Data Structures and Algorithms V Otávio Braga
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1 Data Structures and Algorithms V Otávio Braga
2 We use a stack When an operand is read, output it When an operator is read Pop until the top of the stack has an element of lower precedence Then push it When ) is found, pop until we find the matching ( ( has the lowest precedence when in the stack but has the highest precedence when in the input When we reach the end of input, pop until the stack is empty
3 3+4*5/6 Infix to Postfix Conversion Example 1
4 3+4*5/6 Stack: Output: Infix to Postfix Conversion Example 1
5 3+4*5/6 Stack: Output: 3 Infix to Postfix Conversion Example 1
6 3+4*5/6 Stack: + Output: 3 Infix to Postfix Conversion Example 1
7 3+4*5/6 Stack: + Output: 3 4 Infix to Postfix Conversion Example 1
8 3+4*5/6 Stack: + * Output: 3 4 Infix to Postfix Conversion Example 1
9 3+4*5/6 Stack: + * Output: Infix to Postfix Conversion Example 1
10 Example 1 3+4*5/6 Stack: + Output: *
11 Example 1 3+4*5/6 Stack: + / Output: *
12 Example 1 3+4*5/6 Stack: + / Output: * 6
13 Example 1 3+4*5/6 Stack: + Output: * 6 /
14 Example 1 3+4*5/6 Stack: Output: * 6 / + Done!
15 Example 2 (300+23)*(43-21)/(84+7)
16 Example 2 (300+23)*(43-21)/(84+7) Stack: Output:
17 Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output:
18 Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output: 300
19 Example 2 (300+23)*(43-21)/(84+7) Stack: ( + Output: 300
20 Example 2 (300+23)*(43-21)/(84+7) Stack: ( + Output:
21 Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output:
22 Example 2 (300+23)*(43-21)/(84+7) Stack: Output:
23 Example 2 (300+23)*(43-21)/(84+7) Stack: * Output:
24 Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output:
25 Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output:
26 Example 2 (300+23)*(43-21)/(84+7) Stack: * ( - Output:
27 Example 2 (300+23)*(43-21)/(84+7) Stack: * ( - Output:
28 Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output:
29 Example 2 (300+23)*(43-21)/(84+7) Stack: * Output:
30 Example 2 (300+23)*(43-21)/(84+7) Stack: Output: *
31 Example 2 (300+23)*(43-21)/(84+7) Stack: / Output: *
32 Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: *
33 Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: * 84
34 Example 2 (300+23)*(43-21)/(84+7) Stack: / ( + Output: * 84
35 Example 2 (300+23)*(43-21)/(84+7) Stack: / ( + Output: * 84 7
36 Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: *
37 Example 2 (300+23)*(43-21)/(84+7) Stack: / Output: *
38 Example 2 (300+23)*(43-21)/(84+7) Stack: Output: * / Done!
39 Example 3 (4+8)*(6-5)/((3-2)*(2+2))
40 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output:
41 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output:
42 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output: 4
43 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( + Output: 4
44 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( + Output: 4 8
45 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output: 4 8 +
46 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: 4 8 +
47 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * Output: 4 8 +
48 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output: 4 8 +
49 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output:
50 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( - Output:
51 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( - Output:
52 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output:
53 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * Output:
54 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: *
55 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / Output: *
56 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: *
57 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: *
58 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: * 3
59 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( - Output: * 3
60 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( - Output: * 3 2
61 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: * 3 2 -
62 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: * 3 2 -
63 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * Output: * 3 2 -
64 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: * 3 2 -
65 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: * 3 2-2
66 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( + Output: * 3 2-2
67 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( + Output: *
68 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: *
69 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * Output: *
70 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: * *
71 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / Output: * *
72 Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: * * / Done!
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