"bisect" --- algorytm bisekcji tablicy
**************************************

**Source code:** Lib/bisect.py

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

Ten moduł dostarcza wsparcia dla utrzymywania listy w posortowanym
porządku bez konieczności sortowania listy po każdym wstawieniu. Dla
długich list elementów o kosztownych operacjach porównania, to może
być polepszenie względem bardziej typowego podejścia. Moduł jest zwany
"bisect" ponieważ używa używa podstawowego algorytmu bisekcji aby
wykonać swoją pracę. Kod źródłowy może być najbardziej użyteczny jako
działający przykład algorytmu (warunki brzegowe są już od razu
poprawne!).

Następujące zadania są dostarczone:

bisect.bisect_left(a, x, lo=0, hi=len(a))

   Locate the insertion point for *x* in *a* to maintain sorted order.
   The parameters *lo* and *hi* may be used to specify a subset of the
   list which should be considered; by default the entire list is
   used.  If *x* is already present in *a*, the insertion point will
   be before (to the left of) any existing entries.  The return value
   is suitable for use as the first parameter to "list.insert()"
   assuming that *a* is already sorted.

   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.

bisect.bisect_right(a, x, lo=0, hi=len(a))
bisect.bisect(a, x, lo=0, hi=len(a))

   Podobna do funkcji "bisect_left()" ale zwraca punkt wstawiania
   który jest po (po prawej stronie od) jakichkolwiek wpisów *x* w
   *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.

bisect.insort_left(a, x, lo=0, hi=len(a))

   Insert *x* in *a* in sorted order.  This is equivalent to
   "a.insert(bisect.bisect_left(a, x, lo, hi), x)" assuming that *a*
   is already sorted.  Keep in mind that the O(log n) search is
   dominated by the slow O(n) insertion step.

bisect.insort_right(a, x, lo=0, hi=len(a))
bisect.insort(a, x, lo=0, hi=len(a))

   Podobna do funkcji "insort_left()", ale wstawiając *x* w *a* po
   jakichkolwiek wpisach *x*.

Zobacz także:

  SortedCollection recipe that 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.


Searching Sorted Lists
======================

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


Other 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']

Unlike the "sorted()" function, it does not make sense for the
"bisect()" functions to have *key* or *reversed* arguments because
that would lead to an inefficient design (successive calls to bisect
functions would not "remember" all of the previous key lookups).

Zamiast tego, lepiej jest przeszukać listę uprzednio obliczonych
wartości kluczowych aby odnaleźć indeks poszukiwanego zapisu:

   >>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)]
   >>> data.sort(key=lambda r: r[1])
   >>> keys = [r[1] for r in data]         # precomputed 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)
