1. Lists, Stacks and Queues

2. More complete list ADT struct Node{ double data; Node* next; };
class List {
public:
List(); // constructor
List(const List& list); // copy constructor
~List(); // destructor
List& operator=(const List& list); // assignment operator
// plus other overloaded operators
bool empty() const; // boolean function
void add(double x); // add to the head
void delete(); // delete the head and get the head element
double head() const; // get the head element
bool search(double x); // search for a given x
void insert(double x); // insert x in a sorted list
void delete(double x); // delete x in a sorted list
void addEnd(double x); // add to the end
void deleteEnd(); // delete the end and get the end element
double end(); // get the element at the end
void display() const; // output
int length() const; // count the number of elements
private:
Node* head;
More complete list ADT

3. list ADT (a general list)
class List {
public:
List(); // constructor
List(const List& list); // copy constructor
~List(); // destructor
bool empty() const; // boolean function
double head() const; // get the head element
void add(double x); // add to the head
void delete(); // delete the head element
void display() const; // output
private: … };
Or to define one function:
Double delete();
Which deletes and returns the head element.

4. list ADT (a sorted list)
class List {
public:
List(); // constructor
List(const List& list); // copy constructor
~List(); // destructor
bool empty() const; // boolean function
double head(); const; // get the first element
void insert(double x); // insert x in a sorted list
void delete(double x); // delete x in a sorted list
void display() const; // output
bool search(double x); // search for a given x
private: … };

5. Implementation and Efficiency
Static array
Dynamic array
Linked lists
with and without ‘dummy head’ tricks
Efficiency
Insertion  construction, composition
Deletion  destruction, decomposition
Search  application, usage

6. Advantages and disadvantages of different implementations of a list
Static array
Dynamic array
Linked list
Insertion
Deletion
Search

7. Stacks

8. Stack Overview Stack ADT Basic operations of stack
Pushing, popping etc.
Implementations of stacks using
array
linked list

9. Stack
A stack is a list in which insertion and deletion take place at the same end
This end is called top
The other end is called bottom
Stacks are known as LIFO (Last In, First Out) lists.
The last element inserted will be the first to be retrieved

10. Push and Pop Primary operations: Push and Pop Push Pop
Add an element to the top of the stack
Pop
Remove the element at the top of the stack
top
empty stack A
top
push an element
top
push another A B
top
pop A

11. Implementation of Stacks
Any list implementation could be used to implement a stack
Arrays (static: the size of stack is given initially)
Linked lists (dynamic: never become full)
We will explore implementations based on arrays and linked list

12. Stack ADT
class Stack {
public:
Stack(); // constructor
Stack(const Stack& stack); // copy constructor
~Stack(); // destructor
bool empty() const;
double top() const; // keep the stack unchanged
void push(const double x);
double pop(); // change the stack …
// optional
void display() const;
bool full() const;
private: };
‘physical’ constructor/destructor
inspection, access
headElement
addHead
deleteHead
update,
‘logical’ constructor/destructor, composition/decomposition
Compare with List, see that it’s ‘operations’ that define the type!
‘stack’ is the same as our ‘unsorted’ list operating at the head 

13. Using Stack result int main() { Stack stack; stack.push(5.0);
stack.display();
cout << "Top: " << stack.top() << endl;
stack.pop();
while (!stack.empty()) stack.pop();
return 0; }
result

14. Stack using linked lists
struct Node{
public:
double data;
Node* next; };
class Stack {
Stack(); // constructor
Stack(const Stack& stack); // copy constructor
~Stack(); // destructor
bool empty() const;
double top() const; // keep the stack unchanged
void push(const double x);
double pop(); // change the stack
bool full(); // unnecessary for linked lists
void display() const;
private:
Node* top;

15. Push (addHead), Pop (deleteHead)
void List::addHead(int newdata){
Nodeptr newPtr = new Node;
newPtr->data = newdata;
newPtr->next = head;
head = newPtr; }
From ‘addHead’ to ‘push’
void Stack::push(double x){
Node* newPtr = new Node;
newPtr->data = x;
newPtr->next = top;
top = newPtr; }

16. Stack using arrays double top(); class Stack { public:
Stack(int size = 10);
Stack(const Stack& stack);
~Stack() { delete[] values; }
bool empty() { return (top == -1); }
double top();
void push(const double x);
double pop();
bool full() { return (top == size); }
void display();
private:
int size; // max stack size = size - 1
int top; // current top of stack
double* values; // element array };

17. Attributes of Stack Operations of Stack size: the max size of stack
top: the index of the top element of stack
values: point to an array which stores elements of stack
Operations of Stack
empty: return true if stack is empty, return false otherwise
full: return true if stack is full, return false otherwise
top: return the element at the top of stack
push: add an element to the top of stack
pop: delete the element at the top of stack
display: print all the data in the stack

18. Stack constructor
Allocate a stack array of size. By default, size = 10.
Initially top is set to -1. It means the stack is empty.
When the stack is full, top will have its maximum value, i.e.
size – 1.
Stack::Stack(int size /*= 10*/) {
values = new double[size];
top = -1;
maxTop = size - 1; }
Although the constructor dynamically allocates the stack array, the stack is still static. The size is fixed after the initialization.

19. void push(const double x);
Push an element onto the stack
Note top always represents the index of the top element. After pushing an element, increment top.
void Stack::push(const double x) {
if (full()) // if stack is full, print error
cout << "Error: the stack is full." << endl;
else
values[++top] = x; }

20. double pop() Pop and return the element at the top of the stack
Don’t forgot to decrement top
double Stack::pop() {
if (empty()) { //if stack is empty, print error
cout << "Error: the stack is empty." << endl;
return -1; }
else {
return values[top--];

21. double top() Return the top element of the stack
Unlike pop, this function does not remove the top element
double Stack::top() {
if (empty()) {
cout << "Error: the stack is empty." << endl;
return -1; }
else
return values[top];

22. void print() Print all the elements void Stack::print() {
cout << "top -->";
for (int i = top; i >= 0; i--)
cout << "\t|\t" << values[i] << "\t|" << endl;
cout << "\t| |" << endl; }

23. A better variant:
A better approach is to let position 0 be the bottom of the stack
An integer to indicate the top of the stack (Stack.h)
[7] ?
[6]
[5] 77
[4]
121
[3] 64
[2]
234
[1] 51
[0]
[7] ?
[6] 95
[5] 77
[4]
121
[3] 64
[2]
234
[1] 51
[0] 29
top =
[7] 80
[6] 95
[5] 77
[4]
121
[3] 64
[2]
234
[1] 51
[0] 29
[7] ?
[6] 95
[5] 77
[4]
121
[3] 64
[2]
234
[1] 51
[0] 29
top =
top =
top =
Push 95
Push 80
Pop 23

24. Stack Application: base conversion
Convert a base ten number into a base two number. 2 26 13 … 6 1 3
Example: 26  11010 24

25. Stack stack();
while (D is not zero) {
push the remainder of D
D  D/2 }
while (not empty stack)
pop

26. Stack.h, Stack.cpp and BaseConversion.cpp
Can be written easily using recursion (do it yourself)

27. Recursive version: convert(D) if D is zero, stop
else push(the remainder)
convert(D/2)
while (not empty stack)
pop

28. Stack Application: Balancing Symbols
To check that every right brace, bracket, and parentheses must correspond to its left counterpart
e.g. [( )] is legal, but [( ] ) is illegal
How?
Need to memorize
Use a counter, several counters, each for a type of parenthesis …

29. Balancing Symbols using a stack
Algorithm
(1)   Make an empty stack.
(2)   Read characters until end of file
i.    If the character is an opening symbol, push it onto the stack
ii.   If it is a closing symbol, then if the stack is empty, report an error
iii.  Otherwise, pop the stack. If the symbol popped is not the
corresponding opening symbol, then report an error
(3)   At end of file, if the stack is not empty, report an error
(paren.cpp)

30. Stack Application: postfix, infix expressions and calculator
Evaluating Postfix expressions
a b c * + d e * f + g * +
Operands are in a stack
Converting infix to postfix
a+b*c+(d*e+f)*g  a b c * + d e * f + g * +
Operators are in a stack
Calculator
Adding more operators …

31. Infix, prefix, and postfix
Consider the arithmetic statement in the assignment statement: x = a * b + c
This is "infix" notation: the operators are between the operands
Compiler must generate machine instructions 1.
LOAD a 2.
MULT b 3.
ADD c 4.
STORE x 31

32. Prefix : Operators come before the operands
Examples
Infix
RPN (Postfix)
Prefix
A + B
A B +
+ A B
A * B + C
A B * C +
+ * A B C
A * (B + C)
A B C + *
* A + B C
A - (B - (C - D))
A B C D---
-A-B-C D
A - B - C - D
A B-C-D-
---A B C D
Prefix : Operators come before the operands 32

33. RPN or Postfix Notation
Reverse Polish Notation (RPN) = Postfix notation
Most compilers convert an expression in infix notation to postfix
The operators are written after the operands
So “a * b + c” becomes “a b * c +”
Easier for compiler to work on loading and operation of variables
Advantage: expressions can be written without parentheses 33

34. Evaluating RPN Expressions (Similar to Compiler Operations)
Example: * * *
2 8 * 16

35. An expression is a list of ‘characters’ or more generally ‘tokens’ or ‘strings
while (not the end of the expression) do {
get the current ‘token’
if it is operand, store it …  a stack
if it is operator,
get back operands
Evaluate
store the result
move to the next }
Use a Stack to store ‘operands’  a stack!

36. while (not the end of the expression) {
get the current ‘token’
if it is operand,
push;
else if it is operator,
pop (one operand);
pop (another operand);
evaluate;
push (the result);
move to the next }

37. list  expression
stack  empty
while (notempty(list)) do {
c = head(list);
if (c == ‘operand’) push(c,stack)
else if (c == ‘operator)
operand2 = pop(stack);
operand1 = pop(stack);
res=evaluate(c,operand1,operand2);
push(res,stack);
list  delete(list) }
Further refine:
- operators: +, -, *, /
- operands: …
- evaluate: …

38. More object-oriented:
List list(expression);
Stack stack();
while (list.notempty) do {
c = list.head();
if (c == ‘operand’) stack.push(c)
else if (c == ‘operator)
operand2 = stack.pop;
operand1 = stack.pop;
res=evaluate(c,operand1,operand2);
stack.push;
list.delete(); }
Further refine:
- operators: +, -, *, /
- operands: …
- evaluate: …

39. (end of strings) 2 4 * 9 5 + - Push 2 onto the stack 4 * 9 5 + -
Pop 4 and 2 from the stack , multiply, and push the result 8 back 8 9 5 + -
Push 9 onto the stack 9 8 5 + -
Push 5 onto the stack 5 9 8 + -
Pop 5 and 9 from the stack, add, and push the result 14 back 14 8 -
Pop 14 and 8 from the stack, subtract, and push the result -6 back -6
(end of strings)
Value of expression is on top of the stack -6

40. Stack Application: function calls and recursion
int fac(int n){
int product;
if(n <= 1) product = 1;
else product = n * fac(n-1);
return product; }
void main(){
int number;
cout << "Enter a positive integer : " << endl;;
cin >> number;
cout << fac(number) << endl;

41. Assume the number typed is 3.
Tracing the program …
Assume the number typed is 3.
fac(3): has the final returned value 6
3<=1 ? No.
product3 = 3*fac(2) product3=3*2=6, return 6,
fac(2):
2<=1 ? No.
product2 = 2*fac(1) product2=2*1=2, return 2,
fac(1):
1<=1 ? Yes.
return 1

42. Call is to ‘push’ and return is to ‘pop’!
fac(1)
prod1=1
fac(2)
prod2=2*fac(1)
fac(3)
prod3=3*fac(2)
Actually for any function call, it is a stack!

43. Let the system do the ‘stack’ for you!
convert(D)
if D is zero, stop
else push(the remainder)
convert(D/2)
while (not empty stack)
pop and display
Stack stack();
while (D is not zero) {
push the remainder of D
D  D/2 }
while (not empty stack)
pop
The same!
convert(D)
if D is zero, stop
else convert(D/2)
display the remainder of D

44. Static and dynamic objects
‘static variables’ are from a Stack
‘dynamic variables’ are from a heap (seen later …)

45. Array versus linked list implementations
push, pop, top are all constant-time operations in both array and linked list implementation
For array implementation, the operations are performed in very fast constant time
Often we use ‘array’ implementations for Stacks

46. Queues A queue is a waiting line – seen in daily life
A line of people waiting for a bank teller
A line of cars at a toll both
"This is the captain, we're 5th in line for takeoff"

47. Queue
A queue is also a list. However, insertion is done at one end, while deletion is performed at the other end.
It is “First In, First Out (FIFO)” order.
Like customers standing in a check-out line in a store, the first customer in is the first customer served.

48. Queue Overview Queue ADT Basic operations of queue
Enqueuing, dequeuing etc.
Implementation of queue
Linked list
Array

49. Enqueue and Dequeue Primary queue operations: Enqueue and Dequeue
Like check-out lines in a store, a queue has a front and a rear.
Enqueue – insert an element at the rear of the queue
Dequeue – remove an element from the front of the queue
Insert (Enqueue)
Remove (Dequeue)
front
rear

50. Implementation of Queue
Just as stacks can be implemented as arrays or linked lists, so with queues.
Dynamic queues have the same advantages over static queues as dynamic stacks have over static stacks

51. Queue ADT class Queue { public: Queue(); Queue(const Queue& queue);
bool empty();
double front(); // optional: front inspection (no queue change)
void enqueue(double x);
double dequeue();
// optional
void display(void);
bool full();
private: … };
‘physical’ constructor/destructor
‘logical’ constructor/destructor
Yes, ‘front’ like ‘top’ in a stack is a redundant definition, but usually ‘front’ is less useful in a queue application than the ‘top’ in a stack

52. Using Queue int main(void) { Queue queue;
cout << "Enqueue 5 items." << endl;
for (int x = 0; x < 5; x++)
queue.enqueue(x);
cout << "Now attempting to enqueue again..." << endl;
queue.enqueue(5);
queue.print();
double value;
value=queue.dequeue();
cout << "Retrieved element = " << value << endl;
queue.enqueue(7);
return 0; }

53. Queue using linked lists
Struct Node {
double data;
Node* next; }
class Queue {
public:
Queue();
Queue(const Queue& queue);
~Queue();
bool empty();
void enqueue(double x);
double dequeue();
// bool full(); // optional
void print(void);
private:
Node* front; // pointer to front node
Node* rear; // pointer to last node
int counter; // number of elements };

54. Implementation of some online member functions …
class Queue {
public:
Queue() { // constructor
front = rear = NULL;
counter = 0; }
~Queue() { // destructor
double value;
while (!empty()) dequeue(value);
bool empty() {
if (counter) return false;
else return true;
void enqueue(double x);
double dequeue();
// bool full() {return false;};
void print(void);
private:
Node* front; // pointer to front node
Node* rear; // pointer to last node
int counter; // number of elements, not compulsary };

55. Enqueue (addEnd) 8 5 8 5 void Queue::enqueue(double x) {
Node* newNode = new Node;
newNode->data = x;
newNode->next = NULL;
if (empty()) {
front = newNode; }
else {
rear->next = newNode;
rear = newNode;
counter++;
rear 8 5
rear 8 5
newNode

56. Dequeue (deleteHead) 3 8 5 8 5 double Queue::dequeue() { double x;
if (empty()) {
cout << "Error: the queue is empty." << endl;
exit(1); // return false; }
else {
x = front->data;
Node* nextNode = front->next;
delete front;
front = nextNode;
counter--;
return x;
front 3 8 5 8 5
front

57. Printing all the elements
void Queue::print() {
cout << "front -->";
Node* currNode = front;
for (int i = 0; i < counter; i++) {
if (i == 0) cout << "\t";
else cout << "\t\t";
cout << currNode->data;
if (i != counter - 1)
cout << endl;
else
cout << "\t<-- rear" << endl;
currNode = currNode->next; }

58. Queue using Arrays
There are several different algorithms to implement Enqueue and Dequeue
Naïve way
When enqueuing, the front index is always fixed and the rear index moves forward in the array.
front
rear
Enqueue(3) 3
Enqueue(6) 6
Enqueue(9) 9

59. Naïve way (cont’d)
When dequeuing, the front index is fixed, and the element at the front the queue is removed. Move all the elements after it by one position. (Inefficient!!!)
rear
rear
rear = -1 6 9 9
front
front
front
Dequeue()
Dequeue()
Dequeue()

60. A better way When enqueued, the rear index moves forward.
When dequeued, the front index also moves forward by one element
(front)
XXXXOOOOO (rear)
OXXXXOOOO (after 1 dequeue, and 1 enqueue)
OOXXXXXOO (after another dequeue, and 2 enqueues)
OOOOXXXXX (after 2 more dequeues, and 2 enqueues)
The problem here is that the rear index cannot move beyond the last element in the array.

61. Using Circular Arrays Using a circular array
When an element moves past the end of a circular array, it wraps around to the beginning, e.g.
OOOOO7963  4OOOO7963 (after Enqueue(4))
How to detect an empty or full queue, using a circular array algorithm?
Use a counter of the number of elements in the queue.

62. full() is not essential, can be embedded
class Queue {
public:
Queue(int size = 10); // constructor
Queue(const Queue& queue); // not necessary!
~Queue() { delete[] values; } // destructor
bool empty(void);
void enqueue(double x); // or bool enqueue();
double dequeue();
bool full();
void print(void);
private:
int front; // front index
int rear; // rear index
int counter; // number of elements
int maxSize; // size of array queue
double* values; // element array };
full() is not essential, can be embedded

63. Attributes of Queue Operations of Queue front/rear: front/rear index
counter: number of elements in the queue
maxSize: capacity of the queue
values: point to an array which stores elements of the queue
Operations of Queue
empty: return true if queue is empty, return false otherwise
full: return true if queue is full, return false otherwise
enqueue: add an element to the rear of queue
dequeue: delete the element at the front of queue
print: print all the data

64. Queue constructor Queue(int size = 10)
Allocate a queue array of size. By default, size = 10.
front is set to 0, pointing to the first element of the array
rear is set to -1. The queue is empty initially.
Queue::Queue(int size /* = 10 */) {
values = new double[size];
maxSize = size;
front = 0;
rear = -1;
counter = 0; }

65. Empty & Full
Since we keep track of the number of elements that are actually in the queue: counter, it is easy to check if the queue is empty or full.
bool Queue::empty() {
if (counter==0) return true;
else return false; }
bool Queue::full() {
if (counter < maxSize) return false;
else return true;

66. Enqueue Or ‘bool’ if you want void Queue::enqueue(double x) {
if (full()) {
cout << "Error: the queue is full." << endl;
exit(1); // return false; }
else {
// calculate the new rear position (circular)
rear = (rear + 1) % maxSize;
// insert new item
values[rear] = x;
// update counter
counter++;
// return true;

67. Dequeue double Queue::dequeue() { double x; if (empty()) {
cout << "Error: the queue is empty." << endl;
exit(1); // return false; }
else {
// retrieve the front item
x = values[front];
// move front
front = (front + 1) % maxSize;
// update counter
counter--;
// return true;
return x;

68. Printing the elements void Queue::print() {
cout << "front -->";
for (int i = 0; i < counter; i++) {
if (i == 0) cout << "\t";
else cout << "\t\t";
cout << values[(front + i) % maxSize];
if (i != counter - 1)
cout << endl;
else
cout << "\t<-- rear" << endl; }

69. Using Queue int main(void) { Queue queue;
cout << "Enqueue 5 items." << endl;
for (int x = 0; x < 5; x++)
queue.enqueue(x);
cout << "Now attempting to enqueue again..." << endl;
queue.enqueue(5);
queue.print();
double value;
value=queue.dequeue();
cout << "Retrieved element = " << value << endl;
queue.enqueue(7);
return 0; }

70. Results Queue implemented using linked list will be never full!
based on array
based on linked list
Queue implemented using linked list will be never full!

71. Queue applications
When jobs are sent to a printer, in order of arrival, a queue.
Customers at ticket counters …