python的算法：二分法查找（2）--bisect模块

Python 有一个 bisect 模块，用于维护有序列表。bisect 模块实现了一个算法用于插入元素到有序列表。在一些情况下，这比反复排序列表或构造一个大的列表再排序的效率更高。Bisect 是二分法的意思，这里使用二分法来排序，它会将一个元素插入到一个有序列表的合适位置，这使得不需要每次调用 sort 的方式维护有序列表。

先看一个最简单的用法：

import bisect

l=[1,3,3,6,8,12,15]
x=4

left_insert_point=bisect.bisect_left(l,x)
right_insert_point=bisect.bisect_right(l,x)
print(left_insert_point)
print(right_insert_point)

两个的结果，都是3

import bisect

l=[1,3,3,6,8,12,15]
x=3

left_insert_point=bisect.bisect_left(l,x)
right_insert_point=bisect.bisect_right(l,x)
print(left_insert_point)
print(right_insert_point)

结果分别是1，3

bisect的模块不复杂，现在，我们先看bisect_left这个函数：

def bisect_left(a, x, lo=0, hi=None):
    """Return the index where to insert item x in list a, assuming a is sorted.
    The return value i is such that all e in a[:i] have e < x, and all e in
    a[i:] have e >= x.  So if x already appears in the list, a.insert(x) will
    insert just before the leftmost x already there.
    Optional args lo (default 0) and hi (default len(a)) bound the
    slice of a to be searched.
    """

    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if a[mid] < x: lo = mid+1
        else: hi = mid
    return lo

这里，假定的，就是，a是一个有序的数组。

假设，我们有这么一个数组：

p=[1,4,3,3,6,8,12,15,0,9,3,28]

这实际上，p不是有序的e。

根据bisect_left的算法，每次都是二分。如果查找4的插入位置，当找到3的时候，就停止找了。所以，返回是4.

再看bisect_right:

def bisect_right(a, x, lo=0, hi=None):
    """Return the index where to insert item x in list a, assuming a is sorted.
    The return value i is such that all e in a[:i] have e <= x, and all e in
    a[i:] have e > x.  So if x already appears in the list, a.insert(x) will
    insert just after the rightmost x already there.
    Optional args lo (default 0) and hi (default len(a)) bound the
    slice of a to be searched.
    """

    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if x < a[mid]: hi = mid
        else: lo = mid+1
    return lo

类似的，不多做描述。