EC-211 DATA STRUCTURES

LECTURE 5

2

Stack Data Structure

Stack of Books Stack of Notes Stack of Gifts

THE STACK

• A stack is an ordered collection of items in which insertions and deletions are done only at one end, called the Top of the stack.

E

D

C

B

A

top

AB

A

C

B

A

D

C

B

A

C

B

A

E

C

B

A

(a) (b) (c) (d) (e) (f)

Motion Picture of a Stack

Notice the Last-in-First-out (LIFO) Behavior

Operations

• Push– Insertion of an item at top of stack

• Pop– Removal of an item from top of stack– Not defined for empty stack (underflow)

Other Operations on Stack

• Checking whether the stack is empty– returns TRUE if the stack is empty– returns FALSE if there is at least one item in the

stack

Stack Applications

• Nested Parentheses– In mathematical expressions that include sets of

nested parenthesis; we want to ensure that1.There are an equal number of right and left

parentheses• ((A+B)

2.Every right parenthesis is preceded by a matching left parenthesis• (A+B))-(C+D

Checking for Balanced Parentheses with StacksLet S be an empty stackBalanced SoFar = TRUEI=0while(I < strlen (Str) and BalancedSoFar ){ Ch = Str [ I ]

++I//push an open braceif ( Ch is ‘(‘ )

Push ‘(‘ on S//Close Braceelse if ( Ch is ‘)’ )

if ( S is not empty)Pop top item from S//pop a matching open

braceelse //no matching open brace

BalancedSoFar = FALSE

Checking for Balanced Parentheses with Stacks

//ignore all characters other than braces

} //end while

if ( BalancedSoFar and S is Empty )Str has Balanced Braces

elseStr does not have balanced Braces

Checking Multiple Types of Brackets

{

(

{

[

(

{

(

{ {

(

{

[

(

Example:{x+(y-[a+b])*c-(d+e)}/(h-[j-k])

{ {x+( {x+(y-[ {x+(y-[a+b] {x+(y-[a+b]) {x+(y-[a+b])*c-(

{x+(y-[a+b])*c-(d+e)} {x+(y-[a+b])*c-(d+e)}/(h-[j-k {x+(y-[a+b])*c-(d+e)}/(h-[j-k])

Checking Multiple Types of Brackets

valid=true; s=the empty stack; while (we have not read the entire string) {

read the next symbol (symb) of the string; if (symb==‘(‘ || symb==‘[‘ || symb==‘{‘)

push(s, symb);

Multiple Types of Brackets contd.

if (symb==‘)‘ || symb==‘]‘ || symb==‘}‘) if (empty(s))

valid=false; else {

i=pop(s);if (i is not the matching opener of symb);

valid=false;} //end else

} //end while

Multiple Types of Brackets contd.

if (!empty(s))valid=false;

if (valid)

cout<<“the string is valid”; else

cout<<“the string is invalid”;