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Postfix Evaluation

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Description

Postfix:

Similarly, the expression in which the operator appears after the operands is known as postfix expression. For example, ab+, where a and b are operands, + is an operator that appears after the operands a and b.

 

Example: 456*+

 

 

Algorithm of Postfix Evaluation:

Step1: Add a ")" at the end of the postfix expression.

Step2: Scan every character of the postfix expression and repeat.

Step 3 and 4 until ")" is encountered.

Step 3: If an operand is encountered, then

        a. Pop the top elements from the stack as A and B as A and B.

        b. Evaluate B 0 A, where A is the topmost element below A.

        c. Push the result of the evaluation on the stack.

        [END OF IF]

Step 4: SET RESULT equal to the topmost element of the stack.

Step 5: EXIT.

Code

TIME COMPLEXITY:

In postfix evaluation, we have to scan n symbols

So, the Time complexity of postfix evaluation is O(n)

 

SPACE COMPLEXITY:

We require n stack to evaluate postfix to infix. So, space complexity is O(n)