convert the infix to postfix for A-(B+C)*(D/E)
Answers
Answer:
The Postfix Expression for the given Infix Expression A-(B+C)*(D/E) is ABC+DE/*-
Explanation:
- The given Infix is : A-(B+C)*(D/E)
- Conversion of Infix expression to Postfix expression:
Symbol Postfix string Stack
A A
- A -
( A -(
B AB -(
+ AB -(+
C ABC -(+
) ABC+ -
* ABC+ -*
( ABC+ -*(
D ABC+D -*(
/ ABC+D -*(/
E ABC+DE -*(/
) ABC+DE/
ABC+DE/*-
So, the Postfix Expression for the given Infix Expression is ABC+DE/*-
- Algorithm to convert Infix to Postfix
Step 1 : Scan the given Infix Expression from left to right.
Step 2 : If the scanned character is an operand, put it to Postfix string.
Step 3 : Else,
Step 3.1 : If the precedence order of the scanned operator is greater
than the precedence order of the operator in the stack or the stack is
empty or the stack contains a ‘(‘ or ‘[‘ or ‘{‘, push the operator on
stack.
Step 3.2 : Else, Pop all the operators from the stack which are
greater than or equal to in precedence than that of the scanned
operator and then Push the scanned operator to the stack. If
there is a parenthesis while popping then stop there and push
the scanned operator in the stack.
Step 4 : If the scanned character is an ‘(‘ or ‘[‘ or ‘{‘, push it to the stack.
Step 5 : If the scanned character is an ‘)’or ‘]’ or ‘}’, pop from the stack
and add it to the Postfix string until a ‘(‘ or ‘[‘ or ‘{‘ respectively is
encountered, and then discard both the parenthesis.
Step 6 : Repeat steps 2-6 until infix expression is scanned completely.
Step 7 : Print the Postfix string
Step 8 : Pop and add to the Postfix string from the stack until it is not
empty.
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