Evaluating Postfix - Data Stuctures - Lecture Slides, Slides of Data Structures and Algorithms

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Infix to Postfix

Infix Postfix

A + B A B +

(A + B)*(C – D ) A B + C D – *

A ↑ B * C – D + E/F A B ↑ C*D – E F/+

Infix to Postfix

 Note that the postfix form an expression

does not require parenthesis.

 Consider ‘4+35’ and ‘(4+3)5’. The

parenthesis are not needed in the first but

they are necessary in the second.

 The postfix forms are:

Stack s;

while( not end of input ) {

e = get next element of input

if( e is an operand )

s.push( e );

else {

op2 = s.pop();

op1 = s.pop();

value = result of applying operator ‘e’ to op1 and op2;

s.push( value );

finalresult = s.pop();

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

• 2 3 5 6,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

• 2 3 5 6,

• 6 5 1 1 3 6 5 1 1,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

• 2 3 5 6,

• 6 5 1 1 3 6 5 1 1, 8 6 5 1 1,3,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

• 2 3 5 6,

• 6 5 1 1 3 6 5 1 1, 8 6 5 1 1,3, 2 6 5 1 1,3,8, / 8 2 4 1,3,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack 6 6 2 6, 3 6,2,

• 2 3 5 6,

• 6 5 1 1 3 6 5 1 1, 8 6 5 1 1,3, 2 6 5 1 1,3,8, / 8 2 4 1,3,

• 3 4 7 1,

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack

Evaluate 6 2 3 + - 3 8 2 / + * 2 ↑ 3 +

Input op1 op2 value stack

• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 1 7 7 7,
• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 1 7 7 7,
• ↑
• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 1 7 7 7,
• ↑
• 3 7 2 49 49,
• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 1 7 7 7,
• ↑
• 3 7 2 49 49,
• 2 6,
• 3 6,2,
• • 2 3 5 6,
• 3 6 5 1 1,
• 8 6 5 1 1,3,
• 2 6 5 1 1,3,8,
• / 8 2 4 1,3,
• • 3 4 7 1,
• 2 1 7 7 7,
• ↑
• 3 7 2 49 49,