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Stack ADT Operations Application: Expression Evaluation

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Presentation on theme: "Stack ADT Operations Application: Expression Evaluation"— Presentation transcript:

1 Stack ADT Operations Application: Expression Evaluation
Push, Pop, Top, isEmpty Application: Expression Evaluation Arithmetic Expression Infix-to-Postfix Postfix to Quadruples Boolean Expressions (Assignment #1)

2 Implementing a Stack Using Vector /Array
requires estimate of maximum list length may grow dynamically Ø = empty slots Can contain varied data/objects (not necessarily homogeneous) 30−0 212 rules! Golf #1 Ø Ø Ø top

3 Implementing a Stack Using Linked List
flexible, adjusts to problem size implementing a linked list nodes and references/links/pointers top Golf #1 212 rules! 30−0 Ø

4 Implementing a Stack Using Linked List implementing a linked list 1 2
1 2 3 4 5 6 7 8 Ø 2 -1 7 1 4 3 6 Using Linked List implementing a linked list cursor implementation 212 rules! Ø Ø 30−0 top = 5 Golf #1 freelist = 8 Ø Ø Ø

5 Implementing a Stack push O(1)* O(1) pop O(1) O(1) top/peek O(1) O(1)
Vector/Array Linked List push O(1)* O(1) pop O(1) O(1) top/peek O(1) O(1) isEmpty O(1) O(1) *assuming no need for Vector/Array expansion

6 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: @

7 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z @

8 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z = @

9 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a = @

10 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a * = @

11 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a ( * = @

12 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x ( * = @

13 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x + ( * = @

14 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + ( * = @

15 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + ( * = @

16 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * = @

17 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * = @

18 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * + = @

19 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z + = @

20 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z * + = @

21 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c * + = @

22 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c ^ * + = @

23 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c ( ^ * + = @

24 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 ( ^ * + = @

25 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 − ( ^ * + = @

26 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 ( − ^ * + = @

27 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 ~ ( − ^ * + = @

28 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ ( − ^ * + = @

29 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ ( − ^ * + = @

30 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ ( − ^ * + = @

31 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ + ( − ^ * = @

32 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + ( − ^ * = @

33 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + ( − ^ * = @

34 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + ( − ^ * + = @

35 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + ( − ^ * + = @

36 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ( ^ * + = @

37 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ( ^ * + = @

38 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ( ^ * + = @

39 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * + = @

40 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * + = @

41 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * + = @

42 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * + = @

43 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * / + = @

44 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = @

45 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = @

46 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = @

47 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = @

48 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = @

49 Infix to Postfix infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + =

50 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = z

51 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = a z

52 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = x a z

53 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = y x a z

54 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = y x a z

55 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = t0 a z + x y t0

56 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 t0 a z

57 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 t1 z

58 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 z t1

59 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 c z t1

60 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 2 c z t1

61 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 d 2 c z t1

62 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 d 2 c z t1

63 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 t2 2 c z t1

64 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 w t2 2 c z t1

65 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 w t2 2 c z t1

66 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 t3 2 c z t1

67 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 t3 2 c z t1

68 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 t4 c z t1

69 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 t4 c z t1

70 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 t5 z t1

71 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 t5 z t1

72 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 t6 t1 z

73 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 x t6 t1 z

74 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 x t6 t1 z

75 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 t7 t1 z

76 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 t7 t1 z

77 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 t8 z

78 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 t8 z

79 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 = t8 z

80 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 t8 z

81 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 = t8 z

82 Postfix to Quadruples postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + = + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - 2 t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 = t8 z

83 Postfix to Quadruples infix expression: z = a * ( x + y ) + z * c ^ ( 2 − ( − d + w ) ) / x ; --- t t2- ----- t t3 ---- t t t t t + x y t0 * a t0 t1 ~ d t2 + t2 w t3 - w t3 t4 ^ c t4 t5 * Z t5 t6 / t6 x t7 + t1 t7 t8 = t8 z postfix expression: z a x y + * z c 2 d ~ w + − ^ * x / + =

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