A generator in Python is a function that returns an iterator object instead of a single result.

It differs from regular functions in that it uses the yield keyword instead of return. Each call to next(generator) produces the next value from the sequence.

Example:

def multiple_generator(x, n):
    for i in range(1, n + 1):
        yield x * i

multiples_of_5 = multiple_generator(5, 3)

print(next(multiples_of_5))  # 5
print(next(multiples_of_5))  # 10
print(next(multiples_of_5))  # 15

https://t.iss.one/DataScience4 ❤️

Python tip:

You can make dataclass fields immutable by setting frozen=True.
In this case, fields cannot be mutated after the instance is created.

Example below👇

from dataclasses import dataclass

@dataclass(frozen=True)
class Color:
    name: str
    hex_value: str

color = Color("red", "#FF0000")

# color.name = "blue"  # will raise FrozenInstanceError

👉 @codeprogrammer

Accelerating the Sieve of Eratosthenes

1. Quickly recall the algorithm

Classic implementation:

def eratosthenes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = is_prime[1] = False

    for i in range(2, int(n ** 0.5) + 1):
        if is_prime[i]:
            for j in range(i * i, n + 1, i):
                is_prime[j] = False

    return is_prime

Time — O(N log log N). We're not interested in the asymptotics, but in how much we can speed up the implementation itself.

2. Optimization #1 — don't bother with even numbers

The idea is simple:

* all even numbers except 2 are composite
* if we only work with odd numbers, we reduce the array size and the number of iterations by about half

Implementation:

def eratosthenes_odd(n):
    if n < 2:
        return []

    size = (n + 1) // 2
    is_prime = [True] * size
    is_prime[0] = False

    limit = int(n ** 0.5) // 2
    for i in range(1, limit + 1):
        if is_prime[i]:
            p = 2 * i + 1
            start = (p * p) // 2
            for j in range(start, size, p):
                is_prime[j] = False

    return is_prime

3. Optimization #2 — use bytearray instead of list[bool]

Thought:

* bool in Python is an object
* bytearray is a tightly packed buffer
* less overhead and better fits into the CPU cache

Example:

def eratosthenes_bytearray(n):
    is_prime = bytearray(b"\x01") * (n + 1)
    is_prime[0:2] = b"\x00\x00"

    for i in range(2, int(n ** 0.5) + 1):
        if is_prime[i]:
            for j in range(i * i, n + 1, i):
                is_prime[j] = 0

    return is_prime

4. Optimization #3 — a hybrid of the two approaches

def eratosthenes_fast(n):
    if n < 2:
        return []

    size = (n + 1) // 2
    is_prime = bytearray(b"\x01") * size
    is_prime[0] = 0

    limit = int(n ** 0.5) // 2
    for i in range(1, limit + 1):
        if is_prime[i]:
            p = 2 * i + 1
            start = (p * p) // 2
            is_prime[start::p] = b"\x00" * (((size - start - 1) // p) + 1)

    return is_prime

5. Time comparison

Test with n = 10_000_000:

>>> eratosthenes.py
real  0.634s

>>> eratosthenes_odd.py
real  0.245s

>>> eratosthenes_bytearray.py
real  0.801s

>>> eratosthenes_fast.py
real  0.028s

Conclusions:

* skipping even numbers (#1) gives ~2.6× speedup
* bytearray itself doesn't speed up — it's more about memory
* the hybrid (#3) gives ~22.6× speedup

Key trick in #3:

is_prime[start::p] = b"\x00" * (((size - start - 1) // p) + 1)

There's no Python loop here — everything is done by a C-level operation on the slice. On such tasks, this makes a huge difference.

General idea: in Python, we often speed up not the asymptotics, but the memory model and the number of passes over the data. Loops + memory → the main factors.

👉 @DataScience4