Download Lab10NestedLoops

J A V A
L A B
M A N U A L
LAB
OBJECT ORIENTED PROGRAMMING IN JAVA
10
PURPOSE OF THIS LAB
More Loops and Nested Loops
SESSION
In this lab you will print a table using a single loop. In addition, nested loops are an important tool in
programming. Some tables can be printed using a nested loop but, there are many other uses. Since you
can't write a nested loop unless understand how it is executed, you will practice doing a walk through of
some nested loops.
TO PREPARE FOR THIS
LAB

Read Wu: Chapter 6

Read through this laboratory session

Using your memory device, copy the files Primes.java and NestedLoops.java from
http://www.mscs.mu.edu/~marian/60/Labs/lab10
TO COMPLETE THIS LAB

This is an individual lab. You may ask the lab tutor for help and you may consult with your
neighbor if you are having difficulties.

In this lab, you will modify the and add to the two copied programs. When done with each
program, do a final run of each program and place a copy of the printed output in each file.

When you have completed the lab, hand in your printouts to the lab tutor.
MARIAN MANYO, MARQUETTE UINVERSITY
PAGE 10.1
10.1 FINDING PRIME NUMBERS
The positive factors, or divisors, of 2 are 1 and 2 .
The positive factors, or divisors, of 6 are 1, 2, 3, and 6.
The positive factors, or divisors, of 9 are 1, 3 and 9.
S t e p 1 : List the factors of 7 ________________________________________________
List the factors of 12 ________________________________________________
List the factors of 13 ________________________________________________
List the factors of 49 ________________________________________________
D e f i n t i o n : A prime number is a positive integer that has two distinct factors, 1 and itself.
The number one is not a prime number since it does not have two distinct factors. The number two is the
smallest prime number and the only even number that is a prime.
C i r c l e the numbers that are prime numbers:
-1 0 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
int number, is divisible by int divisor if number % divisor == 0.
For example: since 12 % 4 == 0 is true, 12 is divisible by 4
since 12 % 5 == 0 is false, 12 is not divisible by 5
Therefore, to determine if a positive integer number is a prime number, check if any of the integers between 2
and (number – 1) are divisors, or factors, of number.
The following algorithm, described using pseudocode, determines if int number is a prime number.
assume boolean isPrime = true
for factor between values of 2 and (number -1)
if (number % divisor == 0)
isPrime = false
Notice the following about the above pseudocode:

begin by assuming that num is a prime number: boolean isPrime = true;

Since all numbers are divisible by 1 and by themselves, only the numbers between 2 and (number –
1) are checked for divisibility into number

once a factor of num is found, isPrime is false and the existence of additional divisors is irrelevant.
PAGE 10.2
MARIAN MANYO, MARQUETTE UNIVERSITY
J A V A
L A B
M A N U A L
S t e p 1 : Open the file Primes.java and read it for understanding.
class Primes
{
public static void main(String[] args)
{
int number = -1;
do
{
System.out.println(number + " is a prime is " +
Primes.isPrime(number));
number++;
}while(number < 26);
}
private static boolean isPrime(int number)
{
return false;
}
}
The method
private static boolean isPrime(int number)
returns true if number is a prime number and false otherwise. In order for the above file to compile, the
dummy method isPrime must return a boolean value, I chose false.
Compile and run the program. For which of the test numbers is true printed?
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S t e p 2 : Let's begin to write the isPrime method. Initially, we assume number is a prime number by
assigning true to isPrime. If number is less than two, false is assigned to isPrime . If number is greater
than two, a loop that tries to find a divisor of number is needed. Notice that it is not necessary to explicitly
check if number is equal to two since isPrime is initially set to true and will not be changed. Revise the
isPrime method as shown
private static boolean isPrime(int number)
{
boolean isPrime = true;
if(number < 2)
isPrime = false;
else if(number > 2)
{
//look for a divisor of number
//if a divisor is found, set isPrime to false
}
return isPrime;
}
Compile and run the program. For which of the numbers tested in the main method, does isPrime return
true?
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MARIAN MANYO, MARQUETTE UINVERSITY
PAGE 10.3
S t e p 3 : Add the loop that looks for a divisor of number. When a divisor is found, isPrime is set to false
and, for efficiency, the loop should stop. When a break statement is executed inside of a loop, the loop
terminates and the next statement following the loop is executed.
private static boolean isPrime(int number)
{
boolean isPrime = true;
if(number < 2)
isPrime = false;
else if(number > 2)
{
for(int divisor = 2; divisor < number; divisor++)
{
if(number % divisor == 0)
{
isPrime = false;
break;
}
}
}
return isPrime;
//when the loop ends, isPrime is returned
}
Compile and run the program. For which of the numbers tested in the main method, does isPrime return
true?
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We now have a working method. However, that does not mean that we are done. You should always reread your code to see if improvements can be made to its appearance, its readability, its logic or its
efficiency. What improvements can be made to the isPrime method?

Since two is the only even prime number, we could make a special case for even numbers, so that
only odd numbers are checked by the loop.

If the loop no longer needs to check for divisibility by two, it no longer needs to check for divisibility
by any other even number. That is, we only need to check for divisibility by the odd numbers 3, 5,
7, ...

The number 53 is a prime number. How many possible divisors must be checked. Do we need to
check all of the odd numbers between 3 and 52, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 24, 25, 27, 29, 31,
33, 35, 37, 39, 41, 43, 45, 47, 49, and 51? The answer is no, but where can we stop?
The factors of 36, are 1, 2, 3, 4, 6,
9, 12, 18 and 36. Note:
1
2
3
4
6
x
x
x
x
x
PAGE 10.4
36
18
12
9
6
=
=
=
=
=
36
36
36
36
26
The factors of 49, are 1, 7
and 49. Note:
1 x 49 = 49
7 x 7 = 49
Note that for each example, half of the
factors are greater than the square root
and the other half are less than the
square root.
In addition, if a divisor of the number
(other than 1 or itself) does exist, the loop
will find the smaller number in the pair of
factors first. This is sufficient to
determine that the number is not prime.
MARIAN MANYO, MARQUETTE UNIVERSITY
J A V A
L A B
M A N U A L
S t e p 4 : Revise the isPrime method to reflect the suggested improvements.
private static boolean isPrime(int number)
{
boolean isPrime = true;
if(number < 2)
isPrime = false;
else if(number > 2)
{
if(number % 2 == 0)
//even numbers are not prime
isPrime = false;
else
{
double sqrt = Math.sqrt(number); //evaluate once
for(int divisor = 3; isPrime && divisor <= sqrt; divisor += 2)
{
if(number % divisor == 0)
isPrime = false;
//break has been removed
}
}
}
return isPrime;
}
Compile and run the program. For which of the numbers tested in the main method, does isPrime return
true?
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S t e p 5 : Note that the only values stored in number that allow the code
for(int divisor = 3; isPrime && divisor <= sqrt; divisor += 2)
{
if(number % divisor == 0)
isPrime = false;
}
to execute are odd. Use a table of values to do a walk through of the loop.
number = 125,
sqrt ≈ 11.18
MARIAN MANYO, MARQUETTE UINVERSITY
number = 53,
sqrt ~ 7.28
PAGE 10.5
What condition makes the loop end when number = 125?
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What condition makes the loop end when number = 53?
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10.2 PRINTING A CHART
A loop can be used to print a chart of values. For example, this chart contains all of the prime numbers
between 1 and 150.
Primes Between 1 and 150
2
17
41
67
97
127
3
19
43
71
101
131
5
23
47
73
103
137
7
29
53
79
107
139
11
31
59
83
109
149
13
37
61
89
113
There are 35 primes between 1 and 150
Begin by analyzing what is printed.
Print the heading
For every number between 1 and 150, if the number is a prime number, print it.
Print the footer
S t e p 6 : Add the following to Primes.java
In the main method, comment out the existing statements and add the single statement
printPrimeChart(1, 150);
Outside of the main method, add a third method to the Primes class
public void printPrimeChart(int min, int max)
{
System.out.println("
Primes Between " + min + " and " + max + "\n");
for(int num = min; num <= max; num++)
{
if(isPrime(num))
{
System.out.print(num + "
");
}
}
System.out.println("\n\n" +
"There are " + count + " primes between " + min + " and " + max);
}
Compile and run the program. Is the expected chart printed as planned? Explain the problem.
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PAGE 10.6
MARIAN MANYO, MARQUETTE UNIVERSITY
J A V A
L A B
M A N U A L
__________________________________________________________________________________________
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S t e p 7 : Obviously, we need to print newline characters to force new rows. In many charts, every
calculated value is printed and the placement of the newline character is determined by the loop counter,
num. However, in the prime chart, not all values of num are printed. Therefore, another criteria is needed
to determine when the newline character should be printed.
If six columns of numbers are desired, a newline character will be printed after the sixth, twelfth, eighteen,
twenty-fourth, etc. primes are printed. If we introduce a separate counter that is incremented every time a
prime number is printed, then a newline character is printed when the counter is 6, 12, 18, 24, . . . These
values all have something in common – they are divisible by 6.
Modify the printPrimeChart method to incorporate the needed changes.
public static void printPrimeChart(int min, int max)
{
int counter = 0; // determines when a newline character is printed.
System.out.println("
Primes Between " + min + " and " + max + "\n");
for(int num = min; num <= max; num++)
{
if(isPrime(num))
{
System.out.print(num + " ");
count++;
if(count % 6 == 0)
// if count is divisible by 6
{
// print a newline character
System.out.println();
}
}
}
System.out.println("\n\n" +
"There are " + count + " primes between " + min + " and " + max);
}
Compile and run the program. Does the chart print as planned? Explain any problems in the appearance.
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S t e p 8 : Before we handle the alignment problem in our chart, change the code to print seven
columns of prime numbers instead of six. Add another call to printPrimeChart in main to print
prime numbers between 999,000 and 1,000,000.
Compile and run the program. What is the largest prime number less than 1,000,000? How many
prime numbers are between 999,000 and 1,000,000?
__________________________________________________________________________________________
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MARIAN MANYO, MARQUETTE UINVERSITY
PAGE 10.7
10.3 STRING ALIGNMENT
The problem with the current printPrimeChart is that the numbers are not aligned in columns. Columns
can be aligned to the left or right easily using some of the new features added to Java 1.5. The following
have all been added to Java 5:

To the java.io.PrintStream class (System.out is a PrintStream object), a new method
public PrintStream printf(String format, Object ... args)

To the java.lang.String class, a new method
public static String format(String format, Object... args)

A new class java.util.Formatter which contains a method
Formatter format(String format, Object... args) Writes a formatted string to this
object's destination using the specified locale, format string, and arguments.
All of these options have much more versatility that we need for our prime chart or than we care to discuss
here. If you would like to read the online documentation, I suggest that you begin with the Formatter
class. For now, we will use the printf method.
S t e p 9 : Now, call the printf method from the printPrimeChart method, by replacing the statement
System.out.print(num + "
");
with the statement
System.out.printf("%10d", num);
that right aligns each integer value ("%d") in a field-width of ten.
Compile and run the program. Record any alignment problems.
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S t e p 1 0 : To left align each number in field-width of ten, place a negative sign in before the 10 in the
statement
System.out.printf("%-10d", num);
Compile and run the program. Record any alignment problems.
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PAGE 10.8
MARIAN MANYO, MARQUETTE UNIVERSITY
J A V A
L A B
M A N U A L
10.4 NESTED LOOPS
Suppose that we want to write a method to print a rectangle of characters with a variable width and height
with header
void printRectangle(int rows, int columns, char symbol)
For example, the call
printRectangle(3, 5, '?');
should print
?????
?????
?????
We could begin by forming the string "?????" and then print the string three times. For example, the loop
String s = "";
for(int c = 1; c <= columns; c++)
s += symbol;
creates the string "?????". This can be followed with a loop to print the string the correct number of times.
for(int row = 1; row <= height; row++)
System.out.println(s);
The complete method is
void printRectangle(int width, int height, char symbol)
{
String s = "";
for(int c = 1; c <= columns; c++)
s += symbol;
for(int r = 1; r <= rows; r++)
System.out.println(s);
}
A second version of the method is to use a nested loop, an inner loop nested inside of an outer loop. The
outer loop controls the number of rows to be printed.
void printRectangle(int rows, int columns, char symbol)
{
for(int r = 1; r <= rows; r++)
{
//loop to print a row
}
}
The loop to print a row, prints one symbol at a time. After the row is printed, a newline character is
printed.
for(int c = 1; c <= columns; c++)
{
System.out.print(symbol);
}
System.out.println();
MARIAN MANYO, MARQUETTE UINVERSITY
When columns is 5, the loop is
executed 5 times. Each time through
the loop symbol is printed.
When the loop ends, a newline is printed.
PAGE 10.9
void printRectangle(int rows, int columns, char symbol)
{
for(int r = 1; r <= rows; r++)
{
for(int c = 1; c <= columns; c++)
{
System.out.print(symbol);
}
System.out.println();
}
}
Let's do a walk through of this nested loop for the method call
printRectangle(3, 5, '?');
Notice, that when r is 1, the inner loop is executed five times. After the newline is printed, r is
incremented to 2 , and the inner loop is again executed 5 times. etc.
r
r <= rows
r <= 3
c
c <= columns
c <= 5
prints
1
true
1
true
?
2
true
?
3
true
?
4
true
?
5
true
?
6
false
\n
1
true
?
2
true
?
3
true
?
4
true
?
5
true
?
6
false
\n
1
true
?
2
true
?
3
true
?
4
true
?
5
true
?
6
false
\n
2
3
4
true
true
Prints:
?????
?????
?????
false
S t e p 1 : Open the file NestedLoops.java , which calls the method
public void printRectangle(int rows, int columns, int symbol)
from the run method. Compile and run the program to verify that it works as discussed.
PAGE 10.10
MARIAN MANYO, MARQUETTE UNIVERSITY
J A V A
L A B
M A N U A L
S t e p 2 : Suppose we would like to print a triangle similar to
*
**
***
****
*****
in which the number of rows is variable. To begin, let's assume that the number of rows to be printed is 5.
First, make a chart which lists what must be printed in each of the five rows. Note that each row is made
up of spaces followed by stars followed by a newline.
----*
---**
--***
-****
*****
row
1
2
3
4
5
spaces
4
3
2
1
0
stars
1
2
3
4
5
newline
\n
\n
\n
\n
\n
The outer loop will be controlled by the row #
for(row = 1; row <= 5; row++)
{
a loop to print spaces;
a loop to print stars;
print a \n;
}
For the first nested loop that prints the spaces, we need a relationship between the number of the row and
the number of spaces that are printed. Notice that row + spaces = 5 . Therefore, spaces = 5 – row.
For the second nested loop that prints the stars, we need a relationship between the number of the row
and the number of stars that are printed. Notice that stars is equal to row.
The completed loop
for(int row = 1; row <= 5; row++)
{
for(int spaces = 1; spaces <= 5 - row; spaces++)
System.out.print(‘ ’);
for(int stars = 1; stars <= row; stars++)
System.out.print(‘*’);
System.out.println();
}
Ad d a method
public void printTriangle1(int rows, char symbol)
that generalizes the above loop to handle any number of rows. Add several calls to the method from the
run method in NestedLoops.java to test your method.
Compile and run the revised program.
S t e p 3 : Add two methods
public void printTriangle2(int rows, char symbol)
public void printTriangle3(int rows, char symbol)
each of which prints a triangle like the two below which have rows equal to 5. Follow a thought process
similar to the thought process demonstrated above. Each rectangle lines up with the left side of the
monitor.
printTriangle2 (no spaces need to be printed)
*****
****
***
**
*
MARIAN MANYO, MARQUETTE UINVERSITY
printTriangle3 (print only leading spaces)
*
***
*****
*******
*********
PAGE 10.11
10.5 PRACTICE WALK-THROUGHS OF NESTED LOOPS
The following two exercises are typical quiz/test questions. Follow the code on paper first. Then, in the
run method of the program NestedLoops.java , uncomment the call to the appropriate method. Run the
program and check your answers.
S t e p 3 : First, predict what is printed by this code. Then check your answer by uncommenting the call to
quiz1() in the run method. Compile and run the program.
public void quiz1()
{
int j, k=0;
j
j<5
k
k<5
for(j = 1; j < 5; j++)
{
for(k = j; k < 5; k++)
{
System.out.print(j*k + " ");
}
System.out.println();
}
System.out.println("j = " + j + " k = " + k);
}
Prints:
S t e p 4 : First, predict what is printed by this code. Then check your answer by uncommenting the call to
quiz2() in the run method. Compile and run the program.
{
int j, k=0;
for(j = 4; j > 0; j--)
{
for(k = 1; k <= j; k++)
{
System.out.print(j+k + " ");
}
System.out.println();
}
System.out.println("j = " + j + " k = " + k);
}
Prints:
PAGE 10.12
MARIAN MANYO, MARQUETTE UNIVERSITY