bisect — Algorithme de bissection de listes

Code source : 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 linear searches or frequent resorting.

The module is called bisect because it uses a basic bisection algorithm to do its work. Unlike other bisection tools that search for a specific value, the functions in this module are designed to locate an insertion point. Accordingly, the functions never call an __eq__() method to determine whether a value has been found. Instead, the functions only call the __lt__() method and will return an insertion point between values in an array.

Les fonctions suivantes sont fournies :

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

Trouve le point d'insertion de x dans a permettant de conserver l'ordre. Les paramètres lo et hi permettent de limiter les emplacements à vérifier dans la liste, par défaut toute la liste est utilisée. Si x est déjà présent dans a, le point d'insertion proposé sera avant (à gauche) de l'entrée existante. Si a est déjà triée, la valeur renvoyée peut directement être utilisée comme premier paramètre de list.insert().

The returned insertion point ip partitions the array a into two slices such that all(elem < x for elem in a[lo : ip]) is true for the left slice and all(elem >= x for elem in a[ip : hi]) is true for the right slice.

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 and no key function is called.

Modifié dans la version 3.10: ajout du paramètre key.

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 ip partitions the array a into two slices such that all(elem <= x for elem in a[lo : ip]) is true for the left slice and all(elem > x for elem in a[ip : hi]) is true for the right slice.

Modifié dans la version 3.10: ajout du paramètre key.

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

Insère x dans a en préservant l'ordre.

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.

Modifié dans la version 3.10: ajout du paramètre key.

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.

Modifié dans la version 3.10: ajout du paramètre key.

Notes sur la performance

Pour écrire du code sensible à la performance utilisant bisect() et insort(), prenez en compte ces quelques considérations :

  • La bissection est une bonne idée pour rechercher une plage de valeurs. Pour une seule valeur, mieux vaut un dictionnaire.

  • 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).

Voir aussi

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

  • SortedCollection recipe utilise le module bisect pour construire une classe collection exposant des méthodes de recherches naturelles et gérant une fonction clef. Les clefs sont pré-calculées pour économiser des appels inutiles à la fonction clef durant les recherches.

Chercher dans des listes triées

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

Exemples

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)