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Data Structures and Algorithms

V22.0102

Otávio Braga

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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

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack:

•

Output:

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack:

•

Output: 3

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: +

•

Output: 3

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: +

•

Output: 3 4

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: + *

•

Output: 3 4

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: + *

•

Output: 3 4 5

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: +

•

Output: 3 4 5 *

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: + /

•

Output: 3 4 5 *

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: + /

•

Output: 3 4 5 * 6

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack: +

•

Output: 3 4 5 * 6 /

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Infix to Postfix Conversion

Example 1

• 3+4*5/6

• Stack:

•

Output: 3 4 5 * 6 / +

• Done!

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack:

•

Output:

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: (

•

Output:

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: (

•

Output: 300

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: ( +

•

Output: 300

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: ( +

•

Output: 300 23

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: (

•

Output: 300 23 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack:

•

Output: 300 23 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: *

•

Output: 300 23 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

•

Output: 300 23 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

•

Output: 300 23 + 43

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: * ( -

•

Output: 300 23 + 43

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: * ( -

•

Output: 300 23 + 43 21

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: * (

•

Output: 300 23 + 43 21 -

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: *

•

Output: 300 23 + 43 21 -

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack:

•

Output: 300 23 + 43 21 - *

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: /

•

Output: 300 23 + 43 21 - *

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - *

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - * 84

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: / ( +

• Output: 300 23 + 43 21 - * 84

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: / ( +

• Output: 300 23 + 43 21 - * 84 7

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: / (

• Output: 300 23 + 43 21 - * 84 7 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack: /

• Output: 300 23 + 43 21 - * 84 7 +

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7)

• Stack:

• Output: 300 23 + 43 21 - * 84 7 + /

• Done!

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output:

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: (

• Output: 4

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: ( +

• Output: 4

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: ( +

• Output: 4 8

f f

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: (

• Output: 4 8 +

f f

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output: 4 8 +

fi fi i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: *

• Output: 4 8 +

I fi P fi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 +

I fi P fi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 + 6

I fi P fi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * ( -

• Output: 4 8 + 6

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * ( -

• Output: 4 8 + 6 5

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: * (

• Output: 4 8 + 6 5 -

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: *

• Output: 4 8 + 6 5 -

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

• Output: 4 8 + 6 5 - *

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: /

• Output: 4 8 + 6 5 - *

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - *

I fi t P tfi C i

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - *

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - * 3

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( ( -

• Output: 4 8 + 6 5 - * 3

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( ( -

• Output: 4 8 + 6 5 - * 3 2

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( (

• Output: 4 8 + 6 5 - * 3 2 -

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - * 3 2 -

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( *

• Output: 4 8 + 6 5 - * 3 2 -

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 -

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 - 2

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * ( +

• Output: 4 8 + 6 5 - * 3 2 - 2

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * ( +

• Output: 4 8 + 6 5 - * 3 2 – 2 2

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / ( * (

• Output: 4 8 + 6 5 - * 3 2 – 2 2 +

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Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: / (

• Output: 4 8 + 6 5 - * 3 2 – 2 2 + *

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack: /

• Output: 4 8 + 6 5 - * 3 2 – 2 2 + *

Infix to Postfix Conversion

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Infix to Postfix Conversion

Example 3

• (4+8)*(6-5)/((3-2)*(2+2))

• Stack:

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

• Done!