Stacks & Queues
Last in First out
LIFO
How a Stack Works
3 main operations
1. Push → inserts a new elements at the top of the stack
2. Pop → removes & returns the element at the top of
the stack
3. Peek → returns the element at the top of the stack
How a Stack Works
At first, a Stack
is an empty
container.
How a Stack Works - Push
Push ( 13 )
13
How a Stack Works - Push
Push ( 2 )
2
13
How a Stack Works - Push
Push ( -8 )
-8
2
13
How a Stack Works - Pop
-8
Pop ( )
2
Removes &
13
Returns the
value
How a Stack Works - Pop
2
Pop ( )
Removes &
13
Returns the
value
How a Stack Works - Pop
13
Pop ( )
Removes &
Returns the
value
How a Stack Works - Pop
Stack is
empty
You can
NOT Pop
any more
elements
Pop ( )
Removes &
Returns the
value
How a Stack Works - Peek
Peek ( )
-8
2
13
-8
Returns the
value at the
top
How a Stack Works - Peek - one more time
Still returns
Peek ( )
-8
2
13
-8
Returns the
value at the
top
Your Turn - Show how the Stack looks after
executing all the following steps.
Push ( 7 )
Push ( 6 )
Push ( 5 )
Pop ( )
Peek ( )
Pop ( )
Push ( 6 )
Pop ( )
Peek ( )
Implementing a Stack using an Array
maxSize = 6;
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
0
1
0
0
maxSize = 6;
int [ ] myStack = new int [ maxSize ];
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
0
1
0
0
maxSize = 6;
int [ ] myStack = new int [ maxSize ];
int top = -1;
top = -1
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
0
1
0
0
Push ( -8 )
top = -1
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
0
1
Push ( -8 )
1. Increment top
⇒ top++;
top = 0
0
0
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
0
1
Push ( -8 )
1. Increment top
⇒ top++;
2. Update the element at
index top with -8
top = 0
-8
0
⇒ myStack [ top ] = -8;
Implementing a Stack using an Array
0
5
0
4
0
3
0
2
12
1
-8
0
Push ( 12 )
1. Increment top
⇒ top++;
top = 1
2. Update the element at
index top with 12
⇒ myStack [ top ] = 12;
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Push ( 19 )
1. Increment top
top = 2
⇒ top++;
2. Update the element at
index top with 12
⇒ myStack [ top ] = 12;
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Peek ( )
top = 2
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Peek ( )
1. Return the element at
index top
top = 2
⇒ return myStack [ top ] ;
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Pop ( )
top = 2
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Pop ( )
1. Keep a copy of the
element at index top
top = 2
⇒ int x = myStack [ top ] ;
Implementing a Stack using an Array
0
5
0
4
0
3
19
2
12
1
-8
0
Pop ( )
1. Keep a copy of the
element at index top
⇒ int x = myStack [ top ] ;
top = 1
2. Remove the element at
index top
⇒ top -- ;
Implementing a Stack using an Array
5
Pop ( )
0
4
1.
0
3
19
2
12
1
-8
19
0
Keep a copy of the element at
index top
⇒ int x = myStack [ top ] ;
2.
Remove the element at index top
top = 1
⇒ top -- ;
3.
Return the copy
0
⇒ return x;
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// push, pop, and peek functions
}
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// push, pop, and peek functions
}
void Push( int element ) {
top++;
myStack [ top ] = element;
}
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// push, pop, and peek functions
}
int Pop( ) {
int x = myStack [ top ];
top--;
return x;
}
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// push, pop, and peek functions
}
int Peek( ) {
int x = myStack [ top ];
return x;
}
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// other useful functions → isEmpty
}
boolean isEmpty( ) {
if ( top == -1)
return true;
else
return false;
}
The Stack Class in Java
class Stack {
int maxSize;
int [] myStack;
int top;
Stack ( ) {
maxSize = 100;
myStack = new int [ maxSize ];
top = -1;
}
// other useful functions → isFull
}
boolean isFull( ) {
if ( top == maxSize - 1)
return true;
else
return false;
}
Testing The Stack Class
class StackTester {
public static void main ( String [] args ) {
Stack theStack = new Stack ( );
theStack.push( 20 );
theStack.push( 40 );
theStack.push( 60 );
theStack.push( 80 );
while(
! theStack.isEmpty( )
int value = theStack.pop();
System.out.println( value );
}
}
}
)
{
Use the 2 Stacks S1 & S2
to display the contents of S1 in
a reverse order ( From Bottom
to top )
e
d
c
b
a
S1
Use the 2 Stacks S1 & S2
to display the contents of S1 in
a reverse order ( From Bottom
to top )
S2.push ( S1.pop () );
e
d
c
b
a
S2.push ( S1.pop () );
S2.push ( S1.pop () );
S2.push ( S1.pop () );
S2.push ( S1.pop () );
Sout ( S2.pop () );
Sout ( S2.pop () );
Sout ( S2.pop () );
Sout ( S2.pop () );
Sout ( S2.pop () );
Use the 2 Stacks S1 & S2
to display the contents of S1 in
a reverse order ( From Bottom
to top )
e
d
c
b
a
While ( ! S1.isEmpty() )
S2.push ( S1.pop () );
While ( ! S2.isEmpty() )
Sout ( S2.pop () );
Big O for the Stack
Push ⇒ O ( 1 )
Pop ⇒ O ( 1 )
Peek ⇒ O ( 1 )
Search ⇒ O ( N )
Stacks & Queues
First in First out
FIFO
How a Queue Works
3 main operations
1. insert → inserts a new elements at the rear of the
queue
2. remove → removes & returns the element at the
front of the queue
3. Peek → returns the element at the front of the queue
How a Queue Works
Head OR Front
Tail OR Rear
At first, a Queue is an empty
list.
How a Queue Works - Enqueue
29
Head OR Front
Tail OR Rear
Enqueue ( 29 )
How a Queue Works - Enqueue
29
80
Head OR Front
Tail OR Rear
Enqueue ( 80 )
How a Queue Works - Enqueue
29
80 -78
Head OR Front
Tail OR Rear
Enqueue ( -78 )
How a Queue Works - Enqueue
29
80 -78
6
Head OR Front
Tail OR Rear
Enqueue ( 6 )
How a Queue Works - Dequeue
29
80 -78
6
Head OR Front
Tail OR Rear
Dequeue ( )
Removes the element @ the front and
Returns it.
How a Queue Works - Dequeue
80 -78
6
Head OR Front
Tail OR Rear
Dequeue ( )
Removes the element @ the front and
Returns it.
How a Queue Works - Peek
-78
6
Head OR Front
Tail OR Rear
Peek ( )
Returns the element @ the front.
Does NOT remove it
Your Turn - Show how the Queue looks after
executing all the following steps.
Enqueue ( 7 )
Enqueue ( 6 )
Enqueue ( 5 )
Dequeue ( )
Peek ( )
Dequeue ( )
Enqueue ( 6 )
Dequeue ( )
Peek ( )
Your Turn - Show the output of the following
program.
Stack s = new Stack();
q.Enqueue( 6 );
Queue q = new Queue();
System.out.print (
s.Push( 7 );
q.DeQueue( ) );
s.Push( 6 );
s.Push( q.DeQueue( ) );
s.Push( 5 );
System.out.print ( s.Pop( ) );
System.out.print ( s.Pop( ) );
System.out.print ( s.Pop( ) );
q.Enqueue( s.Pop( ) );
q.Enqueue( 5 );
Implementing a Queue using an Array
0
0
0
0
0
0
0
Rear
Front
num_items = 0
At first, a Queue is
an empty container.
Implementing a Queue using an Array
29
0
0
0
0
Rear
Front
Enqueue ( 29 )
num_items = 1
0
0
Implementing a Queue using an Array
29
50
0
0
0
Rear
Front
Enqueue ( 50 )
num_items = 2
0
0
Implementing a Queue using an Array
29
50 -78
0
0
Rear
Front
Enqueue ( -78 )
num_items = 3
0
0
Implementing a Queue using an Array
29
50 -78 13
0
Rear
Front
Enqueue ( 13 )
num_items = 4
0
0
Implementing a Queue using an Array
29
50 -78 13
80
Rear
Front
Enqueue ( 80 )
num_items = 5
0
0
Implementing a Queue using an Array
29
50 -78 13
4
Rear
Front
Enqueue ( 4 )
num_items = 6
80
0
Implementing a Queue using an Array
29
50 -78 13
4
Rear
Front
Dequeue ( )
num_items = 5
80
0
Implementing a Queue using an Array
29
50 -78 13
num_items = 4
4
Rear
Front
Dequeue ( )
80
0
Implementing a Queue using an Array
29
50 -78 13
num_items = 3
4
Rear
Front
Dequeue ( )
80
0
Implementing a Queue using an Array
29
50 -78 13
num_items = 4
4
8
Rear
Front
Enqueue ( 8 )
80
Implementing a Queue using an Array
29
50 -78 13
80
num_items = 4
8
Rear
Front
Enqueue ( 6 )
4
Implementing a Queue using an Array
29
50 -78 13
80
num_items = 4
8
Rear
Front
Rear
Enqueue ( 6 )
4
Implementing a Queue using an Array
29
50 -78 13
80
Front
Rear
Enqueue ( 6 )
num_items = 4
4
8
Implementing a Queue using an Array
6
50 -78 13
80
Front
Rear
Enqueue ( 6 )
num_items = 4
4
8
This is called Wrap-around
and we need it to be able
to insert or delete more
elements after
1. The rear has reached the
end of the array.
2. The front has reached
the end of the array.
The Queue Class in Java
class Queue {
int maxSize;
int [] myQueue;
int front, rear, num_items;
Queue ( int size ) {
maxSize = size ;
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// enqueue, dequeue
// and peek functions
}
The Queue Class in Java
class Queue {
int maxSize;
int [] myQueue;
int front, rear, num_items;
Queue ( int size ) {
maxSize = size ;
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// enqueue, dequeue
// and peek functions
}
void Enqueue( int elm ) {
if ( rear == maxSize - 1 )
rear = -1 ;
rear++;
myQueue[ rear ] = elm;
num_items++;
}
The Queue Class in Java
class Queue {
int Dequeue( ) {
int maxSize;
int elm = myQueue[ front ];
int [] myQueue;
front++;
int front, rear, num_items;
if ( front == maxSize)
Queue ( int size ) {
front = 0 ;
maxSize = size ;
myQueue = new int [ maxSize ];
num_items--;
front = 0;
return elm;
rear = -1;
}
num_items = 0;
}
// enqueue, dequeue
// and peek functions
}
The Queue Class in Java
class Queue {
int Peek( ) {
int maxSize;
int elm = myQueue[ front ];
int [] myQueue;
int front, rear, num_items;
return elm;
Queue ( int size ) {
}
maxSize = size ;
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// enqueue, dequeue
// and peek functions
}
The Queue Class in Java
class Queue {
boolean isEmpty( ) {
int maxSize;
if ( num_items == 0 )
int [] myQueue;
return true;
int front, rear, num_items;
else
Queue ( int size ) {
return false;
maxSize = size ;
}
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// Other useful functions
}
The Queue Class in Java
class Queue {
boolean isFull( ) {
int maxSize;
if ( num_items == maxSize )
int [] myQueue;
return true;
int front, rear, num_items;
else
Queue ( int size ) {
return false;
maxSize = size ;
}
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// Other useful functions
}
The Queue Class in Java
class Queue {
int size( ) {
int maxSize;
return num_items;
int [] myQueue;
}
int front, rear, num_items;
Queue ( int size ) {
maxSize = size ;
myQueue = new int [ maxSize ];
front = 0;
rear = -1;
num_items = 0;
}
// Other useful functions
}
Testing The Queue Class
class QueueTester {
public static void main ( String [] args ) {
Queue theQueue = new Queue ( 3 );
theQueue.Enqueue( 10 );
theQueue.Enqueue( 20 );
theQueue.Dequeue();
theQueue.Enqueue( 30 );
theQueue.Enqueue( 40 );
// wraps around
while(
! theQueue.isEmpty( ) )
int value = theQueue.Dequeue();
System.out.println( value );
}
}
}
{
Testing The Queue Class
class QueueTester {
public static void main ( String [] args ) {
Queue theQueue = new Queue ( 3 );
theQueue.Enqueue( 10 );
theQueue.Enqueue( 20 );
theQueue.Enqueue( 30 );
theQueue.Dequeue();
theQueue.Dequeue();
theQueue.Dequeue();
theQueue.Dequeue();
}
}
// 10
// 20
// 30
Testing The Queue Class
class QueueTester {
public static void main ( String [] args ) {
Queue theQueue = new Queue ( 3 );
theQueue.Enqueue( 10 );
theQueue.Enqueue( 20 );
theQueue.Enqueue( 30 );
theQueue.Dequeue();
theQueue.Dequeue();
theQueue.Dequeue();
theQueue.Dequeue();
// 10
// 20
// 30
// 10
}
}
We didn’t check if the queue is empty or not
Big O for the Queue
Enqueue ⇒ O ( 1 )
Dequeue ⇒ O ( 1 )
Peek ⇒ O ( 1 )
Search ⇒ O ( N )