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.

Examples: 

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 the end of Prefix expression.
• At the end stack will have only 1 string i.e resultant string

Implementation:

// C++ 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 '*':
  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.top();   s.pop();
      string op2 = s.top();   s.pop();

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

      // Push string temp back to stack
      s.push(temp);
    }

    // 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
  return s.top();
}

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

// Java program to convert prefix to Infix 
import java.util.Stack;

class GFG{

// Function to check if character
// is operator or not     
static    boolean isOperator(char x) 
{
    switch(x)
    {
        case '+':
        case '-':
        case '*':
        case '/':
        case '^':
        case '%':
            return true;
    }
    return false;
}

// Convert prefix to Infix expression 
public static String convert(String str)
{
    Stack<String> stack = new Stack<>();
    
    // Length of expression 
    int l = str.length();
    
    // Reading from right to left 
    for(int i = l - 1; i >= 0; i--)
    {
        char c = str.charAt(i);
        if (isOperator(c))
        {
            String op1 = stack.pop();
            String op2 = stack.pop();
            
            // Concat the operands and operator 
            String temp = "(" + op1 + c + op2 + ")";
            stack.push(temp);
        } 
        else
        {
            
            // To make character to string
            stack.push(c + ""); 
        }
    }
    return stack.pop();
}

// Driver code
public static void main(String[] args)
{
    String exp = "*-A/BC-/AKL";
    System.out.println("Infix : " + convert(exp));
}
}

// This code is contributed by abbeyme

# Python Program to convert prefix to Infix
def prefixToInfix(prefix):
    stack = []
    
    # read prefix in reverse order
    i = len(prefix) - 1
    while i >= 0:
        if not isOperator(prefix[i]):
            
            # symbol is operand
            stack.append(prefix[i])
            i -= 1
        else:
          
            # symbol is operator
            str = "(" + stack.pop() + prefix[i] + stack.pop() + ")"
            stack.append(str)
            i -= 1
    
    return stack.pop()

def isOperator(c):
    if c == "*" or c == "+" or c == "-" or c == "/" or c == "^" or c == "(" or c == ")":
        return True
    else:
        return False

# Driver code
if __name__=="__main__":
    str = "*-A/BC-/AKL"
    print(prefixToInfix(str))
    
# This code is contributed by avishekarora

// C# program to convert prefix to Infix 
using System;
using System.Collections;

class GFG{
 
// Function to check if character
// is operator or not     
static bool isOperator(char x) 
{
    switch(x)
    {
        case '+':
        case '-':
        case '*':
        case '/':
        case '^':
        case '%':
            return true;
    }
    return false;
}
 
// Convert prefix to Infix expression 
public static string convert(string str)
{
    Stack stack = new Stack();
     
    // Length of expression 
    int l = str.Length;
     
    // Reading from right to left 
    for(int i = l - 1; i >= 0; i--)
    {
        char c = str[i];
        
        if (isOperator(c))
        {
            string op1 = (string)stack.Pop();
            string op2 = (string)stack.Pop();
             
            // Concat the operands and operator 
            string temp = "(" + op1 + c + op2 + ")";
            stack.Push(temp);
        } 
        else
        {
            
            // To make character to string
            stack.Push(c + ""); 
        }
    }
    return (string)stack.Pop();
}
 
// Driver code
public static void Main(string[] args)
{
    string exp = "*-A/BC-/AKL";
    
    Console.Write("Infix : " + convert(exp));
}
}

// This code is contributed by rutvik_56

// Javascript program to convert prefix to Infix

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

// Convert prefix to Infix expression
function convert(str) {
    let stack = [];

    // Length of expression
    let l = str.length;

    // Reading from right to left
    for (let i = l - 1; i >= 0; i--) {
        let c = str[i];

        if (isOperator(c)) {
            let op1 = stack[stack.length - 1];
            stack.pop();
            let op2 = stack[stack.length - 1];
            stack.pop();

            // Concat the operands and operator
            let temp = "(" + op1 + c + op2 + ")";
            stack.push(temp);
        } else {
            // To make character to string
            stack.push(c + "");
        }
    }
    return stack[stack.length - 1];
}

let exp = "*-A/BC-/AKL";
console.log("Infix : " + convert(exp));

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

Time Complexity: O(n)
Auxiliary Space: O(n)