RecursiveFunctions

def recurPower(base, exp):
    '''
    base: int or float.
    exp: int >= 0
 
    returns: int or float, base^exp
    '''
    # Your code here
    if exp == 0:
        return 1
    elif exp == 1:
        return base
    return (base*recurPower(base, exp-1))

def recurPowerNew(base, exp):
    '''
    base: int or float.
    exp: int >= 0

    returns: int or float; base^exp
    '''
    # Your code here
    if exp == 0:
        return 1
    elif (exp %2 == 1):
        return base * recurPowerNew(base, exp-1)
    return recurPowerNew(base * base, exp / 2)
    
def gcdIter(a, b):
    '''
    a, b: positive integers
    
    returns: a positive integer, the greatest common divisor of a & b.
    '''
    # Your code here
    for i in range(min(a,b)+1, 1, -1):
        if (a%i == 0 and b%i == 0):
            return i
    return 1
    
def gcdRecur(a, b):
    '''
    a, b: positive integers
    
    returns: a positive integer, the greatest common divisor of a & b.
    
    Utiliza el algoritmo de Euclides
    '''
    # Your code here
    if b == 0:
       return a
    return gcdRecur(b, a%b)

def lenIter(aStr):
    '''
    aStr: a string
    
    returns: int, the length of aStr
    '''
    # Your code here
    count = 0
    for ch in aStr:
        count += 1
    return count

def lenRecur(aStr):
    '''
    aStr: a string
    
    returns: int, the length of aStr
    '''
    # Your code here
    if aStr == '':
       return 0
    return 1 + lenRecur(aStr[1:])
    
def isIn(char, aStr):
    '''
    char: a single character
    aStr: an alphabetized string
    
    returns: True if char is in aStr; False otherwise
    '''
    # Your code here
    if aStr=='':
        return False
    elif char == aStr[len(aStr)/2]:
        return True
    elif char < aStr[len(aStr)/2]:
        return isIn(char, aStr[:len(aStr)/2])
    else:
        return isIn(char, aStr[len(aStr)/2+1:])

def semordnilap(str1, str2):
    '''
    str1: a string
    str2: a string
    
    returns: True if str1 and str2 are semordnilap;
             False otherwise.
    '''
    # Your code here
    if str1=='' or str2=='':
        if str1 != str2:
            return False
        return True
    
    return str1[0]==str2[-1] and semordnilap(str1[1:],str2[:-1])