Postfix to Infix Conversion in Python

Infix expression: Infix expressions contain the operator in between the two operands. The operands can themselves contain operators. Though with respect to the middle operator, the expression will be an infix expression.

Infix expressions are of the form

Example: (X + Y) * (X1 + Y1)

Postfix expression: Postfix expressions contain the operator at the end of the two operands. The operands can themselves contain operators. Though with respect to the operator, at the end, the expression will be a postfix expression.

Postfix expressions are of the form

Example: XY - X1Y1+* (Infix: (X - Y) * (X1 + Y1))

Postfix expressions are also known as reverse Polish expressions. Computers are designed to compute the expressions most often in postfix or sometimes in prefixes. However, it is difficult for us to understand and compute a postfix expression.

Postfix Expressions Are Complex

Postfix expressions can be very complicated, with multiple parentheses and operators present in a certain order. We are trained to solve infix expressions. Therefore, we need to convert a prefix expression to an infix expression.

Here are some sample inputs and outputs for a better understanding of the problem at hand.

Examples:

Input: xyz++

Output: (x + (y + z))

Input: xy*z+

Output: ((x*y)+z)

Algorithm

We will create a while loop, and the condition will be that the loop will work until there are symbols in the string.
The interpreter will read the symbols one by one
If the symbol is an operand, then it will be pushed onto the stack.
Else, if the symbol is an operator, we will pop two items from the stack. We will insert the operator with the values as its arguments and construct a string of these. Then we will push this string back onto the stack.
If the stack has only one value, then that value is the required infix string.

Here is the implementation of this algorithm in Python

Code

# Python Program to convert the given postfix expression into an infix expression

# Get Infix for a given postfix
# expression
def PostfixToInfix(postfix) :

    symbols = []

    for _ in postfix:    
         
        # Push operands
        if not Operator(_):        
            symbols.insert(0, _)
             
        # We will assume that the given expression is a valid postfix
        else:
         
            op_1 = symbols[0]
            symbols.pop(0)
            op_2 = symbols[0]
            symbols.pop(0)
            symbols.insert(0, "(" + op_2 + _ +
                             op_1 + ")")
             
    # At the end, the stack will contain only one string
    return symbols[0]

# Defnining a function to check if the symbol is an operator
def Operator(symbols):
    if symbols == "*" or symbols == "+" or symbols == "-" or symbols == "/" or symbols == "^" or symbols == "(" or symbols == ")":
        return True
    else:
        return False

# Calling the function
string = "xy*z+"
print("The infix expression is: ", PostfixToInfix(string))

Output: