lecture 2c stacks

STACKS- INTRODUCTION

Data structures are organized grouping of data items, treated as a unit regarded as data aggregates e.g. arrays, trees, stacks, queues.

Data structures allow a programmer to create data types by grouping together data of more primitive types.

DEFINITIONS• A stack is an ordered list of elements in which

insertions and deletions are made at one end called the top.

• The point of access of a stack is called the top. •  A stack is linear list whose elements may be

created & deleted only in a last in first out order.

DEFINITIONS

• A stack is a linear list for which all insertions & deletions and usually all accesses are made at one end of the list.

•  A stack is an ADT that is a storage mechanism which is defined by the operations performed on it & not at all by the specific manner in which it is implemented.

DEFINITIONS

A stack allows access to only one data item: the last item inserted. If you remove this item, then you can access the next-to-last item inserted, and so on.

A stack is also known as a pushdown list or a LIFO (Last In First Out) list.

DEFINITIONS•  A Push Operation

It appends one new item to the top of the stack or to the top of a non-full stack.

•  A Pop Operation

It removes or deletes the top item from the stack.

DEFINITIONS

• Stack Pointer• It contains the address of the top of the stack. • If an item is appended to or deleted from the

stack, the pointer is incremented or decremented respectively to contain the address of the new top of the stack.

DEFINITIONS

• Stack base• It contains the address of the bottom location in

the received block. If an attempt is made to pop when the stack is empty an error is reported.

•  Stack limit• Contains the address of the other end of the

received block. If an attempt is made to push when the block is fully utilized for the stack an error is reported.

Characteristics of Stacks

It Mainly Uses The Principle Of Last In First Out

Can add and delete without disturbing the arrangement

EXAMPLE

1995 1996

1995

1982

1998

1995

1982

a) Initial state (Empty)

d) After two pops

c) After three pushes

b) After one push

Use of Links (or Pointers)

A Stack can be represented by using links or pointers.

Two nodes with two fields, possibly called DATA and LINK can represent a stack.

(A node is a collection of data and link information).

The data field of each node contains an item in the stack and the corresponding link field points to the node containing the next item in the stack

Use of Links (or Pointers)

The linked field of the last node is zero for we assume that all nodes have an address greater than zero.

For example, a stack with the items A, B, C, D, E inserted in that order, would look as in the figure below:

A 5 element, linked stack

E D C B A 0

Cont’d

The variable STACK points to the topmost node (the last item inserted) in the list.

The empty stack is represented by setting STACK = 0.

The use of links to represent a stack requires more storage than the sequential array.

Array Implementation of Stacks

A stack can be implemented with an array and an integer.

The integer tos (Top of stack) provides the array index of the top element of the stack. Thus if tos is –1, the stack is empty.

The array implementation keeps the bottom of the stack at the beginning of the array.

It grows toward the end of the array.

Cont’d

The array implementation has one serious drawback: you must know the max. no. of items in your collection when you create it.

This presents problems in programs in which this max. no. cannot be predicted accurately when the program starts up.

A linked list can be used to overcome this limitation.

Linked List Implementation of Stacks

The linked list is a very flexible dynamic data structure: items may be added to it or deleted from it at will.

The stack interface can be implemented by using a linked list in which the top of the stack is represented by the first item in the list

Used in linear data structure simply because they figure so prominently in systems programming especially in compiler design.

 Storage management in recursive programming & to implement inherently recursive routines.

Used for processing nested program structures for example bracketed arithmetic/logical expressions; programs with block structures; statements with matching delimiters as; If, Then, Else, End.

USES OF STACKS

APPLICATIONS OF STACKS

1. Interrupts

The management of I/O data transfer goes through three stages i.e.

Initiate the interruptService the interruptReturn from the interrupt

2) Stack as a Temporary Storage

Some computer use stack instead of general purpose registers to store temporary values during computation

These computations are called stack machines or zero address machines.

The h/w recalls the source operands on the stack which would be popped & then supplied to the ALU & the results of the addition would be pushed onto the stack

Cont’d

To perform an addition, the h/w would execute two pops & a push

Two pops would remove the two sources operands from the stack, the add would compute the sum & push would replace the results back on the stack.

Most calculators use stacks, Example:Evaluate: (A+B)(C+D) and store the results in

E: where A is 25; B is 17; C is 3; D is 2

Cont’d

Push 25Push 17ADDPush 3Push 2ADDMultiplyPop E

3) Data Type ConversionEvery instruction should be provided with

source operands of the data type that the instruction requires i.e. ADD requires operands that are two complement integers.

Example 2+3=A stack is used in keeping track of data type of

each of the values that one is working with

LIMITATIONThe concept of the stack being a LIFO structure

removing & adding items from the stack requires a strict order, which is serially.

Insertions & deletions can be performed only from the one position, which is at the top.

This implies that the sequence of Pushes of A, B, C, D. has to be eventually followed by the Pops of D,C,B and A.

The stack limit or the default values may not be enough & this will result in overflows.

LIMITATIONOverflows are conditions that occur when one

tries to push a value onto a stack and there is no available space.

The user should always check therefore that the stack is not full before inserting an item.

Often a stack full condition will signal that more storage needs to be allocated and the program reruns.

LIMITATION

A programmer requires prior knowledge or proper presentation & a good understanding of the program when deciding or the number of stack for optimum performance.

CONCLUSION

In a nutshell stacks are form of an ADT that is a storage mechanism which is defined by the operations performed on it & not at all by the specific manner in which it is implemented & are composed of pointer, top, base & peek button.

They simply aid in writing an algorithm.