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<section version="5.0" xml:id="sd1_exam_2021_winter" xml:lang="en"
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<title>SD1 examination winter 2021</title>
<section xml:id="sd1_exam_2021_winter_task1">
<title>Implementing tasks</title>
<section xml:id="sd1_exam_2021_winter_task1_preparation">
<title>Preparation</title>
<orderedlist>
<listitem>
<para>Download and unzip the above file
<filename>exam.zip</filename>. You should see a directory
»<filename>Exam</filename>« containing a
<filename>pom.xml</filename> file.</para>
</listitem>
<listitem>
<para>Open this project in your <productname>IDEA</productname> IDE
by selecting the <filename>Exam/pom.xml</filename> file.</para>
</listitem>
</orderedlist>
</section>
<section xml:id="sd1_exam_2021_winter_task1_tasks">
<title>Tasks</title>
<qandaset defaultlabel="qanda" xml:id="sd1_exam_2021_winter_task1Qanda">
<qandadiv>
<qandaentry>
<question>
<para>Open the <filename>Readme.md</filename> file in your
project's root. It contains all necessary instructions for
solving the implementation tasks.</para>
</question>
<answer>
<para>Solution see <link
xlink:href="https://gitlab.mi.hdm-stuttgart.de/goik/GoikLectures/-/tree/master/Klausuren/Sd1/2021winter/Solve">winter
2021 Exam</link>.</para>
</answer>
</qandaentry>
</qandadiv>
</qandaset>
</section>
<section xml:id="sd1_exam_2021_winter_examCaveats">
<title>Caveats</title>
<itemizedlist>
<listitem>
<para>When approaching end of examination check your input for
completeness prior to being automatically logged out by the system.
Remember: There is 120 minutes for the examination and another 5
minutes to check for completeness.</para>
</listitem>
<listitem>
<para>Projects residing just on your local workstation's file system
cannot be recovered after finishing the exam.</para>
</listitem>
</itemizedlist>
</section>
</section>
<section xml:id="sd1_exam_2021_winter_task2">
<title><methodname>equals()</methodname> and
<methodname>hashCode()</methodname></title>
<qandaset defaultlabel="qanda" xml:id="sd1_exam_2021_winter_task2Qanda">
<qandadiv>
<qandaentry>
<question>
<para>Consider the following <classname>Person</classname>
class:</para>
<programlisting language="java">public class Person {
private String name, // Guaranteed never
comment; // to be null
private int ageInYears;
// Other methods omitted for brevity
@Override public boolean equals(Object o) {
if (o instanceof Person) {
final Person p = (Person) o;
return ageInYears == p.ageInYears &&
name.equals(p.name);
} else {
return false;
}
}
@Override public int hashCode() {
return ageInYears + 13 * comment.hashCode();
}
}</programlisting>
<para>We assume the above <methodname>equals()</methodname>
implementation to be correct. Answer the following two
questions:</para>
<orderedlist>
<listitem>
<para>Is this implementation correct regarding the <link
xlink:href="https://freedocs.mi.hdm-stuttgart.de/doc/openjdk-21-doc/api/java.base/java/lang/Object.html#hashCode()">contract
between <methodname>equals()</methodname> and
<methodname>hashCode()</methodname></link>? Correct if
necessary.</para>
</listitem>
<listitem>
<para>After correcting possible flaws: Is the resulting
implementation »good« with respect to distinguishing objects?
Amend if possible.</para>
</listitem>
</orderedlist>
<para>Explain your answers.</para>
</question>
<answer>
<orderedlist>
<listitem>
<para>The <methodname>equals(...)</methodname> method defines
two <classname>Person</classname> instances to be equal when
having common age and Name. Thus two instances e.g. <code>(18,
"Eve Porter", "New Friend from holiday")</code> and <code>(18,
"Eve Porter", "Friendly person")</code>of common name and age
but having a different comment will still considered to be
equal.</para>
<para>Since equality is being defined solely on
<property>age</property> and <property>name</property> the
<property>comment</property> attribute must not be used for
implementing <methodname>hashCode()</methodname>. Otherwise
the above example will result in different hash values
contradicting the <methodname>equals(...)</methodname> /
<methodname>hashCode()</methodname> contract. We thus
have:</para>
<programlisting language="java">public class Person {
...
@Override public int hashCode() {
return ageInYears;
}
}</programlisting>
</listitem>
<listitem>
<para>The previously corrected
<methodname>hashCode()</methodname> implementation is correct
with respect to its related <methodname>equals()</methodname>
method. However all <classname>Person</classname> instances of
common <property>age</property> but different
<property>name</property> will be defined to be different by
our <methodname>equals(...)</methodname> method. But they will
all share the same <methodname>hashCode()</methodname> value
throughout. So our <methodname>hashCode()</methodname> method
is not particularly good when it comes to distinguish objects.
Adding the <property>name</property> property to our
<methodname>hashCode()</methodname> calculation solves this
issue:</para>
<programlisting language="java">public class Person {
...
@Override public int hashCode() {
return ageInYears + 13 * name.hashCode();
}
}</programlisting>
</listitem>
</orderedlist>
</answer>
</qandaentry>
</qandadiv>
</qandaset>
</section>
<section xml:id="sd1_exam_2021_winter_task3">
<title>The average of three byte values</title>
<qandaset defaultlabel="qanda" xml:id="sd1_exam_2021_winter_task3Qanda">
<qandadiv>
<qandaentry>
<question>
<para>A newbie programmer codes the following snippet:</para>
<programlisting language="java">/**
* The average of three values
*
* @param a First value
* @param b Second value
* @param c Third value
*
* @return Closest <code>byte</code> value to ⅓ (a + b + c)
*/
public static byte getAverage(byte a, final byte b, final byte c) {
a += b;
a += c;
a /= 3;
return a;
}</programlisting>
<para>A senior programming companion warns about two possible
problems:</para>
<orderedlist>
<listitem>
<para>The implementation is prone to overflow errors.</para>
</listitem>
<listitem>
<para>The implementation will in many cases return
unnecessarily inaccurate results.</para>
</listitem>
</orderedlist>
<para>Explain both points in the answer box below.</para>
<para>In addition provide a solution by modifying the above
implementation without changing the method's signature. You may
present your code in the answer box below as well.</para>
<para>Alternatively correct the implementation of
<package>de.hdm_stuttgart.mi.sd1.task4_no_unit_test</package>.<classname>Mathextend</classname>
within your downloaded and imported <filename>exam.zip</filename>
project using your IDEA IDE. In this case <emphasis role="red">Do
not forget to export and upload after finishing by using task 1 of
this examination</emphasis>.</para>
<tip>
<para><methodname
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Math.html#round(double)">Math.round(double)</methodname>
might be your friend.</para>
</tip>
</question>
<answer>
<orderedlist>
<listitem>
<para>Biggest problem here: The operator <code
language="java">+=</code>'s way of cycling through a <code
language="java">byte</code>'s range when exceeding <code
language="java"
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Byte.html#MAX_VALUE">Byte.MAX_VALUE</code>
or <code language="java"
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Byte.html#MIN_VALUE">Byte.MIN_VALUE</code>
boundaries. Consider:</para>
<informaltable border="1">
<colgroup width="76%"/>
<colgroup width="24%"/>
<tr>
<th>Code</th>
<th>Output</th>
</tr>
<tr>
<td valign="top"><programlisting language="java">byte b = 127;
b += 1;
System.out.println("Result: " + b);</programlisting></td>
<td valign="top"><screen>Result: -128</screen></td>
</tr>
<tr>
<td valign="top"><programlisting language="java">byte b = -128;
b += -1;
System.out.println("Result: " + b);</programlisting></td>
<td valign="top"><screen>Result: +127</screen></td>
</tr>
<tr>
<td valign="top"><programlisting language="java">// Expecting 129 / 3 == +43
System.out.println("Result: " +
getAverage((byte) 127, (byte) 1, (byte) 1));</programlisting></td>
<td valign="top"><screen>Result: -42</screen></td>
</tr>
</informaltable>
</listitem>
<listitem>
<para>Converting fractions to byte values is next on the list
of troubles. The <code language="java">/=</code> operator will
simply cut off fractional values rather then rounding them
properly.</para>
<para>Switching to real values we have <inlineequation>
<m:math display="inline">
<m:mrow>
<m:mrow>
<m:mfrac bevelled="true">
<m:mi>1</m:mi>
<m:mi>3</m:mi>
</m:mfrac>
<m:mo></m:mo>
<m:mrow>
<m:mo>(</m:mo>
<m:mrow>
<m:mi>1</m:mi>
<m:mo>+</m:mo>
<m:mi>1</m:mi>
<m:mo>+</m:mo>
<m:mi>0</m:mi>
</m:mrow>
<m:mo>)</m:mo>
</m:mrow>
</m:mrow>
<m:mo>=</m:mo>
<m:mi>0.66...</m:mi>
</m:mrow>
</m:math>
</inlineequation> . Our byte valued method should thus
return a value of 1 rather than 0. However:</para>
<informaltable border="1">
<colgroup width="76%"/>
<colgroup width="24%"/>
<tr>
<th>Code</th>
<th>Output</th>
</tr>
<tr>
<td valign="top"><programlisting language="java">System.out.println("Result: " +
getAverage((byte) 1, (byte) 1, (byte) 0));</programlisting></td>
<td valign="top"><screen>Result: 0</screen></td>
</tr>
</informaltable>
</listitem>
</orderedlist>
<para>Solving these flaws requires using a data type behaving free
of overflow errors with respect to the given context of summing up
three byte values. Choosing <code>short</code> is sufficient for
adding either <code language="java"
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Byte.html#MAX_VALUE">Byte.MAX_VALUE</code>
or <code language="java"
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Byte.html#MIN_VALUE">Byte.MIN_VALUE</code>
even three times in a row.</para>
<para>Dividing by 3 should be a floating point rather than an
integer operation to avoid cutting off fractional values. On top
we finally use the <classname
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Math.html">Math</classname><code
language="java">.</code><methodname
xlink:href="https://freedocs.mi.hdm-stuttgart.de/lib/openjdk-21-doc/api/java.base/java/lang/Math.html#round(double)">round(double)</methodname>
method avoiding rounding errors like the one shown
previously.</para>
<para>Finally we need a cast for converting back the rounded
value's type <code language="java">double</code> to the method's
return type <code language="java">byte</code>. The final result
reads:</para>
<programlisting language="java">public static byte getAverage(final byte a, final byte b, final byte c) {
short sum = a;
sum += b;
sum += c;
final double avg = sum / 3.; // Floating point rather than integer division
return (byte) Math.round(avg);
}
// Note: final short sum = a + b + c does not even compile as being explained at
// https://freedocs.mi.hdm-stuttgart.de/sd1_sect_arithmeticOperators.html#sd1_explainNoByteByteOperator</programlisting>
<para>Given our sum being within range [-3 * -128, 3 * 127]
dividing by three guarantees <code language="java">avg</code> to
be within [-128, 127]. The <code language="java">(byte)</code>
cast will thus safe with respect to overflow problems of our
returned value.</para>
</answer>
</qandaentry>
</qandadiv>
</qandaset>
</section>
</section>