mirror of https://github.com/python/cpython
144 lines
5.1 KiB
ReStructuredText
144 lines
5.1 KiB
ReStructuredText
:mod:`bisect` --- Array bisection algorithm
|
|
===========================================
|
|
|
|
.. module:: bisect
|
|
:synopsis: Array bisection algorithms for binary searching.
|
|
.. sectionauthor:: Fred L. Drake, Jr. <fdrake@acm.org>
|
|
.. example based on the PyModules FAQ entry by Aaron Watters <arw@pythonpros.com>
|
|
|
|
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 :mod:`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:
|
|
|
|
|
|
.. function:: 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.
|
|
|
|
|
|
.. function:: bisect_right(a, x, lo=0, hi=len(a))
|
|
bisect(a, x, lo=0, hi=len(a))
|
|
|
|
Similar to :func:`bisect_left`, but returns an insertion point which comes
|
|
after (to the right of) any existing entries of *x* in *a*.
|
|
|
|
|
|
.. function:: 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.
|
|
|
|
Also note that while the fast search step is O(log n), the slower insertion
|
|
step is O(n), so the overall operation is slow.
|
|
|
|
|
|
.. function:: insort_right(a, x, lo=0, hi=len(a))
|
|
insort(a, x, lo=0, hi=len(a))
|
|
|
|
Similar to :func:`insort_left`, but inserting *x* in *a* after any existing
|
|
entries of *x*.
|
|
|
|
Also note that while the fast search step is O(log n), the slower insertion
|
|
step is O(n), so the overall operation is slow.
|
|
|
|
Searching Sorted Lists
|
|
----------------------
|
|
|
|
The above :func:`bisect` functions are useful for finding insertion points, but
|
|
can be tricky or awkward to use for common searching tasks. The following three
|
|
functions show how to transform them into the standard lookups for sorted
|
|
lists::
|
|
|
|
def find(a, key):
|
|
'''Find leftmost item exact equal to the key.
|
|
Raise ValueError if no such item exists.
|
|
|
|
'''
|
|
i = bisect_left(a, key)
|
|
if i < len(a) and a[i] == key:
|
|
return a[i]
|
|
raise ValueError('No item found with key equal to: %r' % (key,))
|
|
|
|
def find_le(a, key):
|
|
'''Find largest item less-than or equal to key.
|
|
Raise ValueError if no such item exists.
|
|
If multiple keys are equal, return the leftmost.
|
|
|
|
'''
|
|
i = bisect_left(a, key)
|
|
if i < len(a) and a[i] == key:
|
|
return a[i]
|
|
if i == 0:
|
|
raise ValueError('No item found with key at or below: %r' % (key,))
|
|
return a[i-1]
|
|
|
|
def find_ge(a, key):
|
|
'''Find smallest item greater-than or equal to key.
|
|
Raise ValueError if no such item exists.
|
|
If multiple keys are equal, return the leftmost.
|
|
|
|
'''
|
|
i = bisect_left(a, key)
|
|
if i == len(a):
|
|
raise ValueError('No item found with key at or above: %r' % (key,))
|
|
return a[i]
|
|
|
|
Other Examples
|
|
--------------
|
|
|
|
.. _bisect-example:
|
|
|
|
The :func:`bisect` function is generally useful for categorizing numeric data.
|
|
This example uses :func:`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 :func:`sorted` function, it does not make sense for the :func:`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)
|
|
|
|
.. seealso::
|
|
|
|
`SortedCollection recipe
|
|
<http://code.activestate.com/recipes/577197-sortedcollection/>`_ that
|
|
encapsulates precomputed keys, allowing straight-forward insertion and
|
|
searching using a *key* function.
|