二分查找法

二分查找是一个基础的算法，也是面试中常考的一个知识点。二分查找就是将查找的键和子数组的中间键作比较，如果被查找的键小于中间键，就在左子数组继续查找；如果大于中间键，就在右子数组中查找，否则中间键就是要找的元素。

使用循环和递归两种方法：

import time


def mytime(func):
    def inner(*args, **kwargs):
        t1 = time.time()
        func(*args, **kwargs)
        t2 = time.time()
        print('time costed is {}.'.format(t2-t1))
    return inner


@mytime
def bin_ser(data, li):
    if len(li) > 0:
        left = 0
        right = len(li) - 1
    else:
        print('list is too short!')
        return

    while left < right:
        mid = (left + right) // 2
        if li[mid] > data:
            right = mid
        elif li[mid] < data:
            left = mid
        else:
            print('1-the position is {}.'.format(mid))
            break


@mytime
def bin_ser2(data, li):
    def bin_mid(left, mid, right):
        if li[mid] > data:
            right = mid
        elif li[mid] < data:
            left = mid
        else:
            print('2-the position is {}.'.format(mid))
            left = right
        mid = (left + right) // 2
        if left < right:
            return bin_mid(left, mid, right)
    left = 0
    right = len(li) - 1
    mid = (left + right) // 2
    bin_mid(left, mid, right)

l = list(range(40, 10000))
bin_ser(42, l)
bin_ser2(42, l)