Operand is the quantity (unit of data) on which a mathematical Saturday, April 18, Data Structure. 9. Infix. Postfix. Prefix. A+B. AB+. +AB. Content about infix prefix and post fix and their conversion using the certain algorithms in computer world. Table 4: Additional Examples of Infix, Prefix, and Postfix . In this case, a stack is again the data structure of choice. However, as you scan the postfix expression.

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Conversion of Infix expression to Postfix expression using Stack data structure

Pop and return it as the result of the expression. 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 anx the expression. This way any operator that is compared against it will have higher precedence and will be placed on top of it. This is the case with the addition and the multiplication in this example.

The top of the stack will always be the most recently saved operator. If we do the same thing but instead of moving the symbol to the position of the right parenthesis, we move it to the postfjx, we get prefix notation see Figure 7.

The only thing that can change that order is the presence of parentheses. Consider these three expressions again see Table 3. 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.

Infix, Postfix and Prefix

This means that the two most recent operands need to be used in a multiplication operation. When that right parenthesis does appear, the operator can be popped from the stack. Next token in the given infix expression is a close posgfix, 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.


Postfid the token is a right parenthesis, pop the opstack until the corresponding left parenthesis is removed.

Infix, Postfix and Prefix

As we processed the whole infix expression, now the operator stack has to be cleared by popping out each remaining operator and adding them to the expression string. Data Structure – Expression Parsing Advertisements. Where did the parentheses go? If the addition operator were also moved to its corresponding right parenthesis position and the matching left parenthesis were removed, the complete postfix expression would result see Figure 6.

The expression seems ambiguous. On structurea observation, however, you can see that each parenthesis pair also denotes the beginning and the end of an operand pair with the corresponding operator in the middle. What would happen if we moved the operator before the two operands? When we see a left parenthesis, we will save it to denote that another operator of high precedence will be coming. Prefix structurez notation requires that all operators precede the two operands that they work on.

The position of the parenthesis pair is actually a clue to structudes final position of the enclosed operator.

In this notation, operator is prefix ed to operands, i. Moving Operators to the Right for Postfix Notation.

By popping the stack twice, posffix can get the proper operands and then perform the multiplication in this case getting the result If the token is a right parenthesis, pop the opstack until the corresponding left parenthesis is removed.

When the final operator is processed, there will be only one value left on the stack. The order of the operators in the original expression dwta reversed in the resulting postfix expression. It is only the operators that change position. If two operators of equal precedence appear, then a left-to-right ordering or associativity is used.


The multiplication can be done to that result and the remaining operand C. There are two other very important expression formats that may not seem obvious to you at first. Operators of higher precedence are used before operators of lower precedence.

To evaluate expressions manually infix notation is helpful as it is easily understandable by the human brain. Next is an open parenthesis, so add it to the stack. Likewise, we could move the operator to the end. Only infix notation requires the additional symbols. Line 15 defines the operands to be any upper-case character or digit.

Table 4 shows some additional examples of infix expressions and the equivalent prefix and postfix expressions. Although all this may be obvious to you, remember that computers need to know exactly what operators to perform and in what order.

The order of operations within prefix and postfix expressions is completely determined by the position of the operator and nothing else. When the input expression has been completely processed, check the opstack.

There are two things to note in this example. A B Operator Stack: Recall that the operands in the postfix expression are in their original order since postfix changes only the placement of operators. Then move the enclosed operator to the position of either the left or the right parenthesis depending on whether you want prefix or postfix notation. In order to code the algorithm in Python, we will use a dictionary called prec to hold the precedence values for the operators.

It is only the operators that change position. Any operators still on the stack can be removed and appended to the end of the output list.