bisect — 배열 이진 분할 알고리즘

소스 코드: Lib/bisect.py

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이 모듈은 정렬된 리스트를 삽입 후에 다시 정렬할 필요 없도록 관리할 수 있도록 지원합니다. 값비싼 비교 연산이 포함된 항목의 긴 리스트의 경우, 이는 일반적인 방법에 비해 개선된 것입니다. 이 모듈은 기본적인 이진 분할 알고리즘을 사용하기 때문에 bisect라고 불립니다. 소스 코드는 알고리즘의 실제 예로서 가장 유용할 수 있습니다 (경계 조건은 이미 옳습니다!).

다음과 같은 함수가 제공됩니다:

bisect.bisect_left(a, x, lo=0, hi=len(a), *, key=None)

정렬된 순서를 유지하도록 a에 x를 삽입할 위치를 찾습니다. 매개 변수 lo 와 hi는 고려해야 할 리스트의 부분집합을 지정하는 데 사용될 수 있습니다; 기본적으로 전체 리스트가 사용됩니다. x가 a에 이미 있으면, 삽입 위치는 기존 항목 앞(왼쪽)이 됩니다. 반환 값은 a가 이미 정렬되었다고 가정할 때 list.insert()의 첫 번째 매개 변수로 사용하기에 적합합니다.

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.

key specifies a key function of one argument that is used to extract a comparison key from each element in the array. To support searching complex records, the key function is not applied to the x value.

If key is None, the elements are compared directly with no intervening function call.

버전 3.10에서 변경: Added the key parameter.

bisect.bisect_right(a, x, lo=0, hi=len(a), *, key=None)

bisect.bisect(a, x, lo=0, hi=len(a), *, key=None)

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.

key specifies a key function of one argument that is used to extract a comparison key from each element in the array. To support searching complex records, the key function is not applied to the x value.

If key is None, the elements are compared directly with no intervening function call.

버전 3.10에서 변경: Added the key parameter.

bisect.insort_left(a, x, lo=0, hi=len(a), *, key=None)

Insert x in a in sorted order.

This function first runs bisect_left() to locate an insertion point. Next, it runs the insert() method on a to insert x at the appropriate position to maintain sort order.

To support inserting records in a table, the key function (if any) is applied to x for the search step but not for the insertion step.

Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.

버전 3.10에서 변경: Added the key parameter.

bisect.insort_right(a, x, lo=0, hi=len(a), *, key=None)

bisect.insort(a, x, lo=0, hi=len(a), *, key=None)

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

This function first runs bisect_right() to locate an insertion point. Next, it runs the insert() method on a to insert x at the appropriate position to maintain sort order.

To support inserting records in a table, the key function (if any) is applied to x for the search step but not for the insertion step.

Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.

버전 3.10에서 변경: Added the key parameter.

Performance Notes

When writing time sensitive code using bisect() and insort(), keep these thoughts in mind:

• Bisection is effective for searching ranges of values. For locating specific values, dictionaries are more performant.

• The insort() functions are O(n) because the logarithmic search step is dominated by the linear time insertion step.

• The search functions are stateless and discard key function results after they are used. Consequently, if the search functions are used in a loop, the key function may be called again and again on the same array elements. If the key function isn’t fast, consider wrapping it with functools.cache() to avoid duplicate computations. Alternatively, consider searching an array of precomputed keys to locate the insertion point (as shown in the examples section below).

더 보기

• Sorted Collections is a high performance module that uses bisect to managed sorted collections of data.

• The SortedCollection recipe 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.

정렬된 리스트 검색하기

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

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']

The bisect() and insort() functions also work with lists of tuples. The key argument can serve to extract the field used for ordering records in a table:

>>> from collections import namedtuple
>>> from operator import attrgetter
>>> from bisect import bisect, insort
>>> from pprint import pprint

>>> Movie = namedtuple('Movie', ('name', 'released', 'director'))

>>> movies = [
...     Movie('Jaws', 1975, 'Spielberg'),
...     Movie('Titanic', 1997, 'Cameron'),
...     Movie('The Birds', 1963, 'Hitchcock'),
...     Movie('Aliens', 1986, 'Cameron')
... ]

>>> # Find the first movie released after 1960
>>> by_year = attrgetter('released')
>>> movies.sort(key=by_year)
>>> movies[bisect(movies, 1960, key=by_year)]
Movie(name='The Birds', released=1963, director='Hitchcock')

>>> # Insert a movie while maintaining sort order
>>> romance = Movie('Love Story', 1970, 'Hiller')
>>> insort(movies, romance, key=by_year)
>>> pprint(movies)
[Movie(name='The Birds', released=1963, director='Hitchcock'),
 Movie(name='Love Story', released=1970, director='Hiller'),
 Movie(name='Jaws', released=1975, director='Spielberg'),
 Movie(name='Aliens', released=1986, director='Cameron'),
 Movie(name='Titanic', released=1997, director='Cameron')]

If the key function is expensive, it is possible to avoid repeated function calls by searching a list of precomputed keys to find the index of a record:

>>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)]
>>> data.sort(key=lambda r: r[1])       # Or use operator.itemgetter(1).
>>> keys = [r[1] for r in data]         # Precompute a 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)