var = 'abcdefghijklmnopqrstuvwxyz'
operators = '+-*/^'


def polish(alg):
    '''Converts an algebraic expression into reverse polish notation
        e.x. ((a+b)-(x*y))  -->  ab+xy*- '''

    # base case - a single variable is the simplest expression
    if len(alg) == 1 and alg in var:
        return alg

    # recursive case - returns expression 1 + expression 2 + operator
    else:
        # construct a list containing a dict detailing every operator with it's index, priority, and value
        priority = 0
        ops = list()
        for key, char in enumerate(alg):
            if char == '(':
                priority += 1

            if char == ')':
                priority -= 1

            if char in operators:
                ops.append({'index': key, 'priority': priority, 'op': char})

        # select the operation with lowest priority as principle operator
        p_op = sorted(ops, key=lambda op: op['priority'])[0]
        pivot = p_op['index']

        # split the algebraic expression into sub expressions and operator
        return polish(alg[1:pivot]) + polish(alg[pivot+1:-1]) + p_op['op']