What are Prefix and Infix Expressions?

Before we dive into the conversion process, let’s clarify what prefix and infix expressions are:

• Prefix Expression: Also known as Polish notation, prefix notation requires operators to precede their operands. For example, the expression “+AB” represents the addition of operands A and B.
• Infix Expression: In infix notation, operators are placed between their operands. For instance, “A + B” is an infix expression where A and B are operands, and ‘+’ is the operator.

Conversion of prefix to infix in C++ using stack

Here is the key reasons of conversion of prefix to infix in C++ using stack is needed in Data Structures. Let’s break down the conversion process step by step:

• Start from the Right: In prefix notation, operators precede their operands. So, we start scanning the expression from right to left.
• Encounter Operators First: We encounter operators first in prefix notation. In this example, the operators are ‘*’ (multiplication) and ‘+’ (addition) followed by ‘-‘.
• Identify Operands: After encountering an operator, we identify the next two characters as operands. In this case, ‘A’ and ‘B’ are operands for the ‘+’ operator, and ‘C’ and ‘D’ are operands for the ‘-‘ operator.
• Combine Operands and Operator: For each operator, we combine the corresponding operands and the operator in infix notation. For example, for the ‘+’ operator, we form the expression “(A + B)” and for the ‘-‘ operator, we form “(C – D)”.
• Replace Original Expression: We replace the original expression with the infix expression formed in the previous step. So, “*+AB-CD” becomes “* (A + B) (C – D)”.
• Repeat Until Whole Expression is Converted: We continue this process until the entire expression is converted.
• Final Expression: After converting the whole expression, we get the final infix expression: “((A + B) * (C – D))”.

So, the prefix expression “*+AB-CD” is converted to the infix expression “((A + B) * (C – D))”.

Applications of prefix to infix

Here is the come applications of conversion of prefix to infix in C++ using stack

• Compiler Design: In compiler design, converting expressions between different notations is a common task. This conversion may occur during the parsing phase or as part of optimizations.
• Algorithm Design: Some algorithms, such as those used in symbolic computation or computer algebra systems, require manipulation of mathematical expressions. Converting prefix expressions to infix can be a part of such algorithms.
• Mathematical Software: Mathematical software often deals with complex expressions. Converting prefix expressions to infix can make the output more readable and understandable for users.

Source Code of prefix to infix C++ using stack

here’s an implementation of conversion of prefix to infix in C++ using stack data structure:

#include <iostream>
#include <stack>
#include <string>

using namespace std;

bool isOperator(char c) {
    return (c == '+' || c == '-' || c == '*' || c == '/');
}

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

    for (int i = prefix.length() - 1; i >= 0; i--) {
        if (isOperator(prefix[i])) {
            string operand1 = st.top();
            st.pop();
            string operand2 = st.top();
            st.pop();
            string result = "(" + operand1 + prefix[i] + operand2 + ")";
            st.push(result);
        }
        else {
            string operand(1, prefix[i]);
            st.push(operand);
        }
    }

    return st.top();
}

int main() {
    string prefixExpression;
    cout << "Enter prefix expression: ";
    cin >> prefixExpression;

    string infixExpression = prefixToInfix(prefixExpression);
    cout << endl;
    cout << "Infix expression: " << infixExpression << endl;

    return 0;
}

Conclusion

conversion of prefix to infix in C++ using stack can be useful in various applications, such as expression evaluation and syntax parsing. By understanding the conversion algorithm and implementing it in C++, you can manipulate arithmetic expressions in different notations effectively.