ADT Stacks and Queues

1
ADT Stacks and Queues
2
Stack Logical Level

• An ordered group of homogeneous items or
  elements in which items are added and removed
  from only one end.
• A stack is also called a Last In First Out (LIFO)
  data structure.

3
Stack Logical Level

• Stack Operations
• Boolean IsEmpty ()
• Boolean IsFull ()
• Push (ItemType newitem)
• void Pop ()
• ItemType Top ()

4
Stack Application Level

• A runtime stack of activation records (ar) is
  maintained as a program executes to track
  function calls and scopes.
• Each activation record contains
• space for local variables and parameters
• ptr to dynamic parent
• ptr to static parent
• return address

5
Consider this codeoutline

• // ------------------------------
• void B ( )
• // ------------------------------
• void A ( )
• B ()
• // ------------------------------

6
Consider the following
B
A
main

• main begins executing
• main calls function A
• function A calls function B
• function B returns
• function A returns
• main returns

• Push (mains ar)
• Push (As ar)
• Push (Bs ar)
• Use info in Top ar to return control to A
• Pop
• Use info in Top ar to return control to main
• Pop
• Use info in Top ar to return control to OS
• Pop

Runtime Stack
7
Stack Application Level

• Stacks can be used to analyze nested expressions
  with grouping symbols to determine if they are
  well-formed (all grouping symbols occur in
  matching pairs and are nested properly.)
• ( ( xxx ) x xx) is well-formed
• ( ( xxx x ) is ill-formed

8
General Algorithm
( ( x x x ) x x x )

• get next symbol
• set balanced flag to true
• while (there are more input symbols and
  expression still balanced)
• if (next symbol is opening symbol)
• Push symbol onto stack
• else
• if (next symbol is closing symbol)
• if (stack is empty)
• set balanced to false
• else
• use Top to get copy of opening symbol on
  top of stack
• Pop the stack
• if (opening symbol does not match closing
  symbol)
• set balanced to false
• else
• ignore symbol
• get next symbol
• if (balanced and stack is empty)
• well-formed

(

(
Stack
Expression is Well-formed ! ! !
9
Stack Implementation Level

• Using an array

MAX_ITEMS - 1
. . .
0
-1
items
top
10
Stack Implementation Level

• Using an array

Push ( 70 )
MAX_ITEMS - 1
. . .
70
0
0
items
top
11
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28)
MAX_ITEMS - 1
. . .
28
70
0
1
items
top
12
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88)
MAX_ITEMS - 1
. . .
88
28
70
0
2
items
top
13
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88) Pop
MAX_ITEMS - 1
. . .
88
28
70
0
1
items
top
14
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88) Pop Push ( 95)
MAX_ITEMS - 1
. . .
95
28
70
0
2
items
top
15
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88) Pop Push (
95) Pop
MAX_ITEMS - 1
. . .
95
28
70
0
1
items
top
16
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88) Pop Push (
95) Pop Pop
MAX_ITEMS - 1
. . .
95
28
70
0
0
items
top
17
Stack Implementation Level

• Using an array

Push ( 70 ) Push ( 28) Push ( 88) Pop Push (
95) Pop Pop Pop
MAX_ITEMS - 1
. . .
95
28
70
0
-1
items
top
18
Stack Implementation Level

• Using a linked list

NULL
top
19
Stack Implementation Level

• Using a linked list

Push ( 70 )
NULL
70
top
20
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 )
NULL
28
70
top
21
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 )
NULL
88
28
70
top
22
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 ) Pop
NULL
28
70
top
23
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 ) Pop Push ( 95
)
NULL
95
28
70
top
24
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 ) Pop Push ( 95
) Pop
NULL
28
70
top
25
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 ) Pop Push ( 95
) Pop Pop
NULL
70
top
26
Stack Implementation Level

• Using a linked list

Push ( 70 ) Push ( 28 ) Push ( 88 ) Pop Push ( 95
) Pop Pop Pop
NULL
top
27
To be continued . . .