Note 3: Stack and Queue Concept in Data Structure for Application
Stack:
It is a sequence of items that are accessible at only one end of the sequence. Think of a
stack as a collection of items that are piled one on top of the other, with access limited to
the topmost item. A stack inserts item on the top of the stack and removes item from the
top of the stack. It has LIFO (last-in / first-out) ordering for the items on the stack.
Type of Stack:
Linear Stack
Linked List Stack
Operation of Stack:
Add: a push( ) operation adds an item to the topmost location on the stack.
stack:
stack:
stack:
top = 3
3
2
1
top = 2
add 4 to the
stack
4
top = 3
3
3
2
2
1
1
increase top
push 4 to the stack
Push function:
void push ( short stack[], short stack_size, short top, short item)
{
if ( top >= stack_size –1)
{
cout << “The stack is full!” << endl;
return;
}
stack[+ + top] = item;
}
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Delete: a pop( ) operation removes an item from the topmost location on the stack
stack:
stack:
4
3
stack:
top = 3
top = 3
3
3
2
2
2
1
1
1
delete 4 from
the stack
pop 4 out of the stack
top = 2
decrease top
Pop function:
short pop (short stack[], short stack_size, short top)
{
if ( top = = –1)
{
cout << “The stack is empty!” << endl;
return 0;
}
return stack[top – – ] ;
}
Queue:
A queue is a sequential storage structure that permits access only at the two ends of the
sequence. We refer to the ends of the sequence as the front and rear. A queue inserts
new elements at the rear and removes elements from the front of the sequence. You will
note that a queue removes elements in the same order in which they were stored, and
hence a queue provides FIFO (first-in / first-out), or FCFS (first-come / first-served),
ordering.
Type of the Queue:
Linear Queue: non-circular queue, circular queue, priority queue
Linked List Queue: non-circular queue, circular queue, priority queue
Operation of Queue:
Add: insert operation for the queue is adding item to the new element at the rear of queue.
Delete: remove operation for the queue is deleting item from the front element of queue.
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16
The non-circular queue with 8 elements:
Algorithms:
Variables:
short qfront = -1, qrear = -1, qsize = 8;
Insert:
T
qrear = qsize-1
and
qfront = -1
F
qrear = qsize-1
T
queue
is full
return
1
F
shift all elements left so
that 1st element is at 0
qfront = -1
qrear++
queue[qrear] = value
return 0
Delete:
qfront = qrear
T
queue
is
empty
qfront = -1
qrear = -1
return 1
F
qfront++
value = queue[qfront]
return 0
Graphical Presentation:
0
1
2
3
4
qfront
The circular queue with 8 elements:
Algorithms:
Variables:
short qfront = 0, qcount = 0, qsize = 8;
5
qrear
6
7
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Insert:
qcount = qsize
F
T
qrear = (qfront+qcount)% qsize
queue[qrear] = value
qcount++
return 0
queue
is full
return
1
Delete:
qcount = 0
F
T
queue
is
empty
return
1
value = queue[qfront]
qfront = (qfront+1)% qsize
qcount - return 0
Graphical Presentation:
4
3
2
5
1
6
qrear
0
7
qfront
Structure
Type
Stacks
Queue
Stacks and Queue Structure Table
Array
Link List
Linear Stacks
Non-Circular Queue
Circular Queue
Priority Queue
Linear Stacks
Non-Circular Queue
Circular Queue
Priority Queue
Link List Array
Linear Stacks
Non-Circular Queue
Circular Queue
Priority Queue
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Multiple Stacks and Queues:
Multiple Stacks:
Following pictures are two ways to do two stacks in array:
1. None fixed size of the stacks:
Graphical Picture: without fixed size of stack
Array_ptr
-2
-1
12
0
0
1
2
3
4
5
6
7
8
9
10
11
Stack 2
Stack 1 Top
Stack 2 Top
Stack 1
12
 Stack 1 expands from the 0th element to the right
 Stack 2 expands from the 12th element to the left
 As long as the value of Top1 and Top2 are not next to each other, it has free
elements for input the data in the array
 When both Stacks are full, Top1 and Top 2 will be next to each other
 There is no fixed boundary between Stack 1 and Stack 2
 Elements –1 and –2 are using to store the information needed to manipulate the
stack (subscript for Top 1 and Top 2)
2. Fixed size of the stacks:
Graphical Picture: with fixed size of stack
Array_ptr
-4
-3
-2
-1
5
6
6
0
0
2
3
4
5
6
7
8
9
10
Stack 2
Stack 1 Top
Stack 1 Size
Stack 2 Top
Stack 2 Size
Stack 1
1
 Stack 1 expands from the 0th element to the right
 Stack 2 expands from the 6th element to the left
 As long as the value of Top 1 is less than 6 and greater than 0, Stack 1 has free
elements to input the data in the array
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 As long as the value of Top 2 is less than 11 and greater than 5, Stack 2 has free
elements to input the data in the array
 When the value of Top 1 is 5, Stack 1 is full
 When the value of Top 2 is 10, stack 2 is full
 Elements –1 and –2 are using to store the size of Stack 1 and the subscript of the
array for Top 1 needed to manipulate Stack 1
 Elements –3 and –4 are using to store the size of Stack 2 and the subscript of the
array for Top 2 needed to manipulate Stack 2
Multiple Queues:
Following pictures are two ways to do two queues in array:
1. None fixed size of the queues:
Graphical Picture: without fixed size of the queue
-6
-5
-4
-3
-2
-1
0
5
4
0
0
5
Queue 2 Count
Queue 2 Front
Queue 2 Size
Queue 1 Count
Queue 1 Front
Queue 1 Size
Array_ptr
0
1
2
3
4
5
Queue 1
6
7
8
Queue 2
Temporary
Boundary
 Queue 1 expands from the 0th element to the right and circular back to the 0th
element
 Queue 2 expands from the 8th element to the left and circular back to the 8th
element
 Temporary boundary between the Queue 1 and the Queue 2; as long as there has
free elements in the array and boundary would be shift
 Free elements could be any where in the Queue such as before the front, after the
rear, and between front and rear in the Queue
 Queue 1’s and Queue 2 ‘s size could be change if it is necessary. When the
Queue 1 is full and the Queue 2 has free space; the Queue 1 can increase the size
to use that free space from the Queue 2. Same way for the Queue 2
 Elements –1, –2, and –3 are using to store the size of the Queue 1, the front of the
Queue 1, and the data count for the Queue 1 needed to manipulate the Queue 1
 Elements –4, –5, and –6 are using to store the size of the Queue 2, the front of the
Queue 2, and the data count for the Queue 2 needed to manipulate the Queue 2
 Inserts data to the Queue 1, Q1Rear = (Q1Front + Q1count) % Q1Size
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 Inserts data to the Queue 2, Q2Rear = (Q2Front + Q2count) % Q2Size + Q1Size
 Deletes data from the Queue 1, Q1Front = (Q1Front + 1) % Q1Size
 Deletes data from the Queue 2, Q2Front = (Q2Front + 1) % Q2Size + Q1Size
2. Fixed size of the queue:
Graphical Picture: with fixed size of the queue
-6
-5
-4
-3
-2
-1
0
5
4
0
0
5
Queue 2 Count
Queue 2 Front
Queue 2 Size
Queue 1 Count
Queue 1 Front
Queue 1 Size
Array_ptr
0
1
2
3
4
5
Queue 1
6
7
8
Queue 2
Boundary between
the Queues
 Queue 1 expands from the 0th element to the 4th element and circular back to 0th
element
 Queue 2 expands from the 8th element to the 5th element and circular back to 8th
element
 The boundary is fixed between the Queue 1 and the Queue 2
 Free elements could be any where in the Queue such as before the front, after the
rear, and between front and rear in the Queue
 Elements –1, –2, and –3 are using to store the size of the Queue 1, the front of the
Queue 1, and the data count for the Queue 1 needed to manipulate the Queue 1
 Elements –4, –5, and –6 are using to store the size of the Queue 2, the front of the
Queue 2, and the data count for the Queue 2 needed to manipulate the Queue 2
 Inserts data to the Queue 1, Q1Rear = (Q1Front + Q1count) % Q1Size
 Inserts data to the Queue 2, Q2Rear = (Q2Front + Q2count) % Q2Size + Q1Size
 Deletes data from the Queue 1, Q1Front = (Q1Front + 1) % Q1Size
 Deletes data from the Queue 2, Q2Front = (Q2Front + 1) % Q2Size + Q1Size