This short example makes the move from infix to postfix intuitive. However, as expressions get Simple heuristic algorithm to visually convert infix to postfix. Infix to Postfix Conversion. Procedure for Postfix Conversion. 1. Scan the Infix string from left to right. 2. Initialize an empty Conversion To Postfix. EXAMPLE. Examples of Infix-to-Postfix Conversion a+b*c-d/e*f postfix string a ab abc abc* abc*+ abc*+d abc*+de abc*+de/ abc*+de/f abc*+de/f* abc*+de/f*-. operator stack .

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Infix to Postfix Conversion

Notice that the postfix notation has been created to properly reflect operator precedence. B and C are multiplied first, and A is then added to that result. The arithmetic tto appears between two operands. The left parenthesis will receive the lowest value possible.

Add it to the expression string. Post fix notation also, known as reverse Polish notation eliminates the need for parentheses. As we scan the infix expression from left to right, we will use a stack to keep the operators.

Infix, Prefix and Postfix Expressions — Problem Solving with Algorithms and Data Structures

It is only the operators that change position. Scan the token list from left to right. The rule for line 4 is if the operator on the top of the stack has higher precedence than the one being read, pop and print the one on top and then push the new operator on. To begin conversion of Infix to Postfix expression, first, we should know about operator precedence.


Although the operators moved and now appear either before or after their respective operands, the order of the operands stayed exactly the same relative to one another. When the operands for the division are popped from the stack, they are reversed. If the association is left to right, pop and print the top of the stack and then push the incoming operator. Sign in Get started. If top Stack has higher precedence over the scanned character pop the stack else push the scanned character to stack.

Conversion of Infix expression to Postfix expression using Stack data structure

It uses a stack; but in this case, the stack is used to hold operators rather than numbers. Recall that the operands in the postfix expression are in their original order since postfix changes only the placement of operators.

What is the result of evaluating the following: If two operators of equal precedence appear, then a left-to-right ordering or associativity is used.

Thus, high priority corresponds to high number in the table. The precedence order for arithmetic operators places multiplication and division above addition and subtraction. Convert the input infix string to a list by using the string method split. The order in which the operators appear is not reversed. There are two things to note in this example.

We can now handle this result by placing it back on the stack so that it can be used as an operand for the later operators in the expression. Table 4 shows some additional examples of infix expressions and the equivalent prefix and postfix expressions. The first will show the symbol currently being read.


Then we have an operand, so add it to the expression string. The complete function for the evaluation of postfix expressions is shown in ActiveCode 2.

Repeat this step until the stack is not empty and top Stack has precedence over the character. Moving Operators to the Left for Prefix Notation.

As a final stack example, we will consider the evaluation of an expression that is already in postfix notation. This is the case with the addition and the multiplication in this example.

Infix to Postfix Conversion

The addition operator then appears before the A and the result of the ihfix. We need to develop an algorithm to convert any infix expression to a postfix expression.

Although all this may be obvious to you, remember that computers need to know exactly what operators to perform and in what order. The top operator in the table has the highest precedence.

Line 15 defines the operands to be any upper-case character or digit. If the token is a left parenthesis, push it on the opstack.

The second will show what is on the stack and the third will show the current contents of ezamples postfix string. To do this we will look closer at the conversion process.