求平方根的三种方法

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def close_method(num, precision=1e-4):#这里的精确度太高会导致程序死循环#趋近法
    result = 0.0
    i = 0.00001
    while abs(result ** 2 - num) > precision:
        result += i
        
        if result ** 2 > num:#超过目标值就缩小增量（课本上没有这步）
            i = -i / 10
            result += i
        
    return result

def binary_search_method(num, precision=1e-6):#二分法
    low, high = 0, num
    while high - low > precision:
        mid = (low + high) / 2
        if mid ** 2 > num:
            high = mid
        else:
            low = mid
    return low

def newton_iteration_method(num, precision=1e-6):#牛顿法
    x = num
    while abs(x * x - num) > precision:
        x = 0.5 * (x + num / x)
    return x

while True:
    try:
        input_num = float(input("请输入一个正整数（输入小于等于0的数退出程序）: "))
        if input_num <= 0:
            print("程序退出")
            break
        close_result = close_method(input_num)
        binary_result = binary_search_method(input_num)
        newton_result = newton_iteration_method(input_num)
        print(f"趋近法计算的平方根: {close_result}")
        print(f"二分查找法计算的平方根: {binary_result}")
        print(f"牛顿迭代法计算的平方根: {newton_result}")
    except ValueError:
        print("输入无效，请输入一个数字。")

分解质因数

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def prime_factorize(n, factor=2):
    if n < 2:
        return []
    if n % factor == 0:
        return [factor] + prime_factorize(n // factor, factor)
    return prime_factorize(n, factor + 1)


num = int(input("请输入一个正整数: "))
factors = prime_factorize(num)
result = '*'.join(map(str, factors))
print(f"{num}={result}")

分治法找最大最小数

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import random


def find_max_min(arr, low, high):
    if low == high:
        return arr[low], arr[low]
    elif high - low == 1:
        if arr[low] < arr[high]:
            return arr[high], arr[low]
        else:
            return arr[low], arr[high]
    else:
        '''分治法的递归过程'''
        mid = (low + high) // 2
        max1, min1 = find_max_min(arr, low, mid)
        max2, min2 = find_max_min(arr, mid + 1, high)
        return max(max1, max2), min(min1, min2)


n = int(input("请输入要生成的随机数的数量: "))
arr = [random.randint(1, 1000) for _ in range(n)]#生成的随机数列表
max_num, min_num = find_max_min(arr, 0, len(arr) - 1)
print(f"生成的随机数列表: {arr}")
print(f"最大数: {max_num}, 最小数: {min_num}")