Data Structures and Algorithms V Otávio Braga

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Data Structures and Algorithms

V22.0102

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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

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Example 1

• 3+4*5/6 • Stack: • Output:

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Example 1

• 3+4*5/6 • Stack:

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Example 1

• 3+4*5/6 • Stack: + • Output: 3

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Example 1

• 3+4*5/6 • Stack: +

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Example 1

• 3+4*5/6 • Stack: + * • Output: 3 4

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Example 1

• 3+4*5/6 • Stack: + *

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Example 1

• 3+4*5/6 • Stack: +

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Example 1

• 3+4*5/6 • Stack: + /

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Example 1

• 3+4*5/6 • Stack: + /

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Example 1

• 3+4*5/6 • Stack: +

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Example 1

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

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Example 2

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Example 2

• (300+23)*(43-21)/(84+7) • Stack:

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: ( +

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: ( +

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack:

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7) • Stack: *

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: * (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: * (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: * (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: * (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: * (

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-Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7) • Stack: *

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-Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7) • Stack:

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: /

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: / (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: / (

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: / ( +

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: / ( +

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Example 2

• (300+23)*(43-21)/(84+7) • Stack: / (

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Infix to Postfix Conversion

Example 2

• (300+23)*(43-21)/(84+7) • Stack: /

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Example 2

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

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Example 3

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Example 3

• (4+8)*(6-5)/((3-2)*(2+2)) • Stack:

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Example 3

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

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Example 3

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

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Example 3

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

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Example 3

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

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Example 3

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

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Example 3

• (4+8)*(6-5)/((3-2)*(2+2)) • Stack:

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Example 3

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

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Example 3

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

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Example 3

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

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Example 3

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

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Infix to Postfix Conversion

Example 3

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

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Example 3

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

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Example 3

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

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Example 3

• (4+8)*(6-5)/((3-2)*(2+2)) • Stack:

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Example 3

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

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Example 3

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

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Example 3