bisect — Array bisection algorithm

Вихідний код: Lib/bisect.py

This module provides support for maintaining a list in sorted order without having to sort the list after each insertion. For long lists of items with expensive comparison operations, this can be an improvement over the more common approach. The module is called bisect because it uses a basic bisection algorithm to do its work. The source code may be most useful as a working example of the algorithm (the boundary conditions are already right!).

Передбачені такі функції:

bisect.bisect_left(a, x, lo=0, hi=len(a))

Знайдіть точку вставки для x у a, щоб зберегти відсортований порядок. Параметри lo і hi можуть використовуватися для визначення підмножини списку, яку слід враховувати; за замовчуванням використовується весь список. Якщо x уже присутній у a, точка вставки буде перед будь-якими існуючими записами (зліва від них). Повернене значення придатне для використання як перший параметр для list.insert() за умови, що a вже відсортовано.

The returned insertion point i partitions the array a into two halves so that all(val < x for val in a[lo:i]) for the left side and all(val >= x for val in a[i:hi]) for the right side.

bisect.bisect_right(a, x, lo=0, hi=len(a))
bisect.bisect(a, x, lo=0, hi=len(a))

Similar to bisect_left(), but returns an insertion point which comes after (to the right of) any existing entries of x in a.

The returned insertion point i partitions the array a into two halves so that all(val <= x for val in a[lo:i]) for the left side and all(val > x for val in a[i:hi]) for the right side.

bisect.insort_left(a, x, lo=0, hi=len(a))

Insert x in a in sorted order. This is equivalent to a.insert(bisect.bisect_left(a, x, lo, hi), x) assuming that a is already sorted. Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.

bisect.insort_right(a, x, lo=0, hi=len(a))
bisect.insort(a, x, lo=0, hi=len(a))

Similar to insort_left(), but inserting x in a after any existing entries of x.

Дивись також

SortedCollection recipe that uses bisect to build a full-featured collection class with straight-forward search methods and support for a key-function. The keys are precomputed to save unnecessary calls to the key function during searches.

Пошук у відсортованих списках

The above bisect() functions are useful for finding insertion points but can be tricky or awkward to use for common searching tasks. The following five functions show how to transform them into the standard lookups for sorted lists:

def index(a, x):
    'Locate the leftmost value exactly equal to x'
    i = bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return i
    raise ValueError

def find_lt(a, x):
    'Find rightmost value less than x'
    i = bisect_left(a, x)
    if i:
        return a[i-1]
    raise ValueError

def find_le(a, x):
    'Find rightmost value less than or equal to x'
    i = bisect_right(a, x)
    if i:
        return a[i-1]
    raise ValueError

def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bisect_right(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

def find_ge(a, x):
    'Find leftmost item greater than or equal to x'
    i = bisect_left(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

Other Examples

The bisect() function can be useful for numeric table lookups. This example uses bisect() to look up a letter grade for an exam score (say) based on a set of ordered numeric breakpoints: 90 and up is an „A“, 80 to 89 is a „B“, and so on:

>>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'):
...     i = bisect(breakpoints, score)
...     return grades[i]
...
>>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]]
['F', 'A', 'C', 'C', 'B', 'A', 'A']

Unlike the sorted() function, it does not make sense for the bisect() functions to have key or reversed arguments because that would lead to an inefficient design (successive calls to bisect functions would not «remember» all of the previous key lookups).

Instead, it is better to search a list of precomputed keys to find the index of the record in question:

>>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)]
>>> data.sort(key=lambda r: r[1])
>>> keys = [r[1] for r in data]         # precomputed list of keys
>>> data[bisect_left(keys, 0)]
('black', 0)
>>> data[bisect_left(keys, 1)]
('blue', 1)
>>> data[bisect_left(keys, 5)]
('red', 5)
>>> data[bisect_left(keys, 8)]
('yellow', 8)