# 
# recursion_examples.py
# 
# Example recursive functions from lecture
#
# Computer Science 111
#

def power(b, p):
    """ returns b raised to the p power
        inputs: b is a number (int or float)
                p is a non-negative integer
    """
    if p == 0:
        return 1
    else:
        pow_rest = power(b, p-1)
        return b * pow_rest

def mylen(s):
    """ returns the length of the sequence s
        input: s is a sequence (a string or list)
    """
    if s == '' or s == []:
        return 0
    else:
        len_rest = mylen(s[1:])
        return 1 + len_rest

def num_vowels(s):
    """ returns the number of vowels in the string s
        input: s is a string of 0 or more lowercase letters
    """
    if s == '':
        return 0
    else:
        num_in_rest = num_vowels(s[1:])
        if s[0] in 'aeiou':
            return 1 + num_in_rest
        else:
            return 0 + num_in_rest

def mymax(lst):    
    """ returns the largest element in a list
        input: lst is a *non-empty* list
    """
    if len(lst) == 1:
        return lst[0]
    else:
        max_in_rest = mymax(lst[1:])
        if lst[0] > max_in_rest:
            return lst[0]
        else:
            return max_in_rest