Convert Infix To Prefix Notation

Last Updated : 27 Mar, 2023

Given an infix expression, the task is to convert it to a prefix expression.

Infix Expression: The expression of type a ‘operator’ b (a+b, where + is an operator) i.e., when the operator is between two operands.

Prefix Expression: The expression of type ‘operator’ a b (+ab where + is an operator) i.e., when the operator is placed before the operands.

Examples:

Input: A * B + C / D
Output: + * A B/ C D

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

How to convert infix expression to prefix expression?

To convert an infix expression to a prefix expression, we can use the stack data structure. The idea is as follows:

Step 1: Reverse the infix expression. Note while reversing each ‘(‘ will become ‘)’ and each ‘)’ becomes ‘(‘.

Step 2: Convert the reversed infix expression to “nearly” postfix expression.

While converting to postfix expression, instead of using pop operation to pop operators with greater than or equal precedence, here we will only pop the operators from stack that have greater precedence.

Step 3: Reverse the postfix expression.

The stack is used to convert infix expression to postfix form.

Illustration:

See the below image for a clear idea:

Convert infix expression to prefix expression

Below is the C++ implementation of the algorithm.

C++

// C++ program to convert infix to prefix
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if the character is an operator
bool isOperator(char c)
{
    return (!isalpha(c) && !isdigit(c));
}
 
// Function to get the priority of operators
int getPriority(char C)
{
    if (C == '-' || C == '+')
        return 1;
    else if (C == '*' || C == '/')
        return 2;
    else if (C == '^')
        return 3;
    return 0;
}
 
// Function to convert the infix expression to postfix
string infixToPostfix(string infix)
{
    infix = '(' + infix + ')';
    int l = infix.size();
    stack<char> char_stack;
    string output;
 
    for (int i = 0; i < l; i++) {
 
        // If the scanned character is an
        // operand, add it to output.
        if (isalpha(infix[i]) || isdigit(infix[i]))
            output += infix[i];
 
        // If the scanned character is an
        // ‘(‘, push it to the stack.
        else if (infix[i] == '(')
            char_stack.push('(');
 
        // If the scanned character is an
        // ‘)’, pop and output from the stack
        // until an ‘(‘ is encountered.
        else if (infix[i] == ')') {
            while (char_stack.top() != '(') {
                output += char_stack.top();
                char_stack.pop();
            }
 
            // Remove '(' from the stack
            char_stack.pop();
        }
 
        // Operator found
        else {
            if (isOperator(char_stack.top())) {
                if (infix[i] == '^') {
                    while (
                        getPriority(infix[i])
                        <= getPriority(char_stack.top())) {
                        output += char_stack.top();
                        char_stack.pop();
                    }
                }
                else {
                    while (
                        getPriority(infix[i])
                        < getPriority(char_stack.top())) {
                        output += char_stack.top();
                        char_stack.pop();
                    }
                }
 
                // Push current Operator on stack
                char_stack.push(infix[i]);
            }
        }
    }
    while (!char_stack.empty()) {
        output += char_stack.top();
        char_stack.pop();
    }
    return output;
}
 
// Function to convert infix to prefix notation
string infixToPrefix(string infix)
{
    // Reverse String and replace ( with ) and vice versa
    // Get Postfix
    // Reverse Postfix
    int l = infix.size();
 
    // Reverse infix
    reverse(infix.begin(), infix.end());
 
    // Replace ( with ) and vice versa
    for (int i = 0; i < l; i++) {
 
        if (infix[i] == '(') {
            infix[i] = ')';
        }
        else if (infix[i] == ')') {
            infix[i] = '(';
        }
    }
 
    string prefix = infixToPostfix(infix);
 
    // Reverse postfix
    reverse(prefix.begin(), prefix.end());
 
    return prefix;
}
 
// Driver code
int main()
{
    string s = ("x+y*z/w+u");
   
    // Function call
    cout << infixToPrefix(s) << std::endl;
    return 0;
}

Java

// Java program to convert infix to prefix
import java.util.*;
 
class GFG {
    // Function to check if the character is an operand
    static boolean isalpha(char c)
    {
        if (c >= 'a' && c <= 'z' || c >= 'A' && c <= 'Z') {
            return true;
        }
        return false;
    }
 
    // Function to check if the character is digit
    static boolean isdigit(char c)
    {
        if (c >= '0' && c <= '9') {
            return true;
        }
        return false;
    }
 
    // Function to check if the character is an operator
    static boolean isOperator(char c)
    {
        return (!isalpha(c) && !isdigit(c));
    }
 
    // Function to get priority of operators
    static int getPriority(char C)
    {
        if (C == '-' || C == '+')
            return 1;
        else if (C == '*' || C == '/')
            return 2;
        else if (C == '^')
            return 3;
 
        return 0;
    }
 
    // Reverse the letters of the word
    static String reverse(char str[], int start, int end)
    {
        // Temporary variable to store character
        char temp;
        while (start < end) {
            // Swapping the first and last character
            temp = str[start];
            str[start] = str[end];
            str[end] = temp;
            start++;
            end--;
        }
        return String.valueOf(str);
    }
 
    // Function to convert infix to postfix expression
    static String infixToPostfix(char[] infix1)
    {
        String infix = '(' + String.valueOf(infix1) + ')';
 
        int l = infix.length();
        Stack<Character> char_stack = new Stack<>();
        String output = "";
 
        for (int i = 0; i < l; i++) {
 
            // If the scanned character is an
            // operand, add it to output.
            if (isalpha(infix.charAt(i))
                || isdigit(infix.charAt(i)))
                output += infix.charAt(i);
 
            // If the scanned character is an
            // ‘(‘, push it to the stack.
            else if (infix.charAt(i) == '(')
                char_stack.add('(');
 
            // If the scanned character is an
            // ‘)’, pop and output from the stack
            // until an ‘(‘ is encountered.
            else if (infix.charAt(i) == ')') {
                while (char_stack.peek() != '(') {
                    output += char_stack.peek();
                    char_stack.pop();
                }
 
                // Remove '(' from the stack
                char_stack.pop();
            }
 
            // Operator found
            else {
                if (isOperator(char_stack.peek())) {
                    while (
                        (getPriority(infix.charAt(i))
                         < getPriority(char_stack.peek()))
                        || (getPriority(infix.charAt(i))
                                <= getPriority(
                                    char_stack.peek())
                            && infix.charAt(i) == '^')) {
                        output += char_stack.peek();
                        char_stack.pop();
                    }
 
                    // Push current Operator on stack
                    char_stack.add(infix.charAt(i));
                }
            }
        }
        while (!char_stack.empty()) {
            output += char_stack.pop();
        }
        return output;
    }
 
    static String infixToPrefix(char[] infix)
    {
        // Reverse String and replace ( with ) and vice
        // versa Get Postfix Reverse Postfix
        int l = infix.length;
 
        // Reverse infix
        String infix1 = reverse(infix, 0, l - 1);
        infix = infix1.toCharArray();
 
        // Replace ( with ) and vice versa
        for (int i = 0; i < l; i++) {
 
            if (infix[i] == '(') {
                infix[i] = ')';
                i++;
            }
            else if (infix[i] == ')') {
                infix[i] = '(';
                i++;
            }
        }
 
        String prefix = infixToPostfix(infix);
 
        // Reverse postfix
        prefix = reverse(prefix.toCharArray(), 0, l - 1);
 
        return prefix;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String s = ("x+y*z/w+u");
 
        // Function call
        System.out.print(infixToPrefix(s.toCharArray()));
    }
}
 
// This code is contributed by Rajput-Ji

Python3

# Python code to convert infix to prefix expression
 
 
# Function to check if the character is an operator
def isOperator(c):
    return (not c.isalpha()) and (not c.isdigit())
 
 
 
# Function to get the priority of operators
def getPriority(c):
    if c == '-' or c == '+':
        return 1
    elif c == '*' or c == '/':
        return 2
    elif c == '^':
        return 3
    return 0
 
 
   
# Function to convert the infix expression to postfix
def infixToPostfix(infix):
    infix = '(' + infix + ')'
    l = len(infix)
    char_stack = []
    output = ""
 
    for i in range(l):
         
        # Check if the character is alphabet or digit
        if infix[i].isalpha() or infix[i].isdigit():
            output += infix[i]
             
        # If the character is '(' push it in the stack
        elif infix[i] == '(':
            char_stack.append(infix[i])
         
        # If the character is ')' pop from the stack
        elif infix[i] == ')':
            while char_stack[-1] != '(':
                output += char_stack.pop()
            char_stack.pop()
         
        # Found an operator
        else:
            if isOperator(char_stack[-1]):
                if infix[i] == '^':
                    while getPriority(infix[i]) <= getPriority(char_stack[-1]):
                        output += char_stack.pop()
                else:
                    while getPriority(infix[i]) < getPriority(char_stack[-1]):
                        output += char_stack.pop()
                char_stack.append(infix[i])
 
    while len(char_stack) != 0:
        output += char_stack.pop()
    return output
 
 
 
# Function to convert infix expression to prefix
def infixToPrefix(infix):
    l = len(infix)
 
    infix = infix[::-1]
 
    for i in range(l):
        if infix[i] == '(':
            infix[i] = ')'
        elif infix[i] == ')':
            infix[i] = '('
 
    prefix = infixToPostfix(infix)
    prefix = prefix[::-1]
 
    return prefix
 
 
 
# Driver code
if __name__ == '__main__':
    s = "x+y*z/w+u"
     
    # Function call
    print(infixToPrefix(s))

C#

// C# program to convert infix to prefix
using System;
using System.Collections.Generic;
 
public class GFG {
    // Check if the given character is an alphabet
    static bool isalpha(char c)
    {
        if (c >= 'a' && c <= 'z' || c >= 'A' && c <= 'Z') {
            return true;
        }
        return false;
    }
 
    // Check if the current character is a digit
    static bool isdigit(char c)
    {
        if (c >= '0' && c <= '9') {
            return true;
        }
        return false;
    }
 
    // Function to check if the character is an operator
    static bool isOperator(char c)
    {
        return (!isalpha(c) && !isdigit(c));
    }
 
    // Function to get the precedence order of operators
    static int getPriority(char C)
    {
        if (C == '-' || C == '+')
            return 1;
        else if (C == '*' || C == '/')
            return 2;
        else if (C == '^')
            return 3;
 
        return 0;
    }
 
    // Reverse the letters of the word
    static String reverse(char[] str, int start, int end)
    {
 
        // Temporary variable to store character
        char temp;
        while (start < end) {
 
            // Swapping the first and last character
            temp = str[start];
            str[start] = str[end];
            str[end] = temp;
            start++;
            end--;
        }
        return String.Join("", str);
    }
 
    // Function to convert infix to postfix notation
    static String infixToPostfix(char[] infix1)
    {
        String infix = '(' + String.Join("", infix1) + ')';
 
        int l = infix.Length;
        Stack<char> char_stack = new Stack<char>();
        String output = "";
 
        for (int i = 0; i < l; i++) {
 
            // If the scanned character is an
            // operand, add it to output.
            if (isalpha(infix[i]) || isdigit(infix[i]))
                output += infix[i];
 
            // If the scanned character is an
            // ‘(‘, push it to the stack.
            else if (infix[i] == '(')
                char_stack.Push('(');
 
            // If the scanned character is an
            // ‘)’, pop and output from the stack
            // until an ‘(‘ is encountered.
            else if (infix[i] == ')') {
                while (char_stack.Peek() != '(') {
                    output += char_stack.Peek();
                    char_stack.Pop();
                }
 
                // Remove '(' from the stack
                char_stack.Pop();
            }
 
            // Operator found
            else {
                if (isOperator(char_stack.Peek())) {
                    while (
                        (getPriority(infix[i])
                         < getPriority(char_stack.Peek()))
                        || (getPriority(infix[i])
                                <= getPriority(
                                    char_stack.Peek())
                            && infix[i] == '^')) {
                        output += char_stack.Peek();
                        char_stack.Pop();
                    }
 
                    // Push current Operator on stack
                    char_stack.Push(infix[i]);
                }
            }
        }
        while (char_stack.Count != 0) {
            output += char_stack.Pop();
        }
        return output;
    }
 
    // Driver code
    static String infixToPrefix(char[] infix)
    {
        // Reverse String Replace ( with ) and vice versa
        // Get Postfix
        // Reverse Postfix *
        int l = infix.Length;
 
        // Reverse infix
        String infix1 = reverse(infix, 0, l - 1);
        infix = infix1.ToCharArray();
 
        // Replace ( with ) and vice versa
        for (int i = 0; i < l; i++) {
            if (infix[i] == '(') {
                infix[i] = ')';
                i++;
            }
            else if (infix[i] == ')') {
                infix[i] = '(';
                i++;
            }
        }
        String prefix = infixToPostfix(infix);
 
        // Reverse postfix
        prefix = reverse(prefix.ToCharArray(), 0, l - 1);
 
        return prefix;
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        String s = ("x+y*z/w+u");
       
        // Function call
        Console.Write(infixToPrefix(s.ToCharArray()));
    }
}
 
// This code is contributed by gauravrajput1

Javascript

// Javascript program to convert infix to prefix
// program to implement stack data structure
class Stack {
  constructor() {
    this.items = [];
  }
 
  // add element to the stack
  push(element) {
    return this.items.push(element);
  }
 
  // remove element from the stack
  pop() {
    if (this.items.length > 0) {
      return this.items.pop();
    }
  }
 
  // view the last element
  top() {
    return this.items[this.items.length - 1];
  }
 
  // check if the stack is empty
  isEmpty() {
    return this.items.length == 0;
  }
 
  // the size of the stack
  size() {
    return this.items.length;
  }
 
  // empty the stack
  clear() {
    this.items = [];
  }
}
 
function isalpha(c) {
  if ((c >= "a" && c <= "z") || (c >= "A" && c <= "Z")) {
    return true;
  }
  return false;
}
 
function isdigit(c) {
  if (c >= "0" && c <= "9") {
    return true;
  }
  return false;
}
function isOperator(c) {
  return !isalpha(c) && !isdigit(c);
}
 
function getPriority(C) {
  if (C == "-" || C == "+") return 1;
  else if (C == "*" || C == "/") return 2;
  else if (C == "^") return 3;
  return 0;
}
 
function infixToPostfix(infix) {
  infix = "(" + infix + ")";
 
  var l = infix.length;
  let char_stack = new Stack();
  var output = "";
 
  for (var i = 0; i < l; i++) {
    // If the scanned character is an
    // operand, add it to output.
    if (isalpha(infix[i]) || isdigit(infix[i])) output += infix[i];
    // If the scanned character is an
    // ‘(‘, push it to the stack.
    else if (infix[i] == "(") char_stack.push("(");
    // If the scanned character is an
    // ‘)’, pop and output from the stack
    // until an ‘(‘ is encountered.
    else if (infix[i] == ")") {
      while (char_stack.top() != "(") {
        output += char_stack.top();
        char_stack.pop();
      }
 
      // Remove '(' from the stack
      char_stack.pop();
    }
 
    // Operator found
    else {
      if (isOperator(char_stack.top())) {
        if (infix[i] == "^") {
          while (getPriority(infix[i]) <= getPriority(char_stack.top())) {
            output += char_stack.top();
            char_stack.pop();
          }
        } else {
          while (getPriority(infix[i]) < getPriority(char_stack.top())) {
            output += char_stack.top();
            char_stack.pop();
          }
        }
 
        // Push current Operator on stack
        char_stack.push(infix[i]);
      }
    }
  }
  while (!char_stack.isEmpty()) {
    output += char_stack.top();
    char_stack.pop();
  }
 
  return output;
}
 
function infixToPrefix(infix) {
  /* Reverse String
   * Replace ( with ) and vice versa
   * Get Postfix
   * Reverse Postfix  *  */
  var l = infix.length;
 
  // Reverse infix
  infix = infix.split("").reverse().join("");
 
  // Replace ( with ) and vice versa
  var infixx = infix.split("");
  for (var i = 0; i < l; i++) {
    if (infixx[i] == "(") {
      infixx[i] = ")";
    } else if (infixx[i] == ")") {
      infixx[i] = "(";
    }
  }
  infix = infixx.join("");
 
  var prefix = infixToPostfix(infix);
 
  // Reverse postfix
  prefix = prefix.split("").reverse().join("");
  return prefix;
}
 
// Driver code
 
var s = "x+y*z/w+u";
console.log(infixToPrefix(s));

Output

++x/*yzwu

Complexity Analysis:

Time Complexity: O(n)
- Stack operations like push() and pop() are performed in constant time.
- Since we scan all the characters in the expression once the complexity is linear in time
Auxiliary Space: O(n) because we are keeping a stack.

Suggest improvement

Postfix to Infix

Check for Balanced Brackets in an expression (well-formedness)

Share your thoughts in the comments

Stack implementation in different language

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