Clean-up bisect docs.

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Raymond Hettinger 2010-09-01 19:42:36 +00:00
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:mod:`bisect` --- Array bisection algorithm
===========================================
.. module:: bisect
:synopsis: Array bisection algorithms for binary searching.
.. sectionauthor:: Fred L. Drake, Jr. <fdrake@acm.org>
.. sectionauthor:: Raymond Hettinger <python at rcn.com>
.. 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
@ -19,103 +19,111 @@ example of the algorithm (the boundary conditions are already right!).
The following functions are provided:
.. function:: bisect_left(list, item[, lo[, hi]])
.. function:: bisect_left(a, x, lo=0, hi=len(a))
Locate the proper insertion point for *item* in *list* 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 *item* is already
present in *list*, 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 *list* is already sorted.
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.
.. function:: bisect_right(list, item[, lo[, hi]])
.. function:: bisect(list, item[, lo[, hi]])
.. 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 *item* in *list*.
Similar to :func:`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.
.. function:: insort_left(list, item[, lo[, hi]])
.. function:: insort_left(a, x, lo=0, hi=len(a))
Insert *item* in *list* in sorted order. This is equivalent to
``list.insert(bisect.bisect_left(list, item, lo, hi), item)``. This assumes
that *list* is already sorted.
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.
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(list, item[, lo[, hi]])
.. 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 *item* in *list* after any
existing entries of *item*.
Similar to :func:`insort_left`, but inserting *x* in *a* after any existing
entries of *x*.
.. seealso::
`SortedCollection recipe
<http://code.activestate.com/recipes/577197-sortedcollection/>`_ 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.
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
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 five
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.
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
'''
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,))
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_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.
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
'''
i = bisect_left(a, key)
if i == len(a):
raise ValueError('No item found with key at or above: %r' % (key,))
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
--------------
.. _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.
The :func:`bisect` function can be useful for numeric table lookups. This
example uses :func:`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::
>>> grades = "FEDCBA"
>>> breakpoints = [30, 44, 66, 75, 85]
>>> from bisect import bisect
>>> def grade(total):
... return grades[bisect(breakpoints, total)]
>>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'):
... i = bisect(breakpoints, score)
... return grades[i]
...
>>> grade(66)
'C'
>>> map(grade, [33, 99, 77, 44, 12, 88])
['E', 'A', 'B', 'D', 'F', 'A']
>>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]]
['F', 'A', 'C', 'C', 'B', 'A', '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
@ -137,9 +145,3 @@ of the record in question::
>>> 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.