من O(n²) إلى O(n)

def pair_slow(prices, target):          # O(n²): كل زوج    for i in range(len(prices)):        for j in range(i + 1, len(prices)):            if prices[i] + prices[j] == target:                return prices[i], prices[j]    return None def pair_fast(prices, target):          # O(n): مرور واحد وقاموس    seen = {}    for p in prices:        need = target - p        if need in seen:                # O(1)            return need, p        seen[p] = True    return None prices = [35, 18, 90, 45, 150, 60, 75, 40, 28, 55]print(pair_slow(prices, 100), pair_fast(prices, 100))

import time def pair_slow(prices, target):    for i in range(len(prices)):        for j in range(i + 1, len(prices)):            if prices[i] + prices[j] == target:                return True    return False def pair_fast(prices, target):    seen = set()    for p in prices:        if target - p in seen:            return True        seen.add(p)    return False prices = list(range(1, 2001, 2))     # ألف عدد فرديfor f in (pair_slow, pair_fast):    t = time.perf_counter()    f(prices, 1)                     # لا يوجد زوج مجموعه 1: الحالة الأسوأ    print(f.__name__, round((time.perf_counter() - t) * 1000, 1), "ms")

import randomrandom.seed(2)sales = [random.randint(100, 900) for _ in range(365)]k = 7 def best_slow(a, k):                 # O(n·k)    return max(sum(a[i:i + k]) for i in range(len(a) - k + 1)) def best_fast(a, k):                 # O(n)    window = sum(a[:k])    best = window    for i in range(k, len(a)):        window += a[i] - a[i - k]    # أضف الداخل واطرح الخارج        best = max(best, window)    return best print(best_slow(sales, k), best_fast(sales, k))

sales = [120, 340, 200, 510, 80, 430, 260, 150] prefix = [0]for s in sales:    prefix.append(prefix[-1] + s)      # O(n) مرة واحدةprint(prefix) def range_sum(i, j):                   # مجموع الأيام من i إلى j شاملة: O(1)    return prefix[j + 1] - prefix[i] print(range_sum(2, 5), sum(sales[2:6]))

def pair_sorted(a, target):     # O(n) وذاكرة O(1)    i, j = 0, len(a) - 1    while i < j:        s = a[i] + a[j]        if s == target:            return a[i], a[j]        if s < target:            i += 1        else:            j -= 1    return None print(pair_sorted([18, 28, 35, 40, 45, 55, 60, 75, 90, 150], 100))