Task: Parsing_RPN to infix conversion
C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace PostfixToInfix
{
    class Program
    {
        class Operator
        {
            public Operator(char t, int p, bool i = false)
            {
                Token = t;
                Precedence = p;
                IsRightAssociative = i;
            }

            public char Token { get; private set; }
            public int Precedence { get; private set; }
            public bool IsRightAssociative { get; private set; }
        }

        static IReadOnlyDictionary<char, Operator> operators = new Dictionary<char, Operator>
        {
            { '+', new Operator('+', 2) },
            { '-', new Operator('-', 2) },
            { '/', new Operator('/', 3) },
            { '*', new Operator('*', 3) },
            { '^', new Operator('^', 4, true) }
        };

        class Expression
        {
            public String ex;
            public Operator op;

            public Expression(String e)
            {
                ex = e;
            }

            public Expression(String e1, String e2, Operator o)
            {
                ex = String.Format("{0} {1} {2}", e1, o.Token, e2);
                op = o;
            }
        }

        static String PostfixToInfix(String postfix)
        {
            var stack = new Stack<Expression>();

            foreach (var token in Regex.Split(postfix, @"\s+"))
            {
                char c = token[0];

                var op = operators.FirstOrDefault(kv => kv.Key == c).Value;
                if (op != null && token.Length == 1)
                {
                    Expression rhs = stack.Pop();
                    Expression lhs = stack.Pop();

                    int opPrec = op.Precedence;

                    int lhsPrec = lhs.op != null ? lhs.op.Precedence : int.MaxValue;
                    int rhsPrec = rhs.op != null ? rhs.op.Precedence : int.MaxValue;

                    if ((lhsPrec < opPrec || (lhsPrec == opPrec && c == '^')))
                        lhs.ex = '(' + lhs.ex + ')';

                    if ((rhsPrec < opPrec || (rhsPrec == opPrec && c != '^')))
                        rhs.ex = '(' + rhs.ex + ')';

                    stack.Push(new Expression(lhs.ex, rhs.ex, op));
                }
                else
                {
                    stack.Push(new Expression(token));
                }

                
                Console.WriteLine("{0} -> [{1}]", token,
                    string.Join(", ", stack.Reverse().Select(e => e.ex)));
            }
            return stack.Peek().ex;
        }

        static void Main(string[] args)
        {
            string[] inputs = { "3 4 2 * 1 5 - 2 3 ^ ^ / +", "1 2 + 3 4 + ^ 5 6 + ^" };
            foreach (var e in inputs)
            {
                Console.WriteLine("Postfix : {0}", e);
                Console.WriteLine("Infix : {0}", PostfixToInfix(e));
                Console.WriteLine(); ;
            }
            Console.ReadLine();
        }
    }
}

Python:  


prec_dict =  {'^':4, '*':3, '/':3, '+':2, '-':2}
assoc_dict = {'^':1, '*':0, '/':0, '+':0, '-':0}
 
class Node:
    def __init__(self,x,op,y=None):
        self.precedence = prec_dict[op]
        self.assocright = assoc_dict[op]
        self.op = op
        self.x,self.y = x,y
 
    def __str__(self):
        
        
        if self.y == None:
            return '%s(%s)'%(self.op,str(self.x))
 
        
        str_y = str(self.y)
        if  self.y < self or \
            (self.y == self and self.assocright) or \
            (str_y[0] is '-' and self.assocright):
 
            str_y = '(%s)'%str_y
        
        str_x = str(self.x)
        str_op = self.op
        if self.op is '+' and not isinstance(self.x, Node) and str_x[0] is '-':
            str_x = str_x[1:]
            str_op = '-'
        elif self.op is '-' and not isinstance(self.x, Node) and str_x[0] is '-':
            str_x = str_x[1:]
            str_op = '+'
        elif self.x < self or \
             (self.x == self and not self.assocright and \
              getattr(self.x, 'op', 1) != getattr(self, 'op', 2)):
 
            str_x = '(%s)'%str_x
        return ' '.join([str_y, str_op, str_x])
 
    def __repr__(self):
        
        return 'Node(%s,%s,%s)'%(repr(self.x), repr(self.op), repr(self.y))
 
    def __lt__(self, other):
        if isinstance(other, Node):
            return self.precedence < other.precedence
        return self.precedence < prec_dict.get(other,9)
 
    def __gt__(self, other):
        if isinstance(other, Node):
            return self.precedence > other.precedence
        return self.precedence > prec_dict.get(other,9)

    def __eq__(self, other):
        if isinstance(other, Node):
            return self.precedence == other.precedence
        return self.precedence > prec_dict.get(other,9)
 
 
 
def rpn_to_infix(s, VERBOSE=False):
    
    if VERBOSE : print('TOKEN  STACK')
 
    stack=[]
    for token in s.replace('^','^').split():
        if token in prec_dict:
            stack.append(Node(stack.pop(),token,stack.pop()))
        else:
            stack.append(token)
 
        
        if VERBOSE : print(token+' '*(7-len(token))+repr(stack)) 
 
    return str(stack[0])
  
strTest = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
strResult = rpn_to_infix(strTest, VERBOSE=False)
print ("Input: ",strTest)
print ("Output:",strResult)

print()

strTest = "1 2 + 3 4 + ^ 5 6 + ^"
strResult = rpn_to_infix(strTest, VERBOSE=False)
print ("Input: ",strTest)
print ("Output:",strResult)