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:
// CPP Program to convert postfix to prefix #include <bits/stdc++.h> 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 postfix to Prefix expression string 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 Code int main()
{ string post_exp = "ABC/-AK/L-*" ;
// Function call
cout << "Prefix : " << postToPre(post_exp);
return 0;
} |
// Java Program to convert postfix to prefix import 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 Program to convert postfix to prefix # function to check if # character is operator or not def isOperator(x):
if x = = "+" :
return True
if x = = "-" :
return True
if x = = "/" :
return True
if x = = "*" :
return True
return False
# Convert postfix to Prefix expression def 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 Code if __name__ = = "__main__" :
post_exp = "AB+CD-"
# Function call
print ( "Prefix : " , postToPre(post_exp))
# This code is contributed by AnkitRai01 |
// C# Program to convert postfix to prefix using 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 |
<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> |
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