We write expression in infix notation, e.g. a – b + c, where operators are used Instead, these infix notations are first converted into either postfix or prefix. Infix -> Postfix & Prefix. This is a simple infix to prefix or postfix Converter. Enter the Infix expression below in box and press Convert. Type the Expression below . Algorithm of Infix to Prefix Step 1. Push “)” onto STACK Prefix Infix Postfix converter Tool Online Infix to prefix implementation in c: without Pointer. # include.

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Converting Infix Expressions to Postfix Expressions connversion. Create an empty list for output. Each operator has a precedence level.

In this case, the next symbol is another operand. So, as before, push it and check the next symbol. This type of expression uses one pair of parentheses for each operator.

To begin conversion of Infix to Postfix expression, first, we should know about operator precedence. Moving Operators to the Right for Postfix Notation.

Scan the token list from left to right. Append each operator to the end of the output list. As you scan the expression from left to right, you first encounter the operands 4 and 5.

Infix to postfix conversion algorithm

Also, the order of these saved operators may need to be reversed due to their precedence. As you scan the expression from left to right, you first encounter the operands 4 and 5. The given expression has parentheses to denote the precedence.


If the token is a left parenthesis, push it on the opstack. No parentheses should remain.

These notations are named as how they use operator in ;refix. Moving Operators to the Left for Prefix Notation. Then test the incoming operator against the new top of stack. Problem Solving with Algorithms and Data Structures. The complete function for the evaluation of postfix expressions is shown in ActiveCode 2.

Infix, Postfix and Prefix

To do this we will look closer at the conversion process. Line 15 defines the operands to be any upper-case character or digit. Another way to think about the solution is that whenever an operator is seen on the input, the two most recent operands will be used in the evaluation.

The above table shows the default behavior of operators.

So in order to convert an expression, no matter how complex, to either prefix or postfix notation, fully parenthesize the expression using the order of operations. When that right parenthesis does appear, the operator can be popped from the stack. Next token in the given infix expression is a close parenthesis, as we encountered a close parenthesis we should pop the expressions from the stack and add it to the expression string until an open parenthesis popped from the stack.

Then a close parenthesis, as we saw earlier, we should not push it to the stack instead we should pop all the operators from the stack and add it to the expression string until we encounter an open parenthesis. These changes to the position of the operator with respect to the operands create two new expression formats, prefix and postfix. To reduce the complexity of expression evaluation Prefix or Postfix expressions are used in the computer programs.


There are more complicated rules to handle operators and parentheses. This is the case with the addition and the multiplication in this example. This dictionary will map each operator to an integer that can be compared against the precedence levels of other operators we have arbitrarily used the integers 3, 2, and 1.

Only infix notation requires the additional symbols. In Postfix expressions, operators come after the operands. The rule for line 2 is to push an operator onto the stack if it is empty. Runestone in social media: Operators of higher precedence are used before operators of lower precedence. This type of notation is referred to as infix since the operator is in between the two operands that it is working on.

This way any operator that is compared against it will have higher precedence and will be placed on top of it. A table of operator precedence is provided later. This will provide the reversal that we noted in the first example. As per the precedence, the operators will be pushed to the stack.

At this point, you are still unsure what to do with them until you see the next symbol.