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

(A + B ^ C ) * D + E

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+]
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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