Prefix to Infix Converter Online – Step by Step Evaluation

How to Convert Prefix to Infix Expression Using a Stack

A prefix expression (also called Polish Notation) places operators before their operands. For example, + A B means A + B in standard infix notation. Understanding how to convert between these notations is essential for compiler design, expression evaluation, and data structures coursework.

Our free prefix to infix converter online tool above instantly transforms any valid prefix expression into its equivalent infix form, with a complete step-by-step stack trace showing every push and pop operation.

Prefix to Infix Conversion Algorithm

The algorithm scans the prefix expression from right to left and uses a stack:

1. Initialize an empty stack.
2. Read the prefix expression from right to left.
3. For each symbol: ◦ If the symbol is an operand, push it onto the stack. ◦ If the symbol is an operator: pop two elements (a then b), form the infix string (a operator b), and push it back onto the stack.
4. The final element left in the stack is the complete infix expression.

Prefix to Infix Example: * + A B C

Let’s trace through the conversion of prefix *+ABC:

1. Read C (right to left, operand) → push. Stack: [C]
2. Read B (operand) → push. Stack: [C, B]
3. Read A (operand) → push. Stack: [C, B, A]
4. Read + (operator) → pop A and B, form (A+B), push. Stack: [C, (A+B)]
5. Read * (operator) → pop (A+B) and C, form ((A+B)*C), push. Stack: [((A+B)*C)]

Result: ((A+B)*C)

Why Convert Prefix to Infix?

Converting from prefix to infix is crucial for various applications including compilers, interpreters, and expression evaluation in programming languages. It helps produce human-readable expressions from machine-optimized formats. Understanding this conversion also builds a deeper comprehension of syntax trees and recursive descent parsing.

Prefix to Infix Conversion Code in C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

#define MAX 100

char stack[MAX][MAX];
int top = -1;

void push(char *item) {
    if (top >= MAX - 1) {
        printf("Stack Overflow\n");
        return;
    }
    strcpy(stack[++top], item);
}

char* pop() {
    if (top < 0) {
        printf("Stack Underflow\n");
        return NULL;
    }
    return stack[top--];
}

int isOperator(char ch) {
    return (ch == '+' || ch == '-' || ch == '*' || ch == '/');
}

void prefixToInfix(char *prefix) {
    int len = strlen(prefix);
    char operand1[MAX], operand2[MAX], temp[MAX];
    
    // Scan right to left
    for (int i = len - 1; i >= 0; i--) {
        if (isalnum(prefix[i])) {
            char str[2] = {prefix[i], '\0'};
            push(str);
        } else if (isOperator(prefix[i])) {
            strcpy(operand1, pop());
            strcpy(operand2, pop());
            sprintf(temp, "(%s%c%s)", operand1, prefix[i], operand2);
            push(temp);
        }
    }
    printf("Infix Expression: %s\n", pop());
}

int main() {
    char prefix[] = "*+ABC";
    prefixToInfix(prefix);
    return 0;
}

Conclusion

The conversion of prefix to infix expressions is a vital skill in computer science, especially in the areas of compiler design and expression evaluation. Whether you choose to convert manually, use our free prefix to infix converter online tool, or implement the algorithm in C, Python, or Java, understanding the underlying stack-based algorithm empowers you to handle expression conversions efficiently. The tool above provides instant results with step-by-step visualization to make learning intuitive.