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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate">bisect</code> — Array bisection algorithm</a><ul>
<li><a class="reference internal" href="#performance-notes">Performance Notes</a></li>
<li><a class="reference internal" href="#searching-sorted-lists">Searching Sorted Lists</a></li>
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 <section id="module-bisect">
<h1><a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate">bisect</code></a> — Array bisection algorithm<a class="headerlink" href="#module-bisect" title="Permalink to this headline">¶</a></h1>
Source code: <a class="reference external" href="https://github.com/python/cpython/tree/3.10/Lib/bisect.py">Lib/bisect.py</a>
<hr class="docutils" />
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 the more common
approach. The module is called <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate">bisect</code></a> because it uses a basic bisection
algorithm to do its work. The source code may be most useful as a working
example of the algorithm (the boundary conditions are already right!).
The following functions are provided:
<dl class="py function">
<dt class="sig sig-object py" id="bisect.bisect_left">
bisect.bisect_left(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.bisect_left" title="Permalink to this definition">¶</a></dt>
<dd>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 <code class="docutils literal notranslate">list.insert()</code> assuming that a is already sorted.
The returned insertion point i partitions the array a into two halves so
that <code class="docutils literal notranslate">all(val &lt; x for val in a[lo : i])</code> for the left side and
<code class="docutils literal notranslate">all(val &gt;= x for val in a[i : hi])</code> for the right side.
key specifies a <a class="reference internal" href="../glossary.html#term-key-function">key function</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 x value.
If key is <code class="docutils literal notranslate">None</code>, the elements are compared directly with no
intervening function call.
<div class="versionchanged">
Changed in version 3.10: Added the key parameter.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="bisect.bisect_right">
bisect.bisect_right(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.bisect_right" title="Permalink to this definition">¶</a></dt>
<dt class="sig sig-object py" id="bisect.bisect">
bisect.bisect(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.bisect" title="Permalink to this definition">¶</a></dt>
<dd>Similar to <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code class="xref py py-func docutils literal notranslate">bisect_left()</code></a>, 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 <code class="docutils literal notranslate">all(val &lt;= x for val in a[lo : i])</code> for the left side and
<code class="docutils literal notranslate">all(val &gt; x for val in a[i : hi])</code> for the right side.
key specifies a <a class="reference internal" href="../glossary.html#term-key-function">key function</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 x value.
If key is <code class="docutils literal notranslate">None</code>, the elements are compared directly with no
intervening function call.
<div class="versionchanged">
Changed in version 3.10: Added the key parameter.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="bisect.insort_left">
bisect.insort_left(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.insort_left" title="Permalink to this definition">¶</a></dt>
<dd>Insert x in a in sorted order.
This function first runs <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code class="xref py py-func docutils literal notranslate">bisect_left()</code></a> to locate an insertion point.
Next, it runs the <code class="xref py py-meth docutils literal notranslate">insert()</code> method on a to insert x at the
appropriate position to maintain sort order.
To support inserting records in a table, the key function (if any) is
applied to x for the search step but not for the insertion step.
Keep in mind that the <code class="docutils literal notranslate">O(log n)</code> search is dominated by the slow O(n)
insertion step.
<div class="versionchanged">
Changed in version 3.10: Added the key parameter.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="bisect.insort_right">
bisect.insort_right(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.insort_right" title="Permalink to this definition">¶</a></dt>
<dt class="sig sig-object py" id="bisect.insort">
bisect.insort(a, x, lo=0, hi=len(a), *, key=None)<a class="headerlink" href="#bisect.insort" title="Permalink to this definition">¶</a></dt>
<dd>Similar to <a class="reference internal" href="#bisect.insort_left" title="bisect.insort_left"><code class="xref py py-func docutils literal notranslate">insort_left()</code></a>, but inserting x in a after any existing
entries of x.
This function first runs <a class="reference internal" href="#bisect.bisect_right" title="bisect.bisect_right"><code class="xref py py-func docutils literal notranslate">bisect_right()</code></a> to locate an insertion point.
Next, it runs the <code class="xref py py-meth docutils literal notranslate">insert()</code> method on a to insert x at the
appropriate position to maintain sort order.
To support inserting records in a table, the key function (if any) is
applied to x for the search step but not for the insertion step.
Keep in mind that the <code class="docutils literal notranslate">O(log n)</code> search is dominated by the slow O(n)
insertion step.
<div class="versionchanged">
Changed in version 3.10: Added the key parameter.
</div>
</dd></dl>

<section id="performance-notes">
<h2>Performance Notes<a class="headerlink" href="#performance-notes" title="Permalink to this headline">¶</a></h2>
When writing time sensitive code using bisect() and insort(), keep these
thoughts in mind:
<ul class="simple">
<li>Bisection is effective for searching ranges of values.
For locating specific values, dictionaries are more performant.</li>
<li>The insort() functions are <code class="docutils literal notranslate">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.html#functools.cache" title="functools.cache"><code class="xref py py-func docutils literal notranslate">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">
See also
<ul class="simple">
<li><a class="reference external" href="https://grantjenks.com/docs/sortedcollections/">Sorted Collections</a> is a high performance
module that uses bisect 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<a class="headerlink" href="#searching-sorted-lists" title="Permalink to this headline">¶</a></h2>
The above <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate">bisect()</code></a> 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:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>def index(a, x):
 &#39;Locate the leftmost value exactly equal to x&#39;
 i = bisect_left(a, x)
 if i != len(a) and a[i] == x:
 return i
 raise ValueError

def find_lt(a, x):
 &#39;Find rightmost value less than x&#39;
 i = bisect_left(a, x)
 if i:
 return a[i-1]
 raise ValueError

def find_le(a, x):
 &#39;Find rightmost value less than or equal to x&#39;
 i = bisect_right(a, x)
 if i:
 return a[i-1]
 raise ValueError

def find_gt(a, x):
 &#39;Find leftmost value greater than x&#39;
 i = bisect_right(a, x)
 if i != len(a):
 return a[i]
 raise ValueError

def find_ge(a, x):
 &#39;Find leftmost item greater than or equal to x&#39;
 i = bisect_left(a, x)
 if i != len(a):
 return a[i]
 raise ValueError
</pre></div>
</div>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate">bisect()</code></a> function can be useful for numeric table lookups. This
example uses <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate">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:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; def grade(score, breakpoints=[60, 70, 80, 90], grades=&#39;FDCBA&#39;):
... i = bisect(breakpoints, score)
... return grades[i]
...
&gt;&gt;&gt; [grade(score) for score in [33, 99, 77, 70, 89, 90, 100]]
[&#39;F&#39;, &#39;A&#39;, &#39;C&#39;, &#39;C&#39;, &#39;B&#39;, &#39;A&#39;, &#39;A&#39;]
</pre></div>
</div>
The <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate">bisect()</code></a> and <a class="reference internal" href="#bisect.insort" title="bisect.insort"><code class="xref py py-func docutils literal notranslate">insort()</code></a> functions also work with lists of
tuples. The key argument can serve to extract the field used for ordering
records in a table:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from collections import namedtuple
&gt;&gt;&gt; from operator import attrgetter
&gt;&gt;&gt; from bisect import bisect, insort
&gt;&gt;&gt; from pprint import pprint

&gt;&gt;&gt; Movie = namedtuple(&#39;Movie&#39;, (&#39;name&#39;, &#39;released&#39;, &#39;director&#39;))

&gt;&gt;&gt; movies = [
... Movie(&#39;Jaws&#39;, 1975, &#39;Speilberg&#39;),
... Movie(&#39;Titanic&#39;, 1997, &#39;Cameron&#39;),
... Movie(&#39;The Birds&#39;, 1963, &#39;Hitchcock&#39;),
... Movie(&#39;Aliens&#39;, 1986, &#39;Scott&#39;)
... ]

&gt;&gt;&gt; # Find the first movie released after 1960
&gt;&gt;&gt; by_year = attrgetter(&#39;released&#39;)
&gt;&gt;&gt; movies.sort(key=by_year)
&gt;&gt;&gt; movies[bisect(movies, 1960, key=by_year)]
Movie(name=&#39;The Birds&#39;, released=1963, director=&#39;Hitchcock&#39;)

&gt;&gt;&gt; # Insert a movie while maintaining sort order
&gt;&gt;&gt; romance = Movie(&#39;Love Story&#39;, 1970, &#39;Hiller&#39;)
&gt;&gt;&gt; insort(movies, romance, key=by_year)
&gt;&gt;&gt; pprint(movies)
[Movie(name=&#39;The Birds&#39;, released=1963, director=&#39;Hitchcock&#39;),
 Movie(name=&#39;Love Story&#39;, released=1970, director=&#39;Hiller&#39;),
 Movie(name=&#39;Jaws&#39;, released=1975, director=&#39;Speilberg&#39;),
 Movie(name=&#39;Aliens&#39;, released=1986, director=&#39;Scott&#39;),
 Movie(name=&#39;Titanic&#39;, released=1997, director=&#39;Cameron&#39;)]
</pre></div>
</div>
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:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; data = [(&#39;red&#39;, 5), (&#39;blue&#39;, 1), (&#39;yellow&#39;, 8), (&#39;black&#39;, 0)]
&gt;&gt;&gt; data.sort(key=lambda r: r[1]) # Or use operator.itemgetter(1).
&gt;&gt;&gt; keys = [r[1] for r in data] # Precompute a list of keys.
&gt;&gt;&gt; data[bisect_left(keys, 0)]
(&#39;black&#39;, 0)
&gt;&gt;&gt; data[bisect_left(keys, 1)]
(&#39;blue&#39;, 1)
&gt;&gt;&gt; data[bisect_left(keys, 5)]
(&#39;red&#39;, 5)
&gt;&gt;&gt; data[bisect_left(keys, 8)]
(&#39;yellow&#39;, 8)
</pre></div>
</div>
</section>
</section>

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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate">bisect</code> — Array bisection algorithm</a><ul>
<li><a class="reference internal" href="#performance-notes">Performance Notes</a></li>
<li><a class="reference internal" href="#searching-sorted-lists">Searching Sorted Lists</a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
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