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

**소스 코드:** 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!).

다음과 같은 함수가 제공됩니다:

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

   정렬된 순서를 유지하도록 *a*에 *x*를 삽입할 위치를 찾습니다. 매개
   변수 *lo* 와 *hi*는 고려해야 할 리스트의 부분집합을 지정하는 데 사
   용될 수 있습니다; 기본적으로 전체 리스트가 사용됩니다. *x*가 *a*에
   이미 있으면, 삽입 위치는 기존 항목 앞(왼쪽)이 됩니다. 반환 값은 *a*
   가 이미 정렬되었다고 가정할 때 "list.insert()"의 첫 번째 매개 변수
   로 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: *key* 매개 변수를 추가했습니다.

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

   "bisect_left()"와 비슷하지만, *a*에 있는 *x*의 기존 항목 뒤(오른쪽)
   에 오는 삽입 위치를 반환합니다.

   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: *key* 매개 변수를 추가했습니다.

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: *key* 매개 변수를 추가했습니다.

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

   "insort_left()"와 비슷하지만, *a*에 *x*를 *x*의 기존 항목 다음에 삽
   입합니다.

   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: *key* 매개 변수를 추가했습니다.


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.

  * bisect를 사용하여 직접적인 검색 메서드와 키 함수 지원을 포함하는
    완전한 기능을 갖춘 컬렉션 클래스를 만드는 SortedCollection recipe.
    검색 중에 불필요한 키 함수 호출을 피하고자 키는 미리 계산됩니다.


정렬된 리스트 검색하기
======================

위의 bisect functions는 삽입 위치를 찾는 데 유용하지만, 일반적인 검색
작업에 사용하기가 까다롭거나 어색할 수 있습니다. 다음 다섯 함수는 정렬
된 리스트에 대한 표준 조회로 변환하는 방법을 보여줍니다:

   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


예제
====

"bisect()" 함수는 숫자 테이블 조회에 유용할 수 있습니다. 이 예제는
"bisect()"를 사용하여 (가령) 시험 점수에 대한 문자 등급을 조회하는데,
정렬된 숫자 경계점 집합에 기반합니다: 90 이상은 'A', 80에서 89는 'B'
등입니다:

   >>> 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')]

키 함수가 비싸면, 미리 계산된 키 목록을 검색하여 레코드의 인덱스를 찾
으면 반복돠는 함수 호출을 피할 수 있습니다:

   >>> 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)
