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<p><strong>There is no time limit for this exam. Just submit your answers before the deadline.</strong></p>
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<h2 class="hd hd-2 unit-title">Part 1</h2>
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Recursion 1
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<pre>
public static String subsequences(String word) {
if (word.isEmpty()) {
return ""; // base case
} else {
char firstLetter = word.charAt(0);
String restOfWord = word.substring(1);
String subsequencesOfRest = subsequences(restOfWord);
String result = "";
for (String subsequence : subsequencesOfRest.split(",", -1)) {
result += "," + subsequence;
result += "," + firstLetter + subsequence;
}
result = result.substring(1); // remove extra leading comma
return result;
}
}
</pre>
<p>What does subsequences("c") return?</p>
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</div><p>What does subsequences("gc") return?</p>
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</label>
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Recursion 2
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<p>
Consider this recursive function:
</p>
<pre><code>
public static int factorial(int n) {
if (n == 0) {
return 1;
} else {
return n * factorial(n-1);
}
}
</code></pre>
<p>
Suppose the machine is running <code>factorial(7)</code> recursively, and has just entered a call for <code>factorial(0)</code>. Which of the following are true about the state of the machine at this point?
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_exam-01-nq_2_1">
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<input type="checkbox" name="input_exam-01-nq_2_1[]" id="input_exam-01-nq_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="exam-01-nq_2_1-choice_0-label" for="input_exam-01-nq_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_exam-01-nq_2_1"> There are multiple active calls to <code>factorial()</code> on the stack.
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<input type="checkbox" name="input_exam-01-nq_2_1[]" id="input_exam-01-nq_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="exam-01-nq_2_1-choice_1-label" for="input_exam-01-nq_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_exam-01-nq_2_1"> There are multiple instances of <code>n</code> on the stack.
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<input type="checkbox" name="input_exam-01-nq_2_1[]" id="input_exam-01-nq_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="exam-01-nq_2_1-choice_2-label" for="input_exam-01-nq_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_exam-01-nq_2_1"> The stack is at its deepest point in the recursion.
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<input type="checkbox" name="input_exam-01-nq_2_1[]" id="input_exam-01-nq_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="exam-01-nq_2_1-choice_3-label" for="input_exam-01-nq_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_exam-01-nq_2_1"> The return value from <code>factorial(0)</code> will be the return value from the whole recursion.
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Datatype definitions
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<p>Consider the datatype definition:</p>
<pre>
Geology = Core(a:int, b:int, c:int, d:int)
+ Planet(core:Core, a:int, b:int, c:int, d:int)
+ System(geology:Geology, a:int, b:int)
</pre>
<p>Suppose you have a reference to a <code>Geology</code> object. How many integers might it have in its representation?</p>
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<h3 class="hd hd-3 problem-header" id="exam-02-nq-problem-title" aria-describedby="block-v1:MITx+6.005.2x+1T2017+type@problem+block@exam-02-nq-problem-progress" tabindex="-1">
Immutable lists
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<p>Consider the immutable <code>ImList&lt;E&gt;</code> datatype, which has these operations:</p>
<table class="table table-condensed no-markdown">
<tbody>
<tr>
<th>empty: void &#8594; ImList</th>
<td>returns an empty list</td>
</tr>
<tr>
<th style="white-space:nowrap">cons: E &#215; ImList &#8594; ImList&#8195;</th>
<td>returns a new list formed by adding an element to the front of another list</td>
</tr>
<tr>
<th>first: ImList &#8594; E</th>
<td>returns the first element of a list, requires the list to be nonempty</td>
</tr>
<tr>
<th>rest: ImList &#8594; ImList</th>
<td>returns the list of all elements of this list except for the first, requires the list to be nonempty</td>
</tr>
</tbody>
</table>
<p>and this datatype definition:</p>
<pre>
ImList&lt;E&gt; = Empty + Cons(first:E, rest:ImList)
</pre>
<p>If we run:</p>
<pre>
ImList&lt;String&gt; a = ImList.empty();
ImList&lt;String&gt; b = a.cons("blue").cons("red");
</pre>
<p>How many <code>ImList</code> objects are in only list <code>a</code> or <code>b</code>, <strong>not</strong> in both?</p>
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</div><p>How many <code>ImList</code> objects are shared by both lists <code>a</code> and <code>b</code>?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_exam-02-nq_3_1">
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</div><p>The actual runtime type of the object returned by <code>b.first()</code> is (choose all that apply):</p>
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<code>Cons</code>
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<code>Empty</code>
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<code>ImList</code>
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<code>ImList&lt;String&gt;</code>
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<code>String</code>
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<span id="solution_exam-02-nq_solution_3"/>
</div><p>The actual runtime type of the object returned by <code>b.rest()</code> is (choose all that apply):</p>
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<code>Cons</code>
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<code>Empty</code>
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<code>ImList</code>
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<code>ImList&lt;String&gt;</code>
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<code>String</code>
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Regular expressions
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<p>Which of these strings completely match the regular expression
<code>12+(3|5)*</code>?</p>
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<code>11111</code>
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<code>12121235</code>
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<code>1222</code>
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<code>1253</code>
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<input type="checkbox" name="input_exam-03-nq_2_1[]" id="input_exam-03-nq_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="exam-03-nq_2_1-choice_4-label" for="input_exam-03-nq_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_exam-03-nq_2_1">
<code>123</code>
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</div><p>Which of these regular expressions completely match <code>foo</code> but not <code>boo</code>?</p>
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<code>(foo)?(boo)?</code>
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<code>[a-z]o+</code>
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<code>(b|fo*)o</code>
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<code>f*o*b*o*</code>
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<code>boofoo</code>
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Grammars
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<p>Which strings match the root nonterminal of this grammar?</p>
<pre>
root ::= integer ('-' integer)+
integer ::= [0-9]+
</pre>
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<code>617</code>
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<code>617-253</code>
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<code>617-253-1000</code>
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<code>---</code>
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<code>integer-integer-integer</code>
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<code>5--5</code>
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<code>3-6-293-1</code>
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Parse trees
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<p>Which of the following statements are true of a parse tree?</p>
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Race conditions
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Suppose two threads will both use <code>x</code>, which is declared with one of the declarations below.
They have no other shared state or interaction.
For which of these declarations of <code>x</code> would we be concerned about race conditions involving <code>x</code>?</p>
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<code>public static boolean x = true;</code>
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<code>public static final boolean x = true;</code>
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<code>public static int x = 7;</code>
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<code>public static final String x = "7";</code>
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Concurrency
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<p>Which of the following make concurrency hard to test and debug?</p>
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<input type="checkbox" name="input_exam-05-nq2_2_1[]" id="input_exam-05-nq2_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="exam-05-nq2_2_1-choice_2-label" for="input_exam-05-nq2_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_exam-05-nq2_2_1"> <code>System.out.println</code> is nondeterministic
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<h2 class="hd hd-2 unit-title">Part 3</h2>
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Interleaving 1
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<pre>
public class Moirai {
public static void main(String[] args) {
Thread clotho = new Thread(new Runnable() {
public void run() { System.out.println("spinning"); };
});
clotho.start();
new Thread(new Runnable() {
public void run() { System.out.println("measuring"); };
}).start();
new Thread(new Runnable() {
public void run() { System.out.println("cutting"); };
});
}
}
</pre>
<p>Which of the following are possible outputs from this program after all started threads have terminated?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_exam-05-interleaving-1_2_1">
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<input type="checkbox" name="input_exam-05-interleaving-1_2_1[]" id="input_exam-05-interleaving-1_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="exam-05-interleaving-1_2_1-choice_0-label" for="input_exam-05-interleaving-1_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_exam-05-interleaving-1_2_1"> spinning<br/>measuring<br/>cutting
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Interleaving 2
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<p>Which of these are possible results for <code>s</code>
if <code>a()</code> and <code>b()</code> run concurrently?</p>
<pre>
private String s = "a";
public void a() { s = s + "z"; }
public void b() { s = "(" + s + ")"; }
</pre>
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<code>"a"</code>
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<code>"az"</code>
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Thread safety strategies
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<p>For each declaration below, pick all the strategies that could be useful for arguing that the program is threadsafe.</p>
<p>A local variable <code>char[] y;</code></p>
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</div><p>A field <code>public static final List&lt;Double&gt; q;</code></p>
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Bad safety argument
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<p>Consider the following ADT with a <b>bad</b> safety argument:</p>
<pre>
/** MyStringBuffer is a threadsafe mutable string of characters. */
public class MyStringBuffer {
private String text;
// Rep invariant:
// none
// Abstraction function:
// represents the sequence text[0],...,text[text.length()-1]
// Thread safety argument:
// text is an immutable (and hence threadsafe) String,
// so this object is also threadsafe
/** @return the string represented by this buffer, with all letters converted to uppercase */
public String toUpperCase() {
return text.toUpperCase();
}
/** @param pos position to insert text into the buffer. Requires 0 &lt;= pos &lt;= text.length().
@param s text to insert
Mutates this buffer to insert s as a substring at position pos. */
public void insert(int pos, String s) {
text = text.substring(0, pos) + s + text.substring(pos);
}
/** @return the string represented by this buffer */
public String toString() {
return text;
}
/** Resets this buffer to the empty string */
public void clear() {
text = "";
}
/** @return the first character of this buffer, or "" if this buffer is empty
public String first() {
if (text.length() &gt; 0) {
return String.valueOf(text.charAt(0));
} else {
return "";
}
}
</pre>
<p>Which of these methods are counterexamples to this buggy safety argument, because they have a race condition? In particular, you should mark some method A as a counterexample if it's possible for one thread running method A at the same time as another thread is running some other method, some particular interleaving would violate A's postcondition?</p>
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<p>Since <code>BufferedReader.readLine()</code> is a <em>blocking</em> method, which of these is true:</p>
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<input type="checkbox" name="input_exam-07-block-block-block-block_2_1[]" id="input_exam-07-block-block-block-block_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="exam-07-block-block-block-block_2_1-choice_1-label" for="input_exam-07-block-block-block-block_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_exam-07-block-block-block-block_2_1"> When a thread calls <code>readLine</code>, that thread <em>blocks</em> until <code>readLine</code> returns
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<input type="checkbox" name="input_exam-07-block-block-block-block_2_1[]" id="input_exam-07-block-block-block-block_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="exam-07-block-block-block-block_2_1-choice_2-label" for="input_exam-07-block-block-block-block_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_exam-07-block-block-block-block_2_1"> When a thread calls <code>readLine</code>, the call can be <em>blocked</em> and an exception is thrown
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<input type="checkbox" name="input_exam-07-block-block-block-block_2_1[]" id="input_exam-07-block-block-block-block_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="exam-07-block-block-block-block_2_1-choice_3-label" for="input_exam-07-block-block-block-block_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_exam-07-block-block-block-block_2_1"> <code>BufferedReader</code> has its own thread for <code>readLine</code>, which runs a <em>block</em> of code passed in by the client
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Blocking 2
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<p>A thread is blocked. Which of the following <em>might</em> cause this?</p>
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Message passing
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<p>Message passing between two threads can be done
safely with:</p>
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Poison pills
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<p>Putting a poison pill in a message-passing queue is equivalent to what in programming with sockets?</p>
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<h3 class="hd hd-3 problem-header" id="exam-09-array-list-problem-title" aria-describedby="block-v1:MITx+6.005.2x+1T2017+type@problem+block@exam-09-array-list-problem-progress" tabindex="-1">
ArrayList
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<p>Suppose <code>list</code> is an instance of <code>ArrayList&lt;String&gt;</code>.</p>
<p>What is true while A is in a <code>synchronized (list) { ... }</code> block?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_exam-09-array-list_2_1">
<fieldset aria-describedby="status_exam-09-array-list_2_1">
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="exam-09-array-list_2_1-choice_0-label" for="input_exam-09-array-list_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> it owns the lock on <code>list</code>
</label>
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="exam-09-array-list_2_1-choice_1-label" for="input_exam-09-array-list_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> it does not own the lock on <code>list</code>
</label>
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="exam-09-array-list_2_1-choice_2-label" for="input_exam-09-array-list_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> no other thread can use observers of <code>list</code>
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="exam-09-array-list_2_1-choice_3-label" for="input_exam-09-array-list_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> no other thread can use mutators of <code>list</code>
</label>
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="exam-09-array-list_2_1-choice_4-label" for="input_exam-09-array-list_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> no other thread can acquire the lock on <code>list</code>
</label>
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<input type="checkbox" name="input_exam-09-array-list_2_1[]" id="input_exam-09-array-list_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="exam-09-array-list_2_1-choice_5-label" for="input_exam-09-array-list_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_exam-09-array-list_2_1"> no other thread can acquire locks on elements in <code>list</code>
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<h3 class="hd hd-3 problem-header" id="exam-09-synchronized-list-problem-title" aria-describedby="block-v1:MITx+6.005.2x+1T2017+type@problem+block@exam-09-synchronized-list-problem-progress" tabindex="-1">
Synchronized lists
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<p>Suppose <code>sharedList</code> is a <code>List</code> returned by <a href="http://docs.oracle.com/javase/8/docs/api/java/util/Collections.html#synchronizedList-java.util.List-"><code>Collections.synchronizedList</code></a>.</p>
<p>It is now safe to use <code>sharedList</code> from multiple threads without acquiring any locks... except! Which of the following would require a <code>synchronized(sharedList) { ... }</code> block?</p>
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<input type="checkbox" name="input_exam-09-synchronized-list_2_1[]" id="input_exam-09-synchronized-list_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="exam-09-synchronized-list_2_1-choice_0-label" for="input_exam-09-synchronized-list_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_exam-09-synchronized-list_2_1"> call <code>isEmpty</code>
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<input type="checkbox" name="input_exam-09-synchronized-list_2_1[]" id="input_exam-09-synchronized-list_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="exam-09-synchronized-list_2_1-choice_1-label" for="input_exam-09-synchronized-list_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_exam-09-synchronized-list_2_1"> call <code>add</code>
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<div class="field">
<input type="checkbox" name="input_exam-09-synchronized-list_2_1[]" id="input_exam-09-synchronized-list_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="exam-09-synchronized-list_2_1-choice_2-label" for="input_exam-09-synchronized-list_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_exam-09-synchronized-list_2_1"> iterate over the list
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<input type="checkbox" name="input_exam-09-synchronized-list_2_1[]" id="input_exam-09-synchronized-list_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="exam-09-synchronized-list_2_1-choice_3-label" for="input_exam-09-synchronized-list_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_exam-09-synchronized-list_2_1"> call <code>isEmpty</code>, if it returns false, call <code>remove(0)</code>
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