"bisect" --- 배열 이진 분할 알고리즘
************************************

**소스 코드:** Lib/bisect.py

======================================================================

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 분
할 알고리즘을 사용하기 때문에 "bisect"라고 불립니다. 소스 코드는 알고
리즘의 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 *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: 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)
