
``bisect`` --- Array bisection algorithm
****************************************

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!).

The following functions are provided:

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

   Locate the proper 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()``.  This assumes that *a* is already sorted.

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

   Similar to ``bisect_left()``, but returns an insertion point which
   comes after (to the right of) any existing entries of *x* in *a*.

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)``.  This assumes
   that *a* is already sorted.

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

   Similar to ``insort_left()``, but inserting *x* in *a* after any
   existing entries of *x*.


Examples
========

The ``bisect()`` function is generally useful for categorizing numeric
data. This example uses ``bisect()`` to look up a letter grade for an
exam total (say) based on a set of ordered numeric breakpoints: 85 and
up is an 'A', 75..84 is a 'B', etc.

>>> grades = "FEDCBA"
>>> breakpoints = [30, 44, 66, 75, 85]
>>> from bisect import bisect
>>> def grade(total):
...           return grades[bisect(breakpoints, total)]
...
>>> grade(66)
'C'
>>> map(grade, [33, 99, 77, 44, 12, 88])
['E', 'A', 'B', 'D', 'F', '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 inefficent design (successive calls to bisect
functions would not "remember" all of the previous key lookups).

Instead, it is better to search a list of precomputed keys to find the
index of the record in question:

   >>> 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)
