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diff --git a/devdocs/python~3.12/library%2Fbisect.html b/devdocs/python~3.12/library%2Fbisect.html new file mode 100644 index 00000000..467c1bf0 --- /dev/null +++ b/devdocs/python~3.12/library%2Fbisect.html @@ -0,0 +1,101 @@ + <span id="bisect-array-bisection-algorithm"></span><h1>bisect — Array bisection algorithm</h1> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.12/Lib/bisect.py">Lib/bisect.py</a></p> <p>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 linear searches or frequent resorting.</p> <p>The module is called <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code>bisect</code></a> because it uses a basic bisection algorithm to do its work. Unlike other bisection tools that search for a specific value, the functions in this module are designed to locate an insertion point. Accordingly, the functions never call an <a class="reference internal" href="../reference/datamodel#object.__eq__" title="object.__eq__"><code>__eq__()</code></a> method to determine whether a value has been found. Instead, the functions only call the <a class="reference internal" href="../reference/datamodel#object.__lt__" title="object.__lt__"><code>__lt__()</code></a> method and will return an insertion point between values in an array.</p> <p id="bisect-functions">The following functions are provided:</p> <dl class="py function"> <dt class="sig sig-object py" id="bisect.bisect_left"> +<code>bisect.bisect_left(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dd> +<p>Locate the insertion point for <em>x</em> in <em>a</em> to maintain sorted order. The parameters <em>lo</em> and <em>hi</em> may be used to specify a subset of the list which should be considered; by default the entire list is used. If <em>x</em> is already present in <em>a</em>, 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 <code>list.insert()</code> assuming that <em>a</em> is already sorted.</p> <p>The returned insertion point <em>ip</em> partitions the array <em>a</em> into two slices such that <code>all(elem < x for elem in a[lo : ip])</code> is true for the left slice and <code>all(elem >= x for elem in a[ip : hi])</code> is true for the right slice.</p> <p><em>key</em> specifies a <a class="reference internal" href="../glossary#term-key-function"><span class="xref std std-term">key function</span></a> of one argument that is used to extract a comparison key from each element in the array. To support searching complex records, the key function is not applied to the <em>x</em> value.</p> <p>If <em>key</em> is <code>None</code>, the elements are compared directly and no key function is called.</p> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.10: </span>Added the <em>key</em> parameter.</p> </div> </dd> +</dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.bisect_right"> +<code>bisect.bisect_right(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dt class="sig sig-object py" id="bisect.bisect"> +<code>bisect.bisect(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dd> +<p>Similar to <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code>bisect_left()</code></a>, but returns an insertion point which comes after (to the right of) any existing entries of <em>x</em> in <em>a</em>.</p> <p>The returned insertion point <em>ip</em> partitions the array <em>a</em> into two slices such that <code>all(elem <= x for elem in a[lo : ip])</code> is true for the left slice and <code>all(elem > x for elem in a[ip : hi])</code> is true for the right slice.</p> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.10: </span>Added the <em>key</em> parameter.</p> </div> </dd> +</dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.insort_left"> +<code>bisect.insort_left(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dd> +<p>Insert <em>x</em> in <em>a</em> in sorted order.</p> <p>This function first runs <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code>bisect_left()</code></a> to locate an insertion point. Next, it runs the <code>insert()</code> method on <em>a</em> to insert <em>x</em> at the appropriate position to maintain sort order.</p> <p>To support inserting records in a table, the <em>key</em> function (if any) is applied to <em>x</em> for the search step but not for the insertion step.</p> <p>Keep in mind that the <code>O(log n)</code> search is dominated by the slow O(n) insertion step.</p> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.10: </span>Added the <em>key</em> parameter.</p> </div> </dd> +</dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.insort_right"> +<code>bisect.insort_right(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dt class="sig sig-object py" id="bisect.insort"> +<code>bisect.insort(a, x, lo=0, hi=len(a), *, key=None)</code> </dt> <dd> +<p>Similar to <a class="reference internal" href="#bisect.insort_left" title="bisect.insort_left"><code>insort_left()</code></a>, but inserting <em>x</em> in <em>a</em> after any existing entries of <em>x</em>.</p> <p>This function first runs <a class="reference internal" href="#bisect.bisect_right" title="bisect.bisect_right"><code>bisect_right()</code></a> to locate an insertion point. Next, it runs the <code>insert()</code> method on <em>a</em> to insert <em>x</em> at the appropriate position to maintain sort order.</p> <p>To support inserting records in a table, the <em>key</em> function (if any) is applied to <em>x</em> for the search step but not for the insertion step.</p> <p>Keep in mind that the <code>O(log n)</code> search is dominated by the slow O(n) insertion step.</p> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.10: </span>Added the <em>key</em> parameter.</p> </div> </dd> +</dl> <section id="performance-notes"> <h2>Performance Notes</h2> <p>When writing time sensitive code using <em>bisect()</em> and <em>insort()</em>, keep these thoughts in mind:</p> <ul class="simple"> <li>Bisection is effective for searching ranges of values. For locating specific values, dictionaries are more performant.</li> <li>The <em>insort()</em> functions are <code>O(n)</code> because the logarithmic search step is dominated by the linear time insertion step.</li> <li>The search functions are stateless and discard key function results after they are used. Consequently, if the search functions are used in a loop, the key function may be called again and again on the same array elements. If the key function isn’t fast, consider wrapping it with <a class="reference internal" href="functools#functools.cache" title="functools.cache"><code>functools.cache()</code></a> to avoid duplicate computations. Alternatively, consider searching an array of precomputed keys to locate the insertion point (as shown in the examples section below).</li> </ul> <div class="admonition seealso"> <p class="admonition-title">See also</p> <ul class="simple"> <li> +<a class="reference external" href="https://grantjenks.com/docs/sortedcollections/">Sorted Collections</a> is a high performance module that uses <em>bisect</em> to managed sorted collections of data.</li> <li>The <a class="reference external" href="https://code.activestate.com/recipes/577197-sortedcollection/">SortedCollection recipe</a> 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.</li> </ul> </div> </section> <section id="searching-sorted-lists"> <h2>Searching Sorted Lists</h2> <p>The above <a class="reference internal" href="#bisect-functions">bisect functions</a> 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:</p> <pre data-language="python">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 + +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 +</pre> </section> <section id="examples"> <h2>Examples</h2> <p id="bisect-example">The <a class="reference internal" href="#bisect.bisect" title="bisect.bisect"><code>bisect()</code></a> function can be useful for numeric table lookups. This example uses <a class="reference internal" href="#bisect.bisect" title="bisect.bisect"><code>bisect()</code></a> 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:</p> <pre data-language="python">>>> def grade(score, breakpoints=[60, 70, 80, 90], grades='FDCBA'): +... i = bisect(breakpoints, score) +... return grades[i] +... +>>> [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]] +['F', 'A', 'C', 'C', 'B', 'A', 'A'] +</pre> <p>The <a class="reference internal" href="#bisect.bisect" title="bisect.bisect"><code>bisect()</code></a> and <a class="reference internal" href="#bisect.insort" title="bisect.insort"><code>insort()</code></a> functions also work with lists of tuples. The <em>key</em> argument can serve to extract the field used for ordering records in a table:</p> <pre data-language="python">>>> from collections import namedtuple +>>> from operator import attrgetter +>>> from bisect import bisect, insort +>>> from pprint import pprint + +>>> Movie = namedtuple('Movie', ('name', 'released', 'director')) + +>>> movies = [ +... Movie('Jaws', 1975, 'Spielberg'), +... Movie('Titanic', 1997, 'Cameron'), +... Movie('The Birds', 1963, 'Hitchcock'), +... Movie('Aliens', 1986, 'Cameron') +... ] + +>>> # Find the first movie released after 1960 +>>> by_year = attrgetter('released') +>>> movies.sort(key=by_year) +>>> movies[bisect(movies, 1960, key=by_year)] +Movie(name='The Birds', released=1963, director='Hitchcock') + +>>> # Insert a movie while maintaining sort order +>>> romance = Movie('Love Story', 1970, 'Hiller') +>>> insort(movies, romance, key=by_year) +>>> pprint(movies) +[Movie(name='The Birds', released=1963, director='Hitchcock'), + Movie(name='Love Story', released=1970, director='Hiller'), + Movie(name='Jaws', released=1975, director='Spielberg'), + Movie(name='Aliens', released=1986, director='Cameron'), + Movie(name='Titanic', released=1997, director='Cameron')] +</pre> <p>If the key function is expensive, it is possible to avoid repeated function calls by searching a list of precomputed keys to find the index of a record:</p> <pre data-language="python">>>> data = [('red', 5), ('blue', 1), ('yellow', 8), ('black', 0)] +>>> data.sort(key=lambda r: r[1]) # Or use operator.itemgetter(1). +>>> keys = [r[1] for r in data] # Precompute a 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) +</pre> </section> <div class="_attribution"> + <p class="_attribution-p"> + © 2001–2023 Python Software Foundation<br>Licensed under the PSF License.<br> + <a href="https://docs.python.org/3.12/library/bisect.html" class="_attribution-link">https://docs.python.org/3.12/library/bisect.html</a> + </p> +</div> |