Data Structures and Algorithms V22.0102. Otávio Braga

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Transcription:

Data Structures and Algorithms V22.0102 Otávio Braga

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+4*5/6 Infix to Postfix Conversion Example 1

3+4*5/6 Stack: Output: Infix to Postfix Conversion Example 1

3+4*5/6 Stack: Output: 3 Infix to Postfix Conversion Example 1

3+4*5/6 Stack: + Output: 3 Infix to Postfix Conversion Example 1

3+4*5/6 Stack: + Output: 3 4 Infix to Postfix Conversion Example 1

3+4*5/6 Stack: + * Output: 3 4 Infix to Postfix Conversion Example 1

3+4*5/6 Stack: + * Output: 3 4 5 Infix to Postfix Conversion Example 1

Example 1 3+4*5/6 Stack: + Output: 3 4 5 *

Example 1 3+4*5/6 Stack: + / Output: 3 4 5 *

Example 1 3+4*5/6 Stack: + / Output: 3 4 5 * 6

Example 1 3+4*5/6 Stack: + Output: 3 4 5 * 6 /

Example 1 3+4*5/6 Stack: Output: 3 4 5 * 6 / + Done!

Example 2 (300+23)*(43-21)/(84+7)

Example 2 (300+23)*(43-21)/(84+7) Stack: Output:

Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output:

Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output: 300

Example 2 (300+23)*(43-21)/(84+7) Stack: ( + Output: 300

Example 2 (300+23)*(43-21)/(84+7) Stack: ( + Output: 300 23

Example 2 (300+23)*(43-21)/(84+7) Stack: ( Output: 300 23 +

Example 2 (300+23)*(43-21)/(84+7) Stack: Output: 300 23 +

Example 2 (300+23)*(43-21)/(84+7) Stack: * Output: 300 23 +

Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output: 300 23 +

Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output: 300 23 + 43

Example 2 (300+23)*(43-21)/(84+7) Stack: * ( - Output: 300 23 + 43

Example 2 (300+23)*(43-21)/(84+7) Stack: * ( - Output: 300 23 + 43 21

Example 2 (300+23)*(43-21)/(84+7) Stack: * ( Output: 300 23 + 43 21 -

Example 2 (300+23)*(43-21)/(84+7) Stack: * Output: 300 23 + 43 21 -

Example 2 (300+23)*(43-21)/(84+7) Stack: Output: 300 23 + 43 21 - *

Example 2 (300+23)*(43-21)/(84+7) Stack: / Output: 300 23 + 43 21 - *

Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: 300 23 + 43 21 - *

Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: 300 23 + 43 21 - * 84

Example 2 (300+23)*(43-21)/(84+7) Stack: / ( + Output: 300 23 + 43 21 - * 84

Example 2 (300+23)*(43-21)/(84+7) Stack: / ( + Output: 300 23 + 43 21 - * 84 7

Example 2 (300+23)*(43-21)/(84+7) Stack: / ( Output: 300 23 + 43 21 - * 84 7 +

Example 2 (300+23)*(43-21)/(84+7) Stack: / Output: 300 23 + 43 21 - * 84 7 +

Example 2 (300+23)*(43-21)/(84+7) Stack: Output: 300 23 + 43 21 - * 84 7 + / Done!

Example 3 (4+8)*(6-5)/((3-2)*(2+2))

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output:

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output:

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output: 4

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( + Output: 4

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( + Output: 4 8

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: ( Output: 4 8 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: 4 8 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * Output: 4 8 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output: 4 8 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output: 4 8 + 6

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( - Output: 4 8 + 6

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( - Output: 4 8 + 6 5

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * ( Output: 4 8 + 6 5 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: * Output: 4 8 + 6 5 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: 4 8 + 6 5 - *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / Output: 4 8 + 6 5 - *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: 4 8 + 6 5 - *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: 4 8 + 6 5 - *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: 4 8 + 6 5 - * 3

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( - Output: 4 8 + 6 5 - * 3

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( - Output: 4 8 + 6 5 - * 3 2

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( ( Output: 4 8 + 6 5 - * 3 2 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: 4 8 + 6 5 - * 3 2 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * Output: 4 8 + 6 5 - * 3 2 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: 4 8 + 6 5 - * 3 2 -

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: 4 8 + 6 5 - * 3 2-2

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( + Output: 4 8 + 6 5 - * 3 2-2

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( + Output: 4 8 + 6 5 - * 3 2 2 2

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * ( Output: 4 8 + 6 5 - * 3 2 2 2 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( * Output: 4 8 + 6 5 - * 3 2 2 2 +

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / ( Output: 4 8 + 6 5 - * 3 2 2 2 + *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: / Output: 4 8 + 6 5 - * 3 2 2 2 + *

Example 3 (4+8)*(6-5)/((3-2)*(2+2)) Stack: Output: 4 8 + 6 5 - * 3 2 2 2 + * / Done!