Conversion of Infix to Postfix Expression [ Manual Method ]

Conversion of an Expression : Infix to Postfix Manual Method
Question : Convert Following Expression Into Postfix ??

(A + B ^ C ) * D + E

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Step 1 :

• Expression Wrapped in Round Bracket Should be Evaluated Firstly.
• Again Bracket Contain Two Operators - Addition(+) and Raise to(^) .
• Out of these two '^' Operator has Higher Priority.
• So "B^C" should be Evaluated First

(A + B ^ C ) * D + E
= (A + B C ^ ) * D + E    [B^C Converted Into BC^]

• Now [ B C ^ ] is Converted Expression So Consider it as X

= (A + X ) * D + E    [X = BC^]

Step 2 :

• Evaluate A + X

(A + X ) * D + E
= (A X + ) * D + E    [A+X Converted Into AX+]

• Now [ A X + ] is Converted Expression So Consider it as Y

= Y * D + E    [Y = AX+]

Step 3 :

• Evaluate Y * D
  

Y * D + E
= Y D * + E    [Y*D Converted Into YD*]

• Now [Y D * ] is Converted Expression So Consider it as Z

= Z + E    [Z = YD*]

Step 4 :

• Evaluate Z + E
  

Z + E
= Z E +    [Z+E Converted Into ZE+]

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Final Postfix Expression :

= Z E +    
= Y D * E +          [Put Value of Z]
= A X + D * E +      [Put Value of Y]
= A B C ^ + D * E +  [Put Value of X] 

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Tags / Keywords : | algorithm postfix evaluation, infix, infix-postfix

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