import re

def toTree(infixStr):
    # divide string into tokens, and reverse so I can get them in order with pop()
    tokens = re.split(r' *([\+\-\*\^/]) *', infixStr)
    tokens = [t for t in reversed(tokens) if t!='']
    precs = {'+':0 , '-':0, '/':1, '*':1, '^':2}

    #convert infix expression tokens to a tree, processing only
    #operators above a given precedence
    def toTree2(tokens, minprec):
        node = tokens.pop()
        while len(tokens)>0:
            prec = precs[tokens[-1]]
            if prec<minprec:
                break
            op=tokens.pop()

            # get the argument on the operator's right
            # this will go to the end, or stop at an operator
            # with precedence <= prec
            arg2 = toTree2(tokens,prec+1)
            node = (op, node, arg2)
        return node

    return toTree2(tokens,0)

print toTree("5+3*4^2+1")