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Data Structures and Algorithms V22.0102 Otávio Braga

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Page 1: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Data Structures and AlgorithmsV22.0102

Otávio Braga

Page 2: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix Conversion

• 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

Page 3: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

Page 4: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack:

• Output:

Page 5: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack:

• Output: 3

Page 6: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: +

• Output: 3

Page 7: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: +

• Output: 3 4

Page 8: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: + *

• Output: 3 4

Page 9: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: + *

• Output: 3 4 5

Page 10: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: +

• Output: 3 4 5 *

Page 11: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: + /

• Output: 3 4 5 *

Page 12: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: + /

• Output: 3 4 5 * 6

Page 13: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack: +

• Output: 3 4 5 * 6 /

Page 14: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 1

• 3+4*5/6

• Stack:

• Output: 3 4 5 * 6 / +

• Done!

Page 15: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

Page 16: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack:

• Output:

Page 17: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: (

• Output:

Page 18: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: (

• Output: 300

Page 19: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: ( +

• Output: 300

Page 20: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: ( +

• Output: 300 23

Page 21: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: (

• Output: 300 23 +

Page 22: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack:

• Output: 300 23 +

Page 23: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: *

• Output: 300 23 +

Page 24: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

• Output: 300 23 +

Page 25: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

• Output: 300 23 + 43

Page 26: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: * ( -

• Output: 300 23 + 43

Page 27: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: * ( -

• Output: 300 23 + 43 21

Page 28: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

• Output: 300 23 + 43 21 -

Page 29: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: *

• Output: 300 23 + 43 21 -

Page 30: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack:

• Output: 300 23 + 43 21 - *

Page 31: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: /

• Output: 300 23 + 43 21 - *

Page 32: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - *

Page 33: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - * 84

Page 34: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: / ( +

• Output: 300 23 + 43 21 - * 84

Page 35: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: / ( +

• Output: 300 23 + 43 21 - * 84 7

Page 36: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - * 84 7 +

Page 37: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack: /

• Output: 300 23 + 43 21 - * 84 7 +

Page 38: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 2

• (300+23)*(43-21)/(84+7)

• Stack:

• Output: 300 23 + 43 21 - * 84 7 + /

• Done!

Page 39: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

Page 40: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output:

Page 41: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: (

• Output:

Page 42: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: (

• Output: 4

Page 43: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: ( +

• Output: 4

Page 44: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: ( +

• Output: 4 8

Page 45: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: (

• Output: 4 8 +

Page 46: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output: 4 8 +

Page 47: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: *

• Output: 4 8 +

Page 48: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 +

Page 49: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 + 6

Page 50: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * ( -

• Output: 4 8 + 6

Page 51: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * ( -

• Output: 4 8 + 6 5

Page 52: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 + 6 5 -

Page 53: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: *

• Output: 4 8 + 6 5 -

Page 54: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output: 4 8 + 6 5 - *

Page 55: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: /

• Output: 4 8 + 6 5 - *

Page 56: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - *

Page 57: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - *

Page 58: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - * 3

Page 59: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( ( -

• Output: 4 8 + 6 5 - * 3

Page 60: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( ( -

• Output: 4 8 + 6 5 - * 3 2

Page 61: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - * 3 2 -

Page 62: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - * 3 2 -

Page 63: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( *

• Output: 4 8 + 6 5 - * 3 2 -

Page 64: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 -

Page 65: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 - 2

Page 66: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * ( +

• Output: 4 8 + 6 5 - * 3 2 - 2

Page 67: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * ( +

• Output: 4 8 + 6 5 - * 3 2 – 2 2

Page 68: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 – 2 2 +

Page 69: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( *

• Output: 4 8 + 6 5 - * 3 2 – 2 2 +

Page 70: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - * 3 2 – 2 2 + *

Page 71: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: /

• Output: 4 8 + 6 5 - * 3 2 – 2 2 + *

Page 72: Data Structures and AlgorithmsInfix to Postfix Conversion •We use a stack •When an operand is read, output it •When an operator is read –Pop until the top of the stack has

Infix to Postfix ConversionExample 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output: 4 8 + 6 5 - * 3 2 – 2 2 + * /

• Done!


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MAPware-7000 Ladder Logic Guide - Prime Controls Co ...€¦ · Multiplexer A particular register in a range of registers (Operand A) is read and copied to a target register (Operand