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# Conversion of Prefix to Postfix notation

Last Updated on April 25, 2023 by Prepbytes We have been given an arithmetic expression, and we have to write a program that converts prefix to postfix. The expression is given in the form of a string that contains alphabets i.e a-z or A-Z denotes operands and operators are ( +, –, *, / ). In short, we have to program a prefix to postfix converter.

Here are some examples, that will give you a clear understanding of what is exactly meant by prefix to postfix conversion.

Example 1:

Example 2:

Input: ab Output: ab

Before discussing the solution of the prefix to postfix. Let us first discuss arithmetic notations in brief.

### Introduction to Arithmetic Notations

Any arithmetic expression consists of operands and operators . The way we arrange our operators and operands to write the arithmetic expression is called Notation .

There are three different notations for writing the Arithmetic expression :

• Infix Expression An expression is said to be in infix notation if the operators in the expression are placed in between the operands on which the operator works. For Example,

``a + b * c``

Infix expressions are easy to read ,write and understand by humans , but not by computer. It’s costly , in terms of time and space , to process Infix expressions

• Postfix Expression (Reverse Polish Notation) An expression is said to be in postfix notation if the operators in the expression are placed after the operands on which the operator works. For Example,

``abc*+``

It’s the most used notation for evaluating arithmetic expressions

• Prefix Expression (or Polish Notation ) An expression is said to be in prefix notation if the operators in the expression are placed before the operands on which the operator works. For Example,

``+a*bc``

### Precedence Order and Associativity of Operators

The precedence order of operators is given in the below table.

In this article, we are going to see how we can convert prefix to postfix expressions. For simplicity and understanding purposes, we will consider only ‘+’, ‘-’, ’/’, ‘*’, ‘(’ and ‘)’.

### Prefix to Postfix Conversion

To convert a prefix to postfix expression, we will use a stack to hold the operands. Whenever an operator is found, we pop two operands from the stack and push a new operand. The final element at the top of the stack will be our postfix expression.

### Algorithm for Prefix to Postfix Converter

Here is the stepwise algorithm to convert prefix to postfix expressions.

• Step 1: Scan all symbols one by one from right to left in the given prefix expression.
• Step 2: If the reading symbol is an operand, push it into the stack.
• Step 3: If the reading symbol is an operator, then
• a. Pop two expressions from the stack, operand1, and operand2, which is the operand for the current operator
• b. Push operand1 + operand2 + operator into the stack
• Step 4: If there is no symbol left then stop the process. The top of the stack will have the required postfix expression.

NOTE : ‘+’ denotes the concatenation of strings .

### Dry Run for Prefix to Postfix Conversion ### Code Implementation of Prefix to Postfix Converter

Here is the code to perform prefix to postfix conversion in C++.

```#include <bits/stdc++.h>
using namespace std;

bool isOperand(char ch){
return (ch>='a' && ch<='z') || (ch>='A' && ch <='Z');
}

string prefixToPostfix(string prefix) {
stack<string> st;

int len = prefix.size();
for (int i = len - 1; i >= 0; i--) {
if(isOperand(prefix[i])){

st.push(string(1,prefix[i]));

}
else{
string operand1=st.top();
st.pop();

string operand2=st.top();
st.pop();

st.push( operand1 + operand2  + string(1,prefix[i]));
}
}
return st.top();
}

int main() {
string postfix=prefixToPostfix(prefix);
cout<<"Prefix expression : "<<prefix<<endl;
cout<<"Postfix expression : "<<postfix<<endl;

return 0;
}
```

Output:

``````Prefix expression : *-a/bc-/ade

Time Complexity: O(n), where n is the length of the input string in prefix notation

Space Complexity: O(n), since we are using a stack.

Conclusion In this article, we discussed the approach for prefix to postfix conversion. We have used a stack to code out prefix to postfix converter. Hope this blog helps you understand and solve the problem. To practice more problems you can check out MYCODE | Competitive Programming at PrepBytes.