Assume that the two arrays are the same length.
int[] a1 = {12, 34, 56};
int[] a2 = {20, 50, 80};
swapAll(a1, a2);

41
Array parameter answers
// Swaps the values at the given two indexes.
public static void swap(int[] a, int i, int j) {
int temp = a[i];
a[i] = a[j];
a[j] = temp;
}
// Swaps the entire contents of a1 with those of a2.
public static void swapAll(int[] a1, int[] a2) {
for (int i = 0; i < a1.length; i++) {
int temp = a1[i];
a1[i] = a2[i];
a2[i] = temp;
}
}

42
Array return question
• Write a method merge that accepts two arrays of integers and
returns a new array containing all elements of the first array
followed by all elements of the second.
int[] a1 = {12, 34, 56};
int[] a2 = {7, 8, 9, 10};
int[] a3 = merge(a1, a2);
System.out.println(Arrays.toString(a3));
// [12, 34, 56, 7, 8, 9, 10]
• Write a method merge3 that merges 3 arrays similarly.
int[] a1 = {12, 34, 56};
int[] a2 = {7, 8, 9, 10};
int[] a3 = {444, 222, -1};
int[] a4 = merge3(a1, a2, a3);
System.out.println(Arrays.toString(a4));
// [12, 34, 56, 7, 8, 9, 10, 444, 222, -1]

43
Array return answer 1
// Returns a new array containing all elements of a1
// followed by all elements of a2.
public static int[] merge(int[] a1, int[] a2) {
int[] result = new int[a1.length + a2.length];
result[i] = a1[i];
}
result[a1.length + i] = a2[i];
}
return result;
}

44
Array return answer 2
// Returns a new array containing all elements of a1,a2,a3.
public static int[] merge3(int[] a1, int[] a2, int[] a3) {
int[] a4 = new int[a1.length + a2.length + a3.length];
a4[i] = a1[i];
}
a4[a1.length + i] = a2[i];
}
a4[a1.length + a2.length + i] = a3[i];
}
return a4;
}
// Shorter version that calls merge.
public static int[] merge3(int[] a1, int[] a2, int[] a3) {
return merge(merge(a1, a2), a3);
}

46
A multi-counter problem
• Problem: Write a method mostFrequentDigit that returns
the digit value that occurs most frequently in a number.
– Example: The number 669260267 contains:
one 0, two 2s, four 6es, one 7, and one 9.
mostFrequentDigit(669260267) returns 6.
– If there is a tie, return the digit with the lower value.
mostFrequentDigit(57135203) returns 3.

47
A multi-counter problem
• We could declare 10 counter variables ...
int counter0, counter1, counter2, counter3, counter4,
counter5, counter6, counter7, counter8, counter9;
• But a better solution is to use an array of size 10.
– The element at index i will store the counter for digit value i.
– Example for 669260267:
– How do we build such an array? And how does it help?
index 0 1 2 3 4 5 6 7 8 9
value 1 0 2 0 0 0 4 1 0 0

48
Creating an array of tallies
// assume n = 669260267
int[] counts = new int[10];
while (n > 0) {
// pluck off a digit and add to proper counter
int digit = n % 10;
counts[digit]++;
n = n / 10;
}
index 0 1 2 3 4 5 6 7 8 9
value 1 0 2 0 0 0 4 1 0 0

49
Tally solution
// Returns the digit value that occurs most frequently in n.
// Breaks ties by choosing the smaller value.
public static int mostFrequentDigit(int n) {
int[] counts = new int[10];
while (n > 0) {
int digit = n % 10; // pluck off a digit and tally it
counts[digit]++;
n = n / 10;
}
// find the most frequently occurring digit
int bestIndex = 0;
for (int i = 1; i < counts.length; i++) {
if (counts[i] > counts[bestIndex]) {
bestIndex = i;
}
}
return bestIndex;
}

50
Array histogram question
• Given a file of integer exam scores, such as:
82
66
79
63
83
Write a program that will print a histogram of stars indicating the
number of students who earned each unique exam score.
85: *****
86: ************
87: ***
88: *
91: ****

51
Array histogram answer
// Reads a file of test scores and shows a histogram of score distribution.
import java.io.*;
import java.util.*;
public class Histogram {
public static void main(String[] args) throws FileNotFoundException {
Scanner input = new Scanner(new File("midterm.txt"));
int[] counts = new int[101]; // counters of test scores 0 - 100
while (input.hasNextInt()) { // read file into counts array
int score = input.nextInt();
counts[score]++; // if score is 87, then counts[87]++
}
for (int i = 0; i < counts.length; i++) { // print star histogram
if (counts[i] > 0) {
System.out.print(i + ": ");
for (int j = 0; j < counts[i]; j++) {
System.out.print("*");
}
System.out.println();
}
}
}
}

52
Section attendance question
• Read a file of section attendance (see next slide):
yynyyynayayynyyyayanyyyaynayyayyanayyyanyayna
ayyanyyyyayanaayyanayyyananayayaynyayayynynya
yyayaynyyayyanynnyyyayyanayaynannnyyayyayayny
• And produce the following output:
Section 1
Student points: [20, 17, 19, 16, 13]
Student grades: [100.0, 85.0, 95.0, 80.0, 65.0]
Section 2
Student points: [17, 20, 16, 16, 10]
Student grades: [85.0, 100.0, 80.0, 80.0, 50.0]
Section 3
Student points: [17, 18, 17, 20, 16]
Student grades: [85.0, 90.0, 85.0, 100.0, 80.0]
• Students earn 3 points for each section attended up to 20.

53
– Each line represents a section.
– A line consists of 9 weeks' worth of data.
• Each week has 5 characters because there are 5 students.
– Within each week, each character represents one student.
• a means the student was absent (+0 points)
• n means they attended but didn't do the problems (+2 points)
• y means they attended and did the problems (+3 points)
Section input file
yynyyynayayynyyyayanyyyaynayyayyanayyyanyayna
ayyanyyyyayanaayyanayyyananayayaynyayayynynya
yyayaynyyayyanynnyyyayyanayaynannnyyayyayayny
week 1 2 3 4 5 6 7 8 9
student 123451234512345123451234512345123451234512345
section 1
section 2
section 3

54
Section attendance answer
import java.io.*;
import java.util.*;
public class Sections {
Scanner input = new Scanner(new File("sections.txt"));
int section = 1;
while (input.hasNextLine()) {
String line = input.nextLine(); // process one section
int[] points = new int[5];
for (int i = 0; i < line.length(); i++) {
int student = i % 5;
int earned = 0;
if (line.charAt(i) == 'y') { // c == 'y' or 'n' or 'a'
earned = 3;
} else if (line.charAt(i) == 'n') {
earned = 2;
}
points[student] = Math.min(20, points[student] + earned);
}
double[] grades = new double[5];
for (int i = 0; i < points.length; i++) {
grades[i] = 100.0 * points[i] / 20.0;
}
System.out.println("Section " + section);
System.out.println("Student points: " + Arrays.toString(points));
System.out.println("Student grades: " + Arrays.toString(grades));
section++;
}
}

55
Data transformations
• In many problems we transform data between forms.
– Example: digits  count of each digit  most frequent digit
– Often each transformation is computed/stored as an array.
– For structure, a transformation is often put in its own method.
• Sometimes we map between data and array indexes.
– by position (store the i th value we read at index i )
– tally (if input value is i, store it at array index i )
– explicit mapping (count 'J' at index 0, count 'X' at index 1)
• Exercise: Modify our Sections program to use static methods
that use arrays as parameters and returns.

56
Array param/return answer
// This program reads a file representing which students attended
// which discussion sections and produces output of the students'
// section attendance and scores.
import java.io.*;
import java.util.*;
public class Sections2 {
Scanner input = new Scanner(new File("sections.txt"));
int section = 1;
while (input.hasNextLine()) {
// process one section
String line = input.nextLine();
int[] points = countPoints(line);
double[] grades = computeGrades(points);
results(section, points, grades);
section++;
}
}
// Produces all output about a particular section.
public static void results(int section, int[] points, double[] grades) {
System.out.println("Section " + section);
System.out.println("Student scores: " + Arrays.toString(points));
System.out.println("Student grades: " + Arrays.toString(grades));
}
...

57
Array param/return answer
...
// Computes the points earned for each student for a particular section.
public static int[] countPoints(String line) {
int[] points = new int[5];
for (int i = 0; i < line.length(); i++) {
int student = i % 5;
int earned = 0;
if (line.charAt(i) == 'y') { // c == 'y' or c == 'n'
earned = 3;
} else if (line.charAt(i) == 'n') {
earned = 2;
}
points[student] = Math.min(20, points[student] + earned);
}
return points;
}
// Computes the percentage for each student for a particular section.
public static double[] computeGrades(int[] points) {
double[] grades = new double[5];
for (int i = 0; i < points.length; i++) {
grades[i] = 100.0 * points[i] / 20.0;
}
return grades;
}
}

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