numbers = [2, 10, 103, 220, 241, 245, 503]

def contains1(numbers, n):
    """ Returns True if n is in the list numbers. """
    # Brute force: look at every number and see.
    for i in numbers:
        if i == n:
            return True
    return False

def contains2(numbers, n):
    """ Returns True if n is in the list of numbers. """
    # binary search
    i_start = 0
    i_end = len(numbers) - 1
    count = 0
    while True:
        count += 1
        if count > 50:
            return "too many iterations"
        #print "i_start, i_end = ", i_start, i_end
        #print "list there is", numbers[i_start], numbers[i_end]
        i_middle = (i_start + i_end)/2

        if n == numbers[i_middle]:
            return True
        elif n < numbers[i_middle]:
            i_end = i_middle - 1
        elif n > numbers[i_middle]:
            i_start = i_middle + 1
        else:
            print "This shouldn't happen"
            return "?"

        if i_end < i_start:
            return False


def contains3(numbers, n):
    """ Returns True if n is in the list of numbers """
    # recursive binary search
    i_start = 0
    i_end = len(numbers) - 1
    return recursive_contains(numbers, n, i_start, i_end)

def recursive_contains(numbers, n, i_start, i_end):
    if i_end < i_start:
        return False
    i_middle = (i_start + i_end)/2
    if n < numbers[i_middle]:
        i_end = i_middle - 1
    elif n > numbers[i_middle]:
        i_start = i_middle + 1
    else:
        return True
    return recursive_contains(numbers, n, i_start, i_end)
    
def contains4(numbers, n):
    # recursive binary search
    # using new arrays (somewhat memory inefficient)
    if not numbers:
        return False
    i_middle = len(numbers)/2
    if n < numbers[i_middle]:
        return contains4(numbers[:i_middle], n)
    elif n > numbers[i_middle]:
        return contains4(numbers[i_middle+1:], n)
    else:
        return True