Python二分查找

1. 非递归实现

def binary_search(alist, item):
    first = 0
    last = len(alist) - 1
    while first <= last:
        mid_point = (first+last)//2
        if alist[mid_point] == item:
            return True
        elif item < alist[mid_point]:
            last = mid_point - 1
        else:
            first = mid_point + 1
    return False

testlist = [0, 1, 2, 8, 13, 17, 19, 32, 42]
print(binary_search(testlist, 3))
print(binary_search(testlist, 13))

False
True

2. 递归实现

def binary_search2(alist, item):
    if len(alist) == 0:
        return False
    else:
        mid_point = len(alist)//2
        if alist[mid_point] == item:
            return True
        else:
            if item < alist[mid_point]:
                return binary_search2(alist[:mid_point], item)
            else:
                return binary_search2(alist[mid_point+1:], item)

testlist2 = [0, 1, 2, 8, 13, 17, 19, 32, 42]
print(binary_search2(testlist2, 3))
print(binary_search2(testlist2, 13))

总结：

最优时间复杂度	最坏时间复杂度
$O(1)$O(1)	$O(logn)$O(logn)