Clean-up bisect docs.
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Raymond Hettinger
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:mod:`bisect` --- Array bisection algorithm
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===========================================
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.. module:: bisect
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:synopsis: Array bisection algorithms for binary searching.
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.. sectionauthor:: Fred L. Drake, Jr. <fdrake@acm.org>
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.. sectionauthor:: Raymond Hettinger <python at rcn.com>
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.. example based on the PyModules FAQ entry by Aaron Watters <arw@pythonpros.com>
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This module provides support for maintaining a list in sorted order without
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@ -19,103 +19,111 @@ example of the algorithm (the boundary conditions are already right!).
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The following functions are provided:
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.. function:: bisect_left(list, item[, lo[, hi]])
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.. function:: bisect_left(a, x, lo=0, hi=len(a))
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Locate the proper insertion point for *item* in *list* to maintain sorted order.
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The parameters *lo* and *hi* may be used to specify a subset of the list which
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should be considered; by default the entire list is used. If *item* is already
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present in *list*, the insertion point will be before (to the left of) any
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existing entries. The return value is suitable for use as the first parameter
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to ``list.insert()``. This assumes that *list* is already sorted.
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Locate the insertion point for *x* in *a* to maintain sorted order.
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The parameters *lo* and *hi* may be used to specify a subset of the list
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which should be considered; by default the entire list is used. If *x* is
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already present in *a*, the insertion point will be before (to the left of)
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any existing entries. The return value is suitable for use as the first
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parameter to ``list.insert()`` assuming that *a* is already sorted.
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The returned insertion point *i* partitions the array *a* into two halves so
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that ``all(val < x for val in a[lo:i])`` for the left side and
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``all(val >= x for val in a[i:hi])`` for the right side.
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.. function:: bisect_right(list, item[, lo[, hi]])
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.. function:: bisect(list, item[, lo[, hi]])
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.. function:: bisect_right(a, x, lo=0, hi=len(a))
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bisect(a, x, lo=0, hi=len(a))
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Similar to :func:`bisect_left`, but returns an insertion point which comes after
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(to the right of) any existing entries of *item* in *list*.
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Similar to :func:`bisect_left`, but returns an insertion point which comes
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after (to the right of) any existing entries of *x* in *a*.
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The returned insertion point *i* partitions the array *a* into two halves so
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that ``all(val <= x for val in a[lo:i])`` for the left side and
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``all(val > x for val in a[i:hi])`` for the right side.
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.. function:: insort_left(list, item[, lo[, hi]])
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.. function:: insort_left(a, x, lo=0, hi=len(a))
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Insert *item* in *list* in sorted order. This is equivalent to
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``list.insert(bisect.bisect_left(list, item, lo, hi), item)``. This assumes
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that *list* is already sorted.
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Insert *x* in *a* in sorted order. This is equivalent to
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``a.insert(bisect.bisect_left(a, x, lo, hi), x)`` assuming that *a* is
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already sorted. Keep in mind that the O(log n) search is dominated by
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the slow O(n) insertion step.
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Also note that while the fast search step is O(log n), the slower insertion
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step is O(n), so the overall operation is slow.
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.. function:: insort_right(list, item[, lo[, hi]])
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.. function:: insort_right(a, x, lo=0, hi=len(a))
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insort(a, x, lo=0, hi=len(a))
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Similar to :func:`insort_left`, but inserting *item* in *list* after any
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existing entries of *item*.
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Similar to :func:`insort_left`, but inserting *x* in *a* after any existing
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entries of *x*.
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.. seealso::
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`SortedCollection recipe
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<http://code.activestate.com/recipes/577197-sortedcollection/>`_ that uses
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bisect to build a full-featured collection class with straight-forward search
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methods and support for a key-function. The keys are precomputed to save
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unnecessary calls to the key function during searches.
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Also note that while the fast search step is O(log n), the slower insertion
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step is O(n), so the overall operation is slow.
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Searching Sorted Lists
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----------------------
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The above :func:`bisect` functions are useful for finding insertion points, but
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can be tricky or awkward to use for common searching tasks. The following three
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The above :func:`bisect` functions are useful for finding insertion points but
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can be tricky or awkward to use for common searching tasks. The following five
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functions show how to transform them into the standard lookups for sorted
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lists::
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def find(a, key):
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'''Find leftmost item exact equal to the key.
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Raise ValueError if no such item exists.
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def index(a, x):
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'Locate the leftmost value exactly equal to x'
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i = bisect_left(a, x)
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if i != len(a) and a[i] == x:
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return i
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raise ValueError
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'''
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i = bisect_left(a, key)
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if i < len(a) and a[i] == key:
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def find_lt(a, x):
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'Find rightmost value less than x'
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i = bisect_left(a, x)
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if i:
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return a[i-1]
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raise ValueError
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def find_le(a, x):
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'Find rightmost value less than or equal to x'
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i = bisect_right(a, x)
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if i:
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return a[i-1]
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raise ValueError
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def find_gt(a, x):
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'Find leftmost value greater than x'
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i = bisect_right(a, x)
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if i != len(a):
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return a[i]
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raise ValueError('No item found with key equal to: %r' % (key,))
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raise ValueError
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def find_le(a, key):
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'''Find largest item less-than or equal to key.
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Raise ValueError if no such item exists.
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If multiple keys are equal, return the leftmost.
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'''
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i = bisect_left(a, key)
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if i < len(a) and a[i] == key:
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def find_ge(a, x):
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'Find leftmost item greater than or equal to x'
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i = bisect_left(a, x)
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if i != len(a):
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return a[i]
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if i == 0:
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raise ValueError('No item found with key at or below: %r' % (key,))
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return a[i-1]
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raise ValueError
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def find_ge(a, key):
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'''Find smallest item greater-than or equal to key.
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Raise ValueError if no such item exists.
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If multiple keys are equal, return the leftmost.
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'''
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i = bisect_left(a, key)
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if i == len(a):
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raise ValueError('No item found with key at or above: %r' % (key,))
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return a[i]
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Other Examples
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--------------
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.. _bisect-example:
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The :func:`bisect` function is generally useful for categorizing numeric data.
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This example uses :func:`bisect` to look up a letter grade for an exam total
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(say) based on a set of ordered numeric breakpoints: 85 and up is an 'A', 75..84
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is a 'B', etc.
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The :func:`bisect` function can be useful for numeric table lookups. This
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example uses :func:`bisect` to look up a letter grade for an exam score (say)
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based on a set of ordered numeric breakpoints: 90 and up is an 'A', 80 to 89 is
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a 'B', and so on::
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>>> grades = "FEDCBA"
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>>> breakpoints = [30, 44, 66, 75, 85]
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>>> from bisect import bisect
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>>> def grade(total):
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... return grades[bisect(breakpoints, total)]
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>>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'):
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... i = bisect(breakpoints, score)
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... return grades[i]
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...
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>>> grade(66)
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'C'
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>>> map(grade, [33, 99, 77, 44, 12, 88])
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['E', 'A', 'B', 'D', 'F', 'A']
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>>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]]
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['F', 'A', 'C', 'C', 'B', 'A', 'A']
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Unlike the :func:`sorted` function, it does not make sense for the :func:`bisect`
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functions to have *key* or *reversed* arguments because that would lead to an
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@ -137,9 +145,3 @@ of the record in question::
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>>> data[bisect_left(keys, 8)]
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('yellow', 8)
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.. seealso::
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`SortedCollection recipe
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<http://code.activestate.com/recipes/577197-sortedcollection/>`_ that
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encapsulates precomputed keys, allowing straight-forward insertion and
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searching using a *key* function.
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