递归小练习

算法入门，看到递归，做了几个小练习。

1. 递归思路

1.1 找准基线条件（停止递归）
1.2 明确函数功能，知道写的函数究竟是干什么的

2. 求解最大（小）值

def get_max_value(lst):
    if len(lst) == 2: #基线条件
        return lst[0] if lst[0] >= lst[1] else lst[1]
    return lst[0] if lst[0]>get_max_value(lst[1:]) else get_max_value(lst[1:])
    
if __name__ == "__main__":
    li = [8, 4, 5, 7, 1, 3, 6, 2]
    print("max value:", get_max_value(li))

max value: 8
Process finished with exit code 0

3. 列表求和

def sum_list(lst):
    if len(lst) == 0:
        return 0
    return lst[0] + sum_list(lst[1:])

if __name__ == "__main__":
    li = [8, 4, 5, 7, 1, 3, 6, 2]
    print('The result of sum：')
    print(sum_list(li))

The result of sum：
36
Process finished with exit code 0

4. 快速排序

def quick_sort(lst):
    if len(lst) <= 1:
        return lst
    # base_value = lst[-1]#选取最后一个元素作为基准值
    mid_index = int(len(lst)/2)
    base_value = lst[mid_index]#选取中间值作为基准值
    rest = lst[0:mid_index] + lst[mid_index+1:]
    smaller = [i for i in rest if i < base_value]
    larger = [j for j in rest if j >= base_value]
    return quick_sort(smaller) + [base_value] + quick_sort(larger)

if __name__ == "__main__":
    li = [8, 4, 5, 7, 1, 3, 6, 2]

    print("排序后的队列:", quick_sort(li))

排序后的队列: [1, 2, 3, 4, 5, 6, 7, 8]
Process finished with exit code 0

5. 合并排序

def merge_sort(lst):
    if len(lst) < 2:
        return lst
    #分的过程
    mid_index = int(len(lst) / 2)
    left = lst[:mid_index]
    right = lst[mid_index:]
    left = merge_sort(left)
    right = merge_sort(right)

    #治的过程
    result = []
    while left and right:
        if left[0] <= right[0]:
            result.append(left.pop(0))
        else:
            result.append(right.pop(0))
    if left:
        result += left
    if right:
        result += right

    return result
    
if __name__ == "__main__":
    li = [8, 4, 5, 7, 1, 3, 6, 2]

    print("排序后的队列:", merge_sort(li))

排序后的队列: [1, 2, 3, 4, 5, 6, 7, 8]
Process finished with exit code 0

6. 二分查找

def er_fen(min_index, max_index, target):
    mid_index = int((min_index+max_index)/2)
    if a[mid_index] == target:
        return mid_index
    if a[mid_index]>target:
        return er_fen(min_index, mid_index, target)
    if a[mid_index]<target:
        return er_fen(mid_index, max_index, target)
        
if __name__ == "__main__":
    a = [1, 3, 6, 7, 9, 10, 100, 1000, 2000, 100000]
    print(er_fen(0, len(a)-1, 1000))

7
Process finished with exit code 0

7. 有一长为1680，宽为640的土地，现要求将其分割成若干正方形，求解正方形的最大边长。

def max_length(a, b):
    if a % b == 0:
        return b
    else:
        return max_length(b, a-int(a/b)*b)

if __name__ == "__main__":
    print('最大边长：')
    print(max_length(1680, 640))

最大边长：
80
Process finished with exit code 0