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| -rw-r--r-- | Doc/library/bisect.rst | 122 |
1 files changed, 62 insertions, 60 deletions
diff --git a/Doc/library/bisect.rst b/Doc/library/bisect.rst index 43354ae..8bf0949 100644 --- a/Doc/library/bisect.rst +++ b/Doc/library/bisect.rst @@ -4,6 +4,7 @@ .. 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 @@ -18,13 +19,16 @@ 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. + 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()``. This assumes that *a* is already sorted. + 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(a, x, lo=0, hi=len(a)) bisect(a, x, lo=0, hi=len(a)) @@ -32,16 +36,16 @@ The following functions are provided: 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(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. - + ``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. .. function:: insort_right(a, x, lo=0, hi=len(a)) insort(a, x, lo=0, hi=len(a)) @@ -49,71 +53,75 @@ The following functions are provided: 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. +.. 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. + 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. - - ''' - i = bisect_left(a, key) - if i < len(a) and a[i] == key: + 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('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. + raise ValueError - ''' - i = bisect_left(a, key) - if i < len(a) and a[i] == key: + 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] - 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. + raise ValueError - ''' - 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. +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 @@ -135,9 +143,3 @@ 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. |