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Learn Python Coding

Learn Python Coding

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Learn Python through simple, practical examples and real coding ideas. Clear explanations, useful snippets, and hands-on learning for anyone starting or improving their programming skills. Admin: @HusseinSheikho || @Hussein_Sheikho

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Learn Python through simple, practical examples and real coding ideas. Clear explanations, useful snippets, and hands-on learning for anyone starting or improving their programming skills. Admin: @HusseinSheikho || @Hussein_Sheikho

بفضل وتيرة التحديث المرتفعة (أحدث البيانات بتاريخ 08 يونيو, 2026) تحافظ القناة على حداثتها ومستوى وصول مرتفع. وتُظهر التحليلات تفاعلاً نشطاً من الجمهور، ما يجعلها نقطة تأثير مهمة ضمن فئة التكنولوجيات والتطبيقات.

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Sorting Algorithm #python #datastructures
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Sorting Algorithm #python #datastructures

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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

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