This week’s section exercise consists of several larger problems that will give you practice with designing classes and working with dynamic array allocation. These problems will help you get practice with the skills that you need for the next assignment, where you will start to implement your very own data structures! As you work on these problems, you may find this Classes and Objects Syntax Sheet to be helpful.
Remember that every week we will also be releasing a Qt Creator project containing starter code and testing infrastructure for that week's section problems. When a problem name is followed by the name of a .cpp
file, that means you can practice writing the code for that problem in the named file of the Qt Creator project. Here is the zip of the section starter code:
1) The Notorious RBQ (RingBufferQueue.h/.cpp
)
Topics: Classes, dynamic arrays
Think back to week 2 when we studied collections. We learned about Queues, a "first-in, first-out" data structure. Today in section, we're going to implement a special type of queue called a Ring Buffer Queue. A Ring Buffer Queue, or RBQ, is implemented by using an underlying array. In our implementation, the capacity is capped; once the array is full, additional elements cannot be added until something is dequeued. Another "interesting" thing about RBQs is that we don't want to shift elements when an element is enqueued or dequeued. Instead, we want to keep track of the front and tail of the Queue. For example, say our queue can hold 5 elements and we enqueue 3 elements: 1, 2, 3. Our queue would look like this:
If we enqueued two more elements, our queue would then be full:
At this point, we cannot add any additional elements until we dequeue at least one element. Dequeuing will remove the element at head, and head will move onto the next element. If we dequeue 2 elements, our queue will look like this:
Now there's room to add more elements! Since we still don't want to shift any elements, adding an additional element will wrap around. So, if we enqueue an element, our queue will look like this:
Notice that the tail's index is less than the head's index!
Your job is to implement a RingBufferQueue
class. Your class should have the following public methods:
Method | Description |
---|---|
void enqueue(int elem) |
Enqueues elem if the queue has room; throws an error if queue is full |
int dequeue() |
Returns and removes the element at the front of the queue; throws a string exception if queue is empty |
int peek() |
Returns element at the front of the queue; throws a string exception if queue is empty |
bool isEmpty() |
Returns true if queue is empty and false otherwise |
bool isFull() |
Returns true if queue is full and false otherwise |
int size() |
Returns number of elements in the queue |
You are welcome to add any private methods or fields that are necessary.
It can be hard to know where to start when writing an entire class, so we've given you this breakdown:
- Start by identifying the private fields you will need, then write the constructor and destructor to initialize the fields and do any cleanup, if necessary. Questions to think about:
- Is it easier to keep track of head and tail (as pictured in the diagrams above)? Or would it be better to track head and size?
- Write
isEmpty()
,isFull()
,size()
, andpeek()
. Questions to think about:- Which of these methods can be const? In general, how do you know when a method can be const?
- Write
enqueue()
anddequeue()
. Remember to handle error conditions! Questions to think about:- Can you call the methods from part 2 to reduce redundancy?
- Would using modular math help with wrapping around?
- Should either of these methods be const?
- Finally, deal with ostream insertion!
If you want more practice with writing classes, think about how you could modify this class to implement a double-ended queue. (A double-ended queue, or deque, is one where you can enqueue and dequeue from either the front or the back).
RingBufferQueue.h
#pragma once
#include <iostream>
class RBQueue {
public:
/* Constructs a new empty queue. */
RBQueue();
~RBQueue();
/* Returns true if the queue contains no elements. */
bool isEmpty() const;
/* Returns true if no additional elements can be enqueued. */
bool isFull() const;
/* Returns number of elements in queue. */
int size() const;
/* Adds the given element to back of queue. */
void enqueue(int elem);
/*
* Removes and returns the front element from the queue
* Throws a string exception if the queue is empty.
*/
int dequeue();
/*
* Returns the front element from the queue without removing it.
* Throws a string exception if the queue is empty.
*/
int peek() const;
private:
// member variables (instance variables / fields)
int* _elements;
int _capacity;
int _numUsed;
int _head;
// by listing this here as a "friend", it can access the private member variables
friend std::ostream& operator <<(std::ostream& out, const RBQueue& queue);
};
RingBufferQueue.cpp
#include "RingBufferQueue.h"
const int kDefaultCapacity = 10;
using namespace std;
RBQueue::RBQueue() {
_capacity = kDefaultCapacity;
_elements = new int[_capacity];
_head = 0;
_numUsed = 0;
}
RBQueue::~RBQueue() {
delete[] _elements;
}
bool RBQueue::isEmpty() const {
return _numUsed == 0;
}
bool RBQueue::isFull() const {
return _numUsed == _capacity;
}
int RBQueue::size() const {
return _numUsed;
}
int RBQueue::peek() const {
if (isEmpty()) {
error("Can't peek from an empty queue!");
}
return _elements[_head];
}
int RBQueue::dequeue() {
if (isEmpty()) {
error("Can't dequeue from an empty queue!");
}
int front = _elements[_head];
_head = (_head + 1) % _capacity;
_numUsed--;
return front;
}
void RBQueue::enqueue(int elem) {
if (isFull()) {
error("Can't enqueue to already full queue!");
}
int tail = (_head + _numUsed) % _capacity;
_elements[tail] = elem;
_numUsed++;
}
ostream& operator <<(ostream& out, const RBQueue& queue) {
out << "{";
if (!queue.isEmpty()) {
// we can access the inner '_elements' member variable because
// this operator is declared as a 'friend' of the queue class
out << queue._elements[queue._head];
for (int i = 1; i < queue._numUsed; i++) {
int index = (queue._head + i) % queue._capacity;
out << ", " << queue._elements[index];
}
}
out << "}";
return out;
}
1.5) The Notorious RBQ, Revisited (RingBufferQueue.h/.cpp
)
Note: we won't be getting to memory and pointers until the lecture on Thursday, 7/21, but this is a great continuation to the RBQ problem if you're interested.
Topics: Classes, dynamic memory allocation, pointers
Remember our good friend the RingBufferQueue
from one problem ago? Last time we visited the RBQ it had fixed capacity – that is, it couldn't grow in size after it was initially created. How limiting! With our newfound pointer and dynamic allocation skills, we can remove this limitation on the RBQ and make it fully functional!
Add functionality to the class RingBufferQueue
from the previous section problem so that the queue resizes to an array twice as large when it runs out of space. In other words, if asked to enqueue when the queue is full, it will enlarge the array to give it enough capacity.
For example, say our queue can hold 5 elements and we enqueue the five values 10, 20, 30, 40, and 50. Our queue would look like this:
index 0 1 2 3 4
+----+----+----+----+----+
value | 10 | 20 | 30 | 40 | 50 |
+----+----+----+----+----+
^ ^
| |
head tail
If the client tries to enqueue a sixth element of 60, your improved queue class should grow to an array twice as large:
index 0 1 2 3 4 5 6 7 8 9
+----+----+----+----+----+----+----+----+----+----+
value | 10 | 20 | 30 | 40 | 50 | 60 | | | | |
+----+----+----+----+----+----+----+----+----+----+
^ ^
| |
head tail
The preceding is the simpler case to handle. But what about if the queue has wrapped around via a series of enqueues and dequeues? For example, if the queue stores the following five elements:
index 0 1 2 3 4
+----+----+----+----+----+
value | 40 | 50 | 10 | 20 | 30 |
+----+----+----+----+----+
^ ^
| |
tail head
If the client tries to add a sixth element of 60, you cannot simply copy the array as it is shown. If you do so, the head and wrapping will be broken. Instead, copy into the new array so that index 0 always becomes the new head of the queue. The picture will look the same as the previous one with the value 60 at index 5.
Write up the implementation of the new and improved RingBufferQueue
. It should have the same members as in the previous problem, but with the new resizing behavior added. You may add new member functions to your class, but you should make them private.
RingBufferQueue.h
#pragma once
#include <iostream>
using namespace std;
class RingBufferQueue {
public:
RingBufferQueue();
~RingBufferQueue();
bool isEmpty() const;
bool isFull() const;
int size() const;
void enqueue(int elem);
int dequeue();
int peek() const;
private:
int* _elements;
int _capacity;
int _size;
int _head;
friend ostream& operator <<(ostream& out, const RingBufferQueue& queue);
void enlarge();
};
RingBufferQueue.cpp
#include "RingBufferQueue.h"
static int kDefaultCapacity = 5;
RingBufferQueue::RingBufferQueue() {
_capacity = kDefaultCapacity;
_elements = new int[_capacity];
_head = 0;
_size = 0;
}
RingBufferQueue::~RingBufferQueue() {
delete[] _elements;
}
void RingBufferQueue::enqueue(int elem) {
if (isFull()) {
enlarge();
}
int tail = (_head + _size) % _capacity;
_elements[tail] = elem;
_size++;
}
int RingBufferQueue::dequeue() {
int front = peek();
_head = (_head + 1) % _capacity;
_size--;
return front;
}
int RingBufferQueue::peek() const {
if (isEmpty()) {
error("Can't peek at an empty queue!");
}
return _elements[_head];
}
bool RingBufferQueue::isEmpty() const {
return _size == 0;
}
bool RingBufferQueue::isFull() const {
return _size == _capacity;
}
int RingBufferQueue::size() const {
return _size;
}
void RingBufferQueue::enlarge() {
int *larger = new int[_capacity * 2];
for (int i = 0; i < _size; i++) {
larger[i] = _elements[(_head + i) % _capacity];
}
delete[] _elements;
_elements = larger;
_capacity *= 2;
_head = 0;
}
ostream& operator <<(ostream& out, const RingBufferQueue& queue) {
out << "{";
if (!queue.isEmpty()) {
// We can access the inner ‘_elements’ member variables because
// this operator is declared as a friend of the RingBufferQueue class
out << queue._elements[queue._head];
for (int i = 1; i < queue.size(); i++) {
int index = (queue._head + i) % queue._capacity;
out << ", " << queue._elements[index];
}
}
out << "}";
return out;
}
2) Cleaning Up Your Messes
Topics: Dynamic allocation and freeing
Whenever you allocate an array with new[]
, you need to deallocate it using delete[]
. It's important when you do so that you only deallocate the array exactly once – deallocating an array zero times causes a memory leak, and deallocating an array multiple times usually causes the program to crash. (Fun fact – deallocating memory twice is called a double free and can lead to security vulnerabilities in your code! Take CS155 for details.)
Below are three code snippets. Trace through each snippet and determine whether all memory allocated with new[]
is correctly deallocated exactly once. If there are any other errors in the program, make sure to report them as well.
Snippet 1
int main() {
int* arya = new int[3];
int* jon = new int[5];
arya = jon;
jon = arya;
delete[] arya;
delete[] jon;
return 0;
}
Snippet 2
int main() {
int* stark = new int[6];
int* lannister = new int[3];
delete[] stark;
stark = lannister;
delete[] stark;
return 0;
}
Snippet 3
int main() {
int* tyrell = new int[137];
int* arryn = tyrell;
delete[] tyrell;
delete[] arryn;
return 0;
}
The first piece of code has two errors in it. First, the line
arya = jon
;
causes a memory leak, because there is no longer a way to deallocate the array of three elements allocated in the first line. Second, since both arya and jon point to the same array, the last two lines will cause an error.
The second piece of code is perfectly fine. Even though we execute
delete[] stark
;
twice, the array referred to each time is different. Remember that you delete arrays, not pointers.
Finally, the last piece of code has a double-delete in it, because the pointers referred to in the last two lines point to the same array.
3) Creative Destruction
Topics: Constructors and Destructors
Constructors and destructors are unusual functions in that they're called automatically in many contexts and usually aren't written explicitly. To help build an intuition for when constructors and destructors are called, trace through the execution of this program and list all times when a constructor or destructor is called.
/* Prints the elements of a stack from the bottom of the stack up to the top
* of the stack. To do this, we transfer the elements from the stack to a
* second stack (reversing the order of the elements), then print out the
* contents of that stack.
*/
void printStack(Stack<int> toPrint) {
Stack<int> temp;
while (!toPrint.isEmpty()) {
temp.push(toPrint.pop());
}
while (!temp.isEmpty()) {
cout << temp.pop() << endl;
}
}
int main() {
Stack<int> elems;
for (int i = 0; i < 10; i++) {
elems.push(i);
}
printStack(elems);
return 0;
}
The ordering is as follows:
- A constructor is called when elem is declared in main.
- A constructor is then called to set
toPrint
equal to a copy ofelem
. - A constructor is then called to initialize the
temp
variable inprintStack
. - When
printStack
exits, a destructor is called to clean up thetemp
variable. - Also when
printStack
exits, a destructor is called to clean up thetoPrint
variable. - When
main
exits, a destructor is called to clean up theelem
variable.
4) Min Heap
Topics: Heaps
We have implemented the Priority Queue ADT using a binary min-heap. Draw a diagram of the heap’s tree structure that results from inserting the following priority values in the order given: 25, 37, 28, 12, 30, 3
5) Max Heap
Topics: Heaps
You have a PriorityQueue class which treats higher (larger integer value) priority elements as frontmost. The internal implementation of the class is a binary max-heap stored in an unfilled array. The initial allocation of the array is for capacity 5 and the array capacity is doubled when asked to enqueue to a queue which is full. You are going to trace the operation of enqueuing and dequeuing elements from the priority queue. You can sketch as a tree if you prefer when working it out, but your final answer should be based on a representation of the underlying array that supports the heap.
(a) Show the contents of the internal array after these elements are enqueued to an empty priority queue in this order. Each element has a string value and a priority in parenthesis.
Red(8), Blue(33), Green(29), Purple(42), Orange(20), Yellow(22), Indigo(10), Teal(21)
(b) Dequeue is called twice on the priority queue. Which two values are removed?
(c) Show the contents of the internal array after the above two elements have been dequeued
(a) Color names are abbreviated
elements: | P(42) | B(33) | G(29) | T(21) | O(20) | Y(22) | I(10) | R(8) | ? | ? |
index: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
(b) Purple(42) and Blue(33)
(c)
elements: | G(29) | T(21) | Y(22) | R(8) | O(20) | I(10) | ? | ? | ? | ? |
index: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
6) Some Pointers on Cats
Topics: Pointer tracing and memory diagrams
Trace through the following function and draw the program’s memory at the designated spot. Indicate which variables are on the stack and which are on the heap, and indicate orphaned memory. Indicate with a question mark (?) memory that we don’t know the values of.
struct Lion {
int roar;
int *meow;
int purr[2];
};
struct Savanna {
int giraffe;
Lion cat;
Lion *kitten;
};
Lion *explore(Savanna *prairie) {
Lion *leader = &(prairie->cat);
leader->meow = new int;
*(leader->meow) = 2;
prairie = new Savanna;
prairie->cat.roar = 6;
prairie->kitten = leader;
prairie->kitten->roar = 8;
prairie->kitten->meow = &(prairie->kitten->purr[1]);
leader->purr[0] = 4;
return leader;
}
void kittens() {
Savanna *habitat = new Savanna[3];
habitat[1].giraffe = 3;
habitat[1].kitten = nullptr;
habitat[0] = habitat[1];
habitat[2].kitten = explore(habitat);
habitat[2].kitten->roar = 4;
// DRAW THE MEMORY AS IT LOOKS HERE
}
Orphaned memory (memory on the heap that we no longer have access to but that was not freed) is represented with dotted lines. For a full walkthrough of the solution, check out: https://tinyurl.com/CatsPointers.