Postfix: An expression is called the postfix expression if the operator appears in the expression after the operands. Simply of the form (operand1 operand2 operator).
Example : AB+CD-* (Infix : (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 Postfix expression, convert it into a Prefix expression.
Conversion of Postfix expression directly to Prefix without going through the process of converting them first to Infix and then to Prefix is much better in terms of computation and better understanding the expression (Computers evaluate using Postfix expression).
Examples:
Input : Postfix : AB+CD-*
Output : Prefix : *+AB-CD
Explanation : Postfix to Infix : (A+B) * (C-D)
Infix to Prefix : *+AB-CD
Input : Postfix : ABC/-AK/L-*
Output : Prefix : *-A/BC-/AKL
Explanation : Postfix to Infix : ((A-(B/C))*((A/K)-L))
Infix to Prefix : *-A/BC-/AKL
Algorithm for Postfix to Prefix:
- Read the Postfix expression from left to right
- 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 before them.
string = operator + operand2 + operand1
And push the resultant string back to Stack- Repeat the above steps until end of Postfix expression.
Below is the implementation of the above idea:
C++
// CPP Program to convert postfix to prefix#include <bits/stdc++.h>using namespace std;// function to check if character is operator or notbool isOperator(char x){ switch (x) { case '+': case '-': case '/': case '*': return true; } return false;}// Convert postfix to Prefix expressionstring postToPre(string post_exp){ stack<string> s; // length of expression int length = post_exp.size(); // reading from left to right for (int i = 0; i < length; i++) { // check if symbol is operator if (isOperator(post_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 = post_exp[i] + op2 + op1; // 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, post_exp[i])); } } string ans = ""; while (!s.empty()) { ans += s.top(); s.pop(); } return ans;}// Driver Codeint main(){ string post_exp = "ABC/-AK/L-*"; // Function call cout << "Prefix : " << postToPre(post_exp); return 0;} |
Java
// Java Program to convert postfix to prefiximport java.util.*;class GFG { // function to check if character // is operator or not static boolean isOperator(char x) { switch (x) { case '+': case '-': case '/': case '*': return true; } return false; } // Convert postfix to Prefix expression static String postToPre(String post_exp) { Stack<String> s = new Stack<String>(); // length of expression int length = post_exp.length(); // reading from right to left for (int i = 0; i < length; i++) { // check if symbol is operator if (isOperator(post_exp.charAt(i))) { // pop two operands from stack String op1 = s.peek(); s.pop(); String op2 = s.peek(); s.pop(); // concat the operands and operator String temp = post_exp.charAt(i) + op2 + op1; // Push String temp back to stack s.push(temp); } // if symbol is an operand else { // push the operand to the stack s.push(post_exp.charAt(i) + ""); } } // concatenate all strings in stack and return the // answer String ans = ""; for (String i : s) ans += i; return ans; } // Driver Code public static void main(String args[]) { String post_exp = "ABC/-AK/L-*"; // Function call System.out.println("Prefix : " + postToPre(post_exp)); }}// This code is contributed by Arnab Kundu |
Python3
# Python3 Program to convert postfix to prefix# function to check if# character is operator or notdef isOperator(x): if x == "+": return True if x == "-": return True if x == "/": return True if x == "*": return True return False# Convert postfix to Prefix expressiondef postToPre(post_exp): s = [] # length of expression length = len(post_exp) # reading from right to left for i in range(length): # check if symbol is operator if (isOperator(post_exp[i])): # pop two operands from stack op1 = s[-1] s.pop() op2 = s[-1] s.pop() # concat the operands and operator temp = post_exp[i] + op2 + op1 # Push string temp back to stack s.append(temp) # if symbol is an operand else: # push the operand to the stack s.append(post_exp[i]) ans = "" for i in s: ans += i return ans# Driver Codeif __name__ == "__main__": post_exp = "AB+CD-" # Function call print("Prefix : ", postToPre(post_exp))# This code is contributed by AnkitRai01 |
C#
// C# Program to convert postfix to prefixusing System;using System.Collections;class GFG { // function to check if character // is operator or not static Boolean isOperator(char x) { switch (x) { case '+': case '-': case '/': case '*': return true; } return false; } // Convert postfix to Prefix expression static String postToPre(String post_exp) { Stack s = new Stack(); // length of expression int length = post_exp.Length; // reading from right to left for (int i = 0; i < length; i++) { // check if symbol is operator if (isOperator(post_exp[i])) { // Pop two operands from stack String op1 = (String)s.Peek(); s.Pop(); String op2 = (String)s.Peek(); s.Pop(); // concat the operands and operator String temp = post_exp[i] + op2 + op1; // Push String temp back to stack s.Push(temp); } // if symbol is an operand else { // Push the operand to the stack s.Push(post_exp[i] + ""); } } String ans = ""; while (s.Count > 0) ans += s.Pop(); return ans; } // Driver Code public static void Main(String[] args) { String post_exp = "ABC/-AK/L-*"; // Function call Console.WriteLine("Prefix : " + postToPre(post_exp)); }}// This code is contributed by Arnab Kundu |
Javascript
<script> // Javascript Program to convert postfix to prefix // function to check if character // is operator or not function isOperator(x) { switch (x) { case '+': case '-': case '/': case '*': return true; } return false; } // Convert postfix to Prefix expression function postToPre(post_exp) { let s = []; // length of expression let length = post_exp.length; // reading from right to left for (let i = 0; i < length; i++) { // check if symbol is operator if (isOperator(post_exp[i])) { // Pop two operands from stack let op1 = s[s.length - 1]; s.pop(); let op2 = s[s.length - 1]; s.pop(); // concat the operands and operator let temp = post_exp[i] + op2 + op1; // Push String temp back to stack s.push(temp); } // if symbol is an operand else { // Push the operand to the stack s.push(post_exp[i] + ""); } } let ans = ""; while (s.length > 0) ans += s.pop(); return ans; } let post_exp = "ABC/-AK/L-*"; // Function call document.write("Prefix : " + postToPre(post_exp)); // This code is contributed by suresh07.</script> |
Output
Prefix : *-A/BC-/AKL
Time Complexity: O(N) // In the above-given approach, there is one loop for iterating over string which takes O(N) time in worst case. Therefore, the time complexity for this approach will be O(N).
Auxiliary Space: O(N) // we are using an empty stack as well as empty string to store the expression hence space taken is linear
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