In [142]:

    

def fibonacci (n):
    if not isinstance(n, int):
        print "Need an integer I'm afraid"
    elif n < 0:
        print "Not defined for negative numbers"
    elif n == 0:
        return 0
    elif  n == 1:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)


    

In [200]:

    

fibonacci(2)


    

    
Out[200]:





1

In [149]:

    

fibonacci(-1)


    

    




Not defined for negative numbers

In [1]:

    

def compare(x, y):
    if x > y:
        return 1
    elif x < y:
        return -1
    else:
        return 0


    

In [2]:

    

compare(1,2)


    

    
Out[2]:





-1

In [3]:

    

compare(2,1)


    

    
Out[3]:





1

In [4]:

    

compare(1,1)


    

    
Out[4]:





0

In [10]:

    

import math


    

In [11]:

    

def hypotenuse(leg1, leg2):
    sides_squared = leg1 ** 2 + leg2 ** 2
    print sides_squared
    result = math.sqrt(sides_squared)
    print result
    return result


    

In [12]:

    

hypotenuse(3,4)


    

    




25
5.0






    
Out[12]:





5.0

In [13]:

    

def hypotenuse(leg1, leg2):
    return math.sqrt(leg1 ** 2 + leg2 ** 2)


    

In [14]:

    

hypotenuse(3,4)


    

    
Out[14]:





5.0

In [17]:

    

def is_between(x, y, z):
    return x <= y and y <= z


    

In [18]:

    

is_between(1.5, math.pi, 4)


    

    
Out[18]:





True

In [19]:

    

is_between(1.5, 4, math.pi)


    

    
Out[19]:





False

In [20]:

    

def ack(m, n):
    if m < 0 or n < 0:
        print "m and n must be nonnegative"
        return None
    elif m == 0:
        return n + 1
    elif m > 0 and n == 0:
        return ack(m - 1, 1)
    elif m > 0 and n > 0:
        return ack(m - 1, ack(m, n - 1))


    

In [21]:

    

print ack(3, 4)


    

    




125

In [23]:

    

print ack(3, 3)


    

    




61

In [25]:

    

def first(word):
    return word[0]

def last(word):
    return word[-1]

def middle(word):
    return word[1:-1]


    

In [26]:

    

middle('ab')


    

    
Out[26]:





''

In [27]:

    

middle('a')


    

    
Out[27]:





''

In [28]:

    

middle('')


    

    
Out[28]:





''

In [37]:

    

def is_palindrome(word):
    if len(word) <= 1:
        return True
    else:
        return first(word) == last(word) and is_palindrome(middle(word))


    

In [38]:

    

is_palindrome('amanaplanacanalpanama')


    

    
Out[38]:





True

In [42]:

    

is_palindrome('abcdefg')


    

    
Out[42]:





False

In [194]:

    




    

    
Out[194]:





False

In [47]:

    

def is_power(a, b):
    return math.log(a, b) % 1 == 0


    

In [51]:

    

is_power(8, 2)


    

    
Out[51]:





True

In [50]:

    

is_power(8, 3)


    

    
Out[50]:





False

In [214]:

    

def is_power(a, b):
    if a == 1:
        return True
    else:
        return a % b == 0 and is_power(a/b, b)


    

In [215]:

    

%timeit is_power(2**25,2)


    

    




100000 loops, best of 3: 7.7 µs per loop

In [72]:

    

is_power(17,2)


    

    
Out[72]:





False

In [14]:

    

def gcd_v1(a, b):
    if a == b:
        return a
    elif a > b:
        return gcd_v1(a - b, b)
    else:
        return gcd_v1(a, b - a)


    

In [15]:

    

def gcd_v2(a, b):
    if a < b:
        a, b = b, a
    r = a % b
    if r == 0:
        return b
    else:
        return gcd_v2(a, r)


    

In [20]:

    

gcd_v1(91, 91*17)


    

    
Out[20]:





91

In [19]:

    

gcd_v2(8, 4)


    

    
Out[19]:





4