Prefix to Infix Conversion

Infix : An expression is called the Infix expression if the operator appears in between the operands in the expression. Simply of the form (operand1 operator operand2).
Example : (A+B) * (C-D)

Prefix : An expression is called the prefix expression if the operator appears in the expression before the operands. Simply of the form (operator operand1 operand2).
Example : *+AB-CD (Infix : (A+B) * (C-D) )

Given a Prefix expression, convert it into a Infix expression.
Computers usually does the computation in either prefix or postfix (usually postfix). But for humans, its easier to understand an Infix expression rather than a prefix. Hence conversion is need for human understanding.


Input :  Prefix :  *+AB-CD
Output : Infix : ((A+B)*(C-D))

Input :  Prefix :  *-A/BC-/AKL
Output : Infix : ((A-(B/C))*((A/K)-L)) 

Algorithm for Prefix to Infix:

  • Read the Prefix expression in reverse order (from right to left)
  • If the symbol is an operand, then push it onto the Stack
  • If the symbol is an operator, then pop two operands from the Stack
    Create a string by concatenating the two operands and the operator between them.
    string = (operand1 + operator + operand2)
    And push the resultant string back to Stack
  • Repeat the above steps until end of Prefix expression.
// CPP Program to convert prefix to Infix
#include <iostream>
#include <stack>
using namespace std;

// function to check if character is operator or not
bool isOperator(char x) {
  switch (x) {
  case '+':
  case '-':
  case '/':
  case '*':
    return true;
  return false;

// Convert prefix to Infix expression
string preToInfix(string pre_exp) {
  stack<string> s;

  // length of expression
  int length = pre_exp.size();

  // reading from right to left
  for (int i = length - 1; i >= 0; i--) {

    // check if symbol is operator
    if (isOperator(pre_exp[i])) {

      // pop two operands from stack
      string op1 =;   s.pop();
      string op2 =;   s.pop();

      // concat the operands and operator
      string temp = "(" + op1 + pre_exp[i] + op2 + ")";

      // Push string temp back to stack

    // if symbol is an operand
    else {

      // push the operand to the stack
      s.push(string(1, pre_exp[i]));

  // Stack now contains the Infix expression

// Driver Code
int main() {
  string pre_exp = "*-A/BC-/AKL";
  cout << "Infix : " << preToInfix(pre_exp);
  return 0;

Infix : ((A-(B/C))*((A/K)-L))

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