Clean-up bisect docs.

* Document the post conditions for bisect_left() and bisect_right().
* Fix the grades example to use more obvious breakpoints
  and to use a list comprehension instead of map() which returns
  an iterator in Py3.x.
* Improve and expand the examples of searching sorted lists.
* Issue 4356 -- move up reference to the SortedCollection recipe.

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.