Saralash

Saralash

Saralash ko‘p masalani soddalashtiradi: tenglar yonma-yon, eng kichiklar boshida.

a.sort()                           # o‘sish tartibida
a.sort(reverse=True)
people.sort(key=lambda p: (-p.score, p.name))

Python’ning sort — O(n log n) va barqaror (teng elementlar tartibi saqlanadi).

Saralangandan keyin: ikki ko‘rsatkich, ikkilik qidiruv, qo‘shni elementlarni solishtirish.

Bo‘l va hukmronlik qil

Bo‘l va hukmronlik qil: masalani ikki (yoki bir nechta) teng qismga bo‘lamiz, har birini rekursiv yechamiz, so‘ng natijalarni birlashtiramiz.

Birlashtirib saralash (merge sort) — O(n log n)

def merge_sort(a):
    if len(a) <= 1:
        return a
    mid = len(a) // 2
    left, right = merge_sort(a[:mid]), merge_sort(a[mid:])
    out, i, j = [], 0, 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            out.append(left[i]); i += 1
        else:
            out.append(right[j]); j += 1
    return out + left[i:] + right[j:]

Boshqa misollar

• Ikkilik daraja: aⁿ = (a^(n/2))² — O(log n).
• Inversiyalar sonini sanash (merge sort ichida).
• Ikkilik qidiruv ham shu g‘oyaning bir turi.