1. 2019, Fall Pusan National University Ki-Joune Li
Stacks and Queues
2019, Fall
Pusan National University
Ki-Joune Li

2. Stack Stack Example A Container Last-In First-Out (LIFO)
Access only to the element at the top
Push : Insert an element at the top
Pop : Remove an element from the top
Example
Function Invocation
Previous frame pointer (registers, local variables)
Return Address, Parameters
top
Bottom

3. Operations – Interface
Maintenance: creation of a new stack, deletion of stack
Push: insert an element on the top
Pop: delete an element from the top
IsEmpty and IsFull: check whether stack is empty or full

4. Stack – Initial Condition and first insertion
A. Construct a stack
1. Prepare an array 1 …
Max-1
* Initially empty  when top = ?
2. top: index to top element  initially 0 or ?
B. Insert the first element 1 …
Max-1
Copy the element to slot at the next of top
top=-1

5. Implementation Internal Implementation – Data Structure
Stack::Stack(int size){
MaxSize=size;
stack=new Type[MaxSize];
top=-1; }
Boolean Stack::isFull() {
if(top==MaxSize-1) return YES;
else return NO; }
Class Stack {
private: int top,MaxSize;
Type *stack;// public:
Stack(int size); Boolean isFull(), isEmpty();
Type pop();
void push(Type element); };
Type Stack::pop() {
if(isEmpty()==YES) stackEmpty();
else return stack[top--]; }
void Stack::push(Type v) {
if(isFull()==YES) stackFull();
else stack[++top]=v; }

6. Queue Queue Example A Container First-In First-Out (FIFO) rear
Access only to the elements at the front and rear
Add: Insert an element to the rear
Delete: Remove an element from the front
Example
Process Scheduling
rear
front
Process 3
Process 9
Process 2
Process 8
Process 4
Ready Queue
CPU

7. Operations – Interface
Maintenance : creation of a new queue, deletion of queue
Add and Delete
IsEmpty and IsFull

8. Queue – Implementation: Initial Condition
A. Construct a queue
1. Prepare an array 1 …
Max-1
* Initially empty  front = ? and rear = ? 2.
front: index to the new element  initially 0 or ?
rear: index to the last element  initially 0 or ?

9. Implementation Data Structures What’s the problem ?
Queue::Queue(int size){
MaxSize=size;
queue=new Type[MaxSize];
front=rear=-1; }
Boolean Queue::isFull() {
if(rear==MaxSize-1) return YES;
else return NO; }
Class Queue {
private: int front,rear,MaxSize;
Type *queue;// public:
Queue(int size); Boolean isFull(), isEmpty();
Type delete();
void add(Type element); };
Type Queue::delete() {
if(isEmpty()==YES) queueEmpty();
else return queue[++front]; }
void Queue::add(Type v) {
if(isFull()==YES) queueFull();
else queue[++rear]=v; }

10. Circular Queue Class CircularQueue { private: int front,rear,MaxSize;
Type *queue;// public:
Queue(int size); Type delete();
void add(Type element); };
Queue::Queue(int size){
MaxSize=size;
queue=new Type[MaxSize];
front=rear=1; }
void Queue::delete(Type v) {
if(front==rear) queueEmpty();
else {
front=(front+1)%MaxSize; return queue[front]; } }
void Queue::add(Type v) {
newRear=(rear+1)%MaxSize; if(front==newRear) queueFull();
else {
rear=newRear; queue[rear]=v; } }

11. Example void Queue::add(Type v) {
newRear=(rear+1)%MaxSize; if(front==newRear) queueFull();
else {
rear=newRear; queue[rear]=v; } }
Example
Typr Queue::delete() {
if(front==rear) queueEmpty();
else {
front=(front+1)%MaxSize; return queue[front]; } }
front 1 2 3 …
MaxSize-1
rear
newRear
front=1
rear=1
front=1
rear=1
newRear=2
front=1
rear=2
newRear=3
front=1
rear=MaxSize-1
newRear=0
front=1
rear=0
newRear=1
front=1
rear=2
front=1
rear=3
front=1
rear=0
front=2
rear=0
front=0
rear=0
front=0
rear=0
front=MaxSize-1
rear=0

12. Application of Stack : Mazing Problem
Maze
Enter
Exit
How to find the path ?

13. Path Finding Algorithm for Mazing Problem
Algorithm PathFinding(int p,int q,int maze[p][q])
// (p,q): coorinates of exit cell
pathStack  initialize Stack; pathStack.push((0,0)); while(pathStack.isEmpty()==NO) { (i,j) pathStack.getTop(); // read but not remove while(there is an unvisited cell (m,n) from (i,j)) {
pathStack.push((m,n));
if(m==p and n==q) { // path found
pathStack.print(); // pop and print
return; }
(i,j)(m,n);
pathStack.pop();
print “No path”;
End Algorithm PathFinding

14. Application of stack : Evaluation of Expressions
How to evaluate this ?
X = A / B – C + D * E – A * C
Infix to Postfix
X = (((A / B) – C) + (D * E)) – (A * C)
Infix Notation
X = (((A B / ) C – ) (D E *) +) (A C *) –
Postfix Notation
Evaluation of Postfix
X = A B / C – D E * + A C * –

15. Evaluation of Expression in Postfix Notation
X = A B / C – D E * + A C * – A B / C - D E T4 - T5
T6= T4 – T5 T6 = A A B
T1=A / B T1 T1 C
T2= T1 - C T2 T2 T2 E D T4 T5 D … T6

16. Infix to Postfix Infix Notation Postfix Notation
X = A / ( B – C ) + D * E – A * C
Infix Notation A / ( B - C ) + D * E - - - ( ( ( ( * / / / / / / + + - A B C - / D E * +
X = A B C – / D E * + A C* –
Postfix Notation