In this tutorial, I will explain why “1000000000000000 in range(1000000000000001)” is so fast in Python 3.
Understanding Python’s range() Magic
Ever wondered how Python’s range() function works behind the scenes? Well, it’s more than just a list of numbers; it’s a smart sequence generator that produces numbers as you need them. Let’s unravel the magic!
Lazy Numbers
Unlike traditional sequences, the range() object doesn’t pre-generate all the numbers at once. It only stores your starting point, endpoint, and step values. As you loop through the object, it calculates the next number on the fly, making it pretty efficient.
Finding the Right Number
Now, here’s the cool part. The range() object is not just lazy; it’s also smart. It can quickly tell you if a particular number is part of its range. No need to scan through all possible integers – it’s a (nearly) instant operation!
Memory-Savvy
What’s even more impressive is that a range() object won’t hog your memory. It always takes up a small, consistent amount of memory, regardless of the size of the range it represents. That’s because it cleverly stores only the start, stop, and step values.
Behind the Scenes
Ever wondered how you could implement your own simplified version of range()? Well, here’s a snippet to get you started:
class MyRange:
# ... (implementation details here)
Here it is:
class my_range:
def __init__(self, start, stop=None, step=1, /):
if stop is None:
start, stop = 0, start
self.start, self.stop, self.step = start, stop, step
if step < 0:
lo, hi, step = stop, start, -step
else:
lo, hi = start, stop
self.length = 0 if lo > hi else ((hi - lo - 1) // step) + 1
def __iter__(self):
current = self.start
if self.step < 0:
while current > self.stop:
yield current
current += self.step
else:
while current < self.stop:
yield current
current += self.step
def __len__(self):
return self.length
def __getitem__(self, i):
if i < 0:
i += self.length
if 0 <= i < self.length:
return self.start + i * self.step
raise IndexError('my_range object index out of range')
def __contains__(self, num):
if self.step < 0:
if not (self.stop < num <= self.start):
return False
else:
if not (self.start <= num < self.stop):
return False
return (num - self.start) % self.step == 0
This basic version covers the essentials, allowing you to iterate through, get the length, and check if a number is in your custom range. It’s missing some features of the real range(), but it’s a good starting point.
So, next time you use range() in Python, remember it’s not just a sequence; it’s a dynamic, memory-friendly wizard that conjures up numbers as you need them!
Python 3’s Range: another explanation
In the world of Python 3, the range() function does something pretty clever. Instead of conjuring up an entire list of numbers all at once, it creates them on the spot, like a magical number generator.
On-the-Fly Numbers
So, here’s the trick: when you use the in operator to check if a number is in the range, Python doesn’t bother making all the numbers at once. Nope! It’s much smarter. It only generates the numbers in the range up to the one you’re checking.
Quick Check Example
Let’s say you have a massive range, like a gazillion numbers:
1000000000000000 in range(1000000000000001)
Python is a speedster here. It only generates the numbers up to 1000000000000000, which is way faster than summoning the entire range. And that’s why your code runs like lightning!
Python 2 vs. Python 3
But, hey, here’s the plot twist. This magical behavior is exclusive to Python 3. In Python 2, the range() function goes old-school, creating a list of all the numbers in the range upfront. So, if you’re still in Python 2 land, checking if a number is in a huge range might take a bit more time.
So, next time you’re dancing with numbers in Python 3, remember: it’s not just a range; it’s a dynamic, on-the-spot performer making your code run faster!
Certainly, let’s make this formal but still friendly:
Enhancing Functionality: A Proposal for a More Versatile min Function
In contemplating the optimization of the min function, one could envision a more adaptable approach. Rather than being confined to a singular implementation, an ideal scenario would involve a generic min function. This would allow for a default implementation, while also permitting users to freely override it for any desired type.
Have you encountered functools.singledispatch in Python 3.4? Remarkably, achieving this level of versatility is feasible through the capabilities offered by singledispatch. This not only avoids contributing to the extensive list of dunder-methods but also provides an elegant solution.
Consider the following implementation:
from functools import singledispatch
# Preserve the original min function
_min = __builtins__.min
# The generic_min(x) returns min(x) if no specialization exists for type(x)
@singledispatch
def generic_min(sequence):
return _min(sequence)
# Specialize min() to operate on range types
@generic_min.register(range)
def _(the_range):
return _min([the_range.start, the_range.stop])
# Override the built-in `min` – acceptable, as it mirrors the original functionality in most cases
__builtins__.min = generic_min
# Utilize the enhanced min() – a notable improvement in efficiency
min_value = min(range(9999999))
This approach not only introduces a generic min function but also showcases how specialization for specific types can be seamlessly integrated. By leveraging the power of singledispatch, the enhanced min function demonstrates a considerable performance boost when applied to range types.
In embracing this proposal, we open the door to a more versatile and efficient min function that aligns with the dynamic nature of Python programming.