"bisect" --- Array bisection algorithm
**************************************

**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.

Note:

  The functions in this module are not thread-safe. If multiple
  threads concurrently use "bisect" functions on the same sequence,
  this may result in undefined behaviour. Likewise, if the provided
  sequence is mutated by a different thread while a "bisect" function
  is operating on it, the result is undefined. For example, using
  "insort_left()" on the same list from multiple threads may result in
  the list becoming unsorted.

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)
   ...     i = bisect([60, 70, 80, 90], score)
   ...     return "FDCBA"[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)
