08 STACKS DATA STRUCTURES AND ALGORITHMS IMPLEMENTATION & APPLICATIONS IMRAN IHSAN ASSISTANT PROFESSOR, AIR UNIVERSITY, ISLAMABAD
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1 DATA STRUCTURES AND ALGORITHMS 08 STACKS IMPLEMENTATION & APPLICATIONS IMRAN IHSAN ASSISTANT PROFESSOR, AIR UNIVERSITY, ISLAMABAD LECTURES ADAPTED FROM: DANIEL KANE, NEIL RHODES DEPARTMENT OF CS & ENGINEERING UNIVERSITY OF CALIFORNIA, SAN DIEGO
2 STACK ABSTRACT DATA TYPE An Abstract Stack (Stack ADT) is an abstract data type which emphasizes specific operations: Uses a explicit linear ordering Insertions and removals are performed individually Inserted objects are pushed onto the stack The top of the stack is the most recently object pushed onto the stack When an object is popped from the stack, the current top is erased Also called a last-in first-out (LIFO) behavior Graphically, we may view these operations as follows: There are two exceptions associated with abstract stacks: It is an undefined operation to call either pop or top on an empty stack 2
3 STACK APPLICATIONS Numerous applications: Parsing code: Matching parenthesis XML (e.g., XHTML) Tracking function calls Dealing with undo/redo operations Reverse-Polish calculators Assembly language The stack is a very simple data structure Given any problem, if it is possible to use a stack, this significantly simplifies the solution Problem solving: Solving one problem may lead to subsequent problems These problems may result in further problems As problems are solved, your focus shifts back to the problem which lead to the solved problem Notice that function calls behave similarly: A function is a collection of code which solves a problem 3
4 STACK DEFINITION Abstract data type with the following operations: Push(Key): Key Top(): Key Pop(): Boolean Empty(): adds key to collection returns most recently-added key removes and returns most recently-added key are there any elements? 4
5 BALANCED BRACKETS Input: A string str consisting of (, ), [, ] characters. Output: Return whether or not the string s parentheses and square brackets are balanced. Balanced: Unbalanced: ([])[](), ([]]() ((([([])]))()) ][ 5
6 BALANCED BRACKETS IsBalanced(str ) Stack stack for char in str: if char in [ (, [ ]: stack.push(char) else: if stack.empty(): return False top stack.pop() if (top = [ and char!= ] ) or (top = ( and char!= ) ): return False return stack.empty() 6
7 STACK IMPLEMENTATION WITH ARRAY numelements: 0 7
8 STACK IMPLEMENTATION WITH ARRAY numelements: 0 Push(a) 8
9 STACK IMPLEMENTATION WITH ARRAY a numelements: 1 Push(a) 9
10 STACK IMPLEMENTATION WITH ARRAY numelements: 2 a b Push(b) 10
11 STACK IMPLEMENTATION WITH ARRAY numelements: 2 a B Top() b 11
12 STACK IMPLEMENTATION WITH ARRAY numelements: 3 a b c Push(c) 12
13 STACK IMPLEMENTATION WITH ARRAY numelements: 2 a b Pop() c 13
14 STACK IMPLEMENTATION WITH ARRAY numelements: 3 a b d Push(d) 14
15 STACK IMPLEMENTATION WITH ARRAY numelements: 4 a b d e Push(e) 15
16 STACK IMPLEMENTATION WITH ARRAY numelements: 5 a b d e f Push(f) 16
17 STACK IMPLEMENTATION WITH ARRAY numelements: 5 a b d e f Push(g) ERROR 17
18 STACK IMPLEMENTATION WITH ARRAY numelements: 5 a b d e f Empty() False 18
19 STACK IMPLEMENTATION WITH ARRAY numelements: 4 a b d e Pop() f 19
20 STACK IMPLEMENTATION WITH ARRAY numelements: 3 a b d Pop() e 20
21 STACK IMPLEMENTATION WITH ARRAY numelements: 2 a b Pop() d 21
22 STACK IMPLEMENTATION WITH ARRAY a numelements: 1 Pop() b 22
23 STACK IMPLEMENTATION WITH ARRAY numelements: 0 Pop() a 23
24 STACK IMPLEMENTATION WITH ARRAY numelements: 0 Empty() True 24
25 STACK IMPLEMENTATION WITH LINKED LIST head / Empty Linked List 25
26 STACK IMPLEMENTATION WITH LINKED LIST head a / Push(a) 26
27 STACK IMPLEMENTATION WITH LINKED LIST head b a / Push(b) 27
28 STACK IMPLEMENTATION WITH LINKED LIST head b a / Top() b 28
29 STACK IMPLEMENTATION WITH LINKED LIST head c b a / Push(c) 29
30 STACK IMPLEMENTATION WITH LINKED LIST head b a / Pop() c 30
31 STACK IMPLEMENTATION WITH LINKED LIST head d b a / Push(d) 31
32 STACK IMPLEMENTATION WITH LINKED LIST head e d b a / Push(e) 32
33 STACK IMPLEMENTATION WITH LINKED LIST head f e d b a / Push(f) 33
34 STACK IMPLEMENTATION WITH LINKED LIST head f e d b a / Empty() False 34
35 STACK IMPLEMENTATION WITH LINKED LIST head e d b a / Pop() f 35
36 STACK IMPLEMENTATION WITH LINKED LIST head d b a / Pop() e 36
37 STACK IMPLEMENTATION WITH LINKED LIST head b a / Pop() d 37
38 STACK IMPLEMENTATION WITH LINKED LIST head a / Pop() b 38
39 STACK IMPLEMENTATION WITH LINKED LIST head / Pop() a 39
40 STACK IMPLEMENTATION WITH LINKED LIST head / Empty() True 40
41 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 41
42 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 42
43 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 43
44 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 44
45 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 45
46 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 46
47 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 47
48 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 48
49 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 49
50 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 50
51 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 51
52 PARSING XHTML STACK APPLICATIONS <html> <head><title>hello</title></head> <body><p>this appears in the <i>browser</i>.</p></body> </html> 52
53 SUMMARY Stacks can be implemented with either an array or a linked list. Each stack operation is O(1): Push, Pop, Top, Empty. Stacks are occasionally known as LIFO queues. 53
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