Infix to Prefix Converter Online – Step by Step Evaluation

How to Convert Infix to Prefix Expression Step by Step

An infix expression is the standard arithmetic format where operators sit between operands (e.g., A + B). A prefix expression (also called Polish Notation) places the operator before its operands (e.g., + A B). Converting infix to prefix is a fundamental data structures concept used in compilers, interpreters, and expression evaluation engines.

Our free infix to prefix converter online tool above handles the conversion automatically and shows every intermediate step — the reversed string, the intermediate postfix form, and the final prefix result.

Understanding the Infix to Prefix Conversion Algorithm

Before diving into the conversion process, it’s essential to understand the three notations:

1. Infix Notation: The operator is placed between operands — A + B.
2. Prefix Notation: The operator precedes operands — + A B.
3. Postfix Notation: The operator follows operands — A B +.

Step-by-Step Infix to Prefix Conversion Method

1. Reverse the Infix Expression: Reverse the string and swap ( with ) and vice versa.
2. Convert to Postfix: Apply the Shunting Yard algorithm to the reversed expression (using slightly modified precedence rules for right-to-left scanning).
3. Reverse the Postfix: Reverse the resulting postfix string to get the final prefix expression.

Example: Convert (A + B) * C to Prefix

1. Reverse: C * )B + A( → with swapped parentheses: C * (B + A)
2. Convert to Postfix: C B A + *
3. Reverse Postfix: * + A B C ← This is the prefix result!

Why Convert Infix to Prefix?

Converting infix to prefix can simplify the evaluation of expressions in programming languages, compilers, and calculators. Prefix notation allows for easier parsing and evaluation of expressions without the need for operator precedence rules or parentheses. It’s particularly valuable in functional programming languages like LISP where prefix notation is the native syntax.

Infix to Prefix Conversion Code Examples

Python Implementation

def precedence(op):
    if op in ('+', '-'): return 1
    if op in ('*', '/'): return 2
    if op == '^': return 3
    return 0

def infix_to_postfix_for_prefix(expr):
    stack, output = [], []
    for ch in expr:
        if ch.isalnum():
            output.append(ch)
        elif ch == '(':
            stack.append(ch)
        elif ch == ')':
            while stack and stack[-1] != '(':
                output.append(stack.pop())
            stack.pop()
        else:
            while stack and stack[-1] != '(' and precedence(ch) < precedence(stack[-1]):
                output.append(stack.pop())
            stack.append(ch)
    while stack:
        output.append(stack.pop())
    return ''.join(output)

def infix_to_prefix(expression):
    # Step 1: Reverse and swap parentheses
    reversed_expr = ''
    for ch in reversed(expression):
        if ch == '(': reversed_expr += ')'
        elif ch == ')': reversed_expr += '('
        else: reversed_expr += ch
    # Step 2: Get postfix of reversed
    postfix = infix_to_postfix_for_prefix(reversed_expr)
    # Step 3: Reverse postfix = prefix
    return postfix[::-1]

print(infix_to_prefix("(A+B)*C"))  # Output: *+ABC

Conclusion

The infix to prefix conversion is an essential concept in data structures and algorithms. Whether you use our free infix to prefix converter online, implement it in Python, C, or Java, or learn the step-by-step process manually, mastering this conversion will strengthen your understanding of expression evaluation, stack data structures, and compiler design.