From c92a473a71a0c395df57d31cd49900057da3c25b Mon Sep 17 00:00:00 2001 From: Serhiy Storchaka Date: Wed, 10 Jan 2024 15:13:27 +0200 Subject: [PATCH] [3.11] gh-113664: Improve style of Big O notation (GH-113695) (GH-113910) Use cursive to make it looking like mathematic formulas. (cherry picked from commit a8629816c6c0e6770248a60529fd7c9ba08aad55) --- Doc/faq/design.rst | 2 +- Doc/glossary.rst | 2 +- Doc/library/asyncio-policy.rst | 8 ++++---- Doc/library/bisect.rst | 6 +++--- Doc/library/collections.rst | 6 +++--- Doc/library/contextvars.rst | 2 +- Doc/library/heapq.rst | 2 +- Doc/library/select.rst | 8 ++++---- Doc/reference/datamodel.rst | 2 +- Doc/using/cmdline.rst | 2 +- Doc/whatsnew/2.3.rst | 4 ++-- Doc/whatsnew/2.7.rst | 2 +- Doc/whatsnew/3.3.rst | 2 +- Misc/NEWS.d/3.5.0a1.rst | 2 +- 14 files changed, 25 insertions(+), 25 deletions(-) diff --git a/Doc/faq/design.rst b/Doc/faq/design.rst index 83c0152c85e84a..d0c136deabad76 100644 --- a/Doc/faq/design.rst +++ b/Doc/faq/design.rst @@ -449,7 +449,7 @@ on the key and a per-process seed; for example, "Python" could hash to to 1142331976. The hash code is then used to calculate a location in an internal array where the value will be stored. Assuming that you're storing keys that all have different hash values, this means that dictionaries take -constant time -- O(1), in Big-O notation -- to retrieve a key. +constant time -- *O*\ (1), in Big-O notation -- to retrieve a key. Why must dictionary keys be immutable? diff --git a/Doc/glossary.rst b/Doc/glossary.rst index ec6cec3acc7939..7dd178d5ad34f9 100644 --- a/Doc/glossary.rst +++ b/Doc/glossary.rst @@ -741,7 +741,7 @@ Glossary list A built-in Python :term:`sequence`. Despite its name it is more akin to an array in other languages than to a linked list since access to - elements is O(1). + elements is *O*\ (1). list comprehension A compact way to process all or part of the elements in a sequence and diff --git a/Doc/library/asyncio-policy.rst b/Doc/library/asyncio-policy.rst index f846f76ca095f4..3cd0f1e9d23cf3 100644 --- a/Doc/library/asyncio-policy.rst +++ b/Doc/library/asyncio-policy.rst @@ -226,7 +226,7 @@ implementation used by the asyncio event loop: It works reliably even when the asyncio event loop is run in a non-main OS thread. - There is no noticeable overhead when handling a big number of children (*O(1)* each + There is no noticeable overhead when handling a big number of children (*O*\ (1) each time a child terminates), but starting a thread per process requires extra memory. This watcher is used by default. @@ -246,7 +246,7 @@ implementation used by the asyncio event loop: watcher is installed. The solution is safe but it has a significant overhead when - handling a big number of processes (*O(n)* each time a + handling a big number of processes (*O*\ (*n*) each time a :py:data:`SIGCHLD` is received). .. versionadded:: 3.8 @@ -260,7 +260,7 @@ implementation used by the asyncio event loop: The watcher avoids disrupting other code spawning processes by polling every process explicitly on a :py:data:`SIGCHLD` signal. - This solution is as safe as :class:`MultiLoopChildWatcher` and has the same *O(N)* + This solution is as safe as :class:`MultiLoopChildWatcher` and has the same *O*\ (*n*) complexity but requires a running event loop in the main thread to work. .. class:: FastChildWatcher @@ -270,7 +270,7 @@ implementation used by the asyncio event loop: processes and waiting for their termination. There is no noticeable overhead when handling a big number of - children (*O(1)* each time a child terminates). + children (*O*\ (1) each time a child terminates). This solution requires a running event loop in the main thread to work, as :class:`SafeChildWatcher`. diff --git a/Doc/library/bisect.rst b/Doc/library/bisect.rst index 75d16dc3e1021c..92372f12ca4425 100644 --- a/Doc/library/bisect.rst +++ b/Doc/library/bisect.rst @@ -79,7 +79,7 @@ The following functions are provided: 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 ``O(log n)`` search is dominated by the slow O(n) + Keep in mind that the *O*\ (log *n*) search is dominated by the slow *O*\ (*n*) insertion step. .. versionchanged:: 3.10 @@ -99,7 +99,7 @@ The following functions are provided: 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 ``O(log n)`` search is dominated by the slow O(n) + Keep in mind that the *O*\ (log *n*) search is dominated by the slow *O*\ (*n*) insertion step. .. versionchanged:: 3.10 @@ -115,7 +115,7 @@ thoughts in mind: * Bisection is effective for searching ranges of values. For locating specific values, dictionaries are more performant. -* The *insort()* functions are ``O(n)`` because the logarithmic search step +* The *insort()* functions are *O*\ (*n*) because the logarithmic search step is dominated by the linear time insertion step. * The search functions are stateless and discard key function results after diff --git a/Doc/library/collections.rst b/Doc/library/collections.rst index a29cc9530390bc..10cd1e8e2f1e1d 100644 --- a/Doc/library/collections.rst +++ b/Doc/library/collections.rst @@ -457,10 +457,10 @@ or subtracting from an empty counter. Deques are a generalization of stacks and queues (the name is pronounced "deck" and is short for "double-ended queue"). Deques support thread-safe, memory efficient appends and pops from either side of the deque with approximately the - same O(1) performance in either direction. + same *O*\ (1) performance in either direction. Though :class:`list` objects support similar operations, they are optimized for - fast fixed-length operations and incur O(n) memory movement costs for + fast fixed-length operations and incur *O*\ (*n*) memory movement costs for ``pop(0)`` and ``insert(0, v)`` operations which change both the size and position of the underlying data representation. @@ -584,7 +584,7 @@ or subtracting from an empty counter. In addition to the above, deques support iteration, pickling, ``len(d)``, ``reversed(d)``, ``copy.copy(d)``, ``copy.deepcopy(d)``, membership testing with the :keyword:`in` operator, and subscript references such as ``d[0]`` to access -the first element. Indexed access is O(1) at both ends but slows to O(n) in +the first element. Indexed access is *O*\ (1) at both ends but slows to *O*\ (*n*) in the middle. For fast random access, use lists instead. Starting in version 3.5, deques support ``__add__()``, ``__mul__()``, diff --git a/Doc/library/contextvars.rst b/Doc/library/contextvars.rst index 0ac2f3d85749b7..647832447de946 100644 --- a/Doc/library/contextvars.rst +++ b/Doc/library/contextvars.rst @@ -131,7 +131,7 @@ Manual Context Management ctx: Context = copy_context() print(list(ctx.items())) - The function has an O(1) complexity, i.e. works equally fast for + The function has an *O*\ (1) complexity, i.e. works equally fast for contexts with a few context variables and for contexts that have a lot of them. diff --git a/Doc/library/heapq.rst b/Doc/library/heapq.rst index 8b00f7b27959b6..ddbada13bddf5b 100644 --- a/Doc/library/heapq.rst +++ b/Doc/library/heapq.rst @@ -270,7 +270,7 @@ winner. The simplest algorithmic way to remove it and find the "next" winner is to move some loser (let's say cell 30 in the diagram above) into the 0 position, and then percolate this new 0 down the tree, exchanging values, until the invariant is re-established. This is clearly logarithmic on the total number of -items in the tree. By iterating over all items, you get an O(n log n) sort. +items in the tree. By iterating over all items, you get an *O*\ (*n* log *n*) sort. A nice feature of this sort is that you can efficiently insert new items while the sort is going on, provided that the inserted items are not "better" than the diff --git a/Doc/library/select.rst b/Doc/library/select.rst index c2941e628d9d78..a0058046d0ce4c 100644 --- a/Doc/library/select.rst +++ b/Doc/library/select.rst @@ -185,8 +185,8 @@ The module defines the following: ----------------------------- Solaris and derivatives have ``/dev/poll``. While :c:func:`!select` is -O(highest file descriptor) and :c:func:`!poll` is O(number of file -descriptors), ``/dev/poll`` is O(active file descriptors). +*O*\ (*highest file descriptor*) and :c:func:`!poll` is *O*\ (*number of file +descriptors*), ``/dev/poll`` is *O*\ (*active file descriptors*). ``/dev/poll`` behaviour is very close to the standard :c:func:`!poll` object. @@ -381,8 +381,8 @@ scalability for network servers that service many, many clients at the same time. :c:func:`!poll` scales better because the system call only requires listing the file descriptors of interest, while :c:func:`!select` builds a bitmap, turns on bits for the fds of interest, and then afterward the whole bitmap has to be -linearly scanned again. :c:func:`!select` is O(highest file descriptor), while -:c:func:`!poll` is O(number of file descriptors). +linearly scanned again. :c:func:`!select` is *O*\ (*highest file descriptor*), while +:c:func:`!poll` is *O*\ (*number of file descriptors*). .. method:: poll.register(fd[, eventmask]) diff --git a/Doc/reference/datamodel.rst b/Doc/reference/datamodel.rst index e04827e34f7927..54ba171ec7696c 100644 --- a/Doc/reference/datamodel.rst +++ b/Doc/reference/datamodel.rst @@ -1854,7 +1854,7 @@ Basic customization This is intended to provide protection against a denial-of-service caused by carefully chosen inputs that exploit the worst case performance of a - dict insertion, O(n\ :sup:`2`) complexity. See + dict insertion, *O*\ (*n*\ :sup:`2`) complexity. See http://ocert.org/advisories/ocert-2011-003.html for details. Changing hash values affects the iteration order of sets. diff --git a/Doc/using/cmdline.rst b/Doc/using/cmdline.rst index 5389d33023096d..0ddf2964ab11f4 100644 --- a/Doc/using/cmdline.rst +++ b/Doc/using/cmdline.rst @@ -366,7 +366,7 @@ Miscellaneous options Hash randomization is intended to provide protection against a denial-of-service caused by carefully chosen inputs that exploit the worst - case performance of a dict construction, O(n\ :sup:`2`) complexity. See + case performance of a dict construction, *O*\ (*n*\ :sup:`2`) complexity. See http://ocert.org/advisories/ocert-2011-003.html for details. :envvar:`PYTHONHASHSEED` allows you to set a fixed value for the hash diff --git a/Doc/whatsnew/2.3.rst b/Doc/whatsnew/2.3.rst index 01c8879ba83870..6127a5df966a18 100644 --- a/Doc/whatsnew/2.3.rst +++ b/Doc/whatsnew/2.3.rst @@ -1196,7 +1196,7 @@ Optimizations * Multiplication of large long integers is now much faster thanks to an implementation of Karatsuba multiplication, an algorithm that scales better than - the O(n\*n) required for the grade-school multiplication algorithm. (Original + the *O*\ (*n*\ :sup:`2`) required for the grade-school multiplication algorithm. (Original patch by Christopher A. Craig, and significantly reworked by Tim Peters.) * The ``SET_LINENO`` opcode is now gone. This may provide a small speed @@ -1308,7 +1308,7 @@ complete list of changes, or look through the CVS logs for all the details. partially sorted order such that, for every index *k*, ``heap[k] <= heap[2*k+1]`` and ``heap[k] <= heap[2*k+2]``. This makes it quick to remove the smallest item, and inserting a new item while maintaining the heap property is - O(lg n). (See https://xlinux.nist.gov/dads//HTML/priorityque.html for more + *O*\ (log *n*). (See https://xlinux.nist.gov/dads//HTML/priorityque.html for more information about the priority queue data structure.) The :mod:`heapq` module provides :func:`~heapq.heappush` and :func:`~heapq.heappop` functions diff --git a/Doc/whatsnew/2.7.rst b/Doc/whatsnew/2.7.rst index 099090487ed94a..25206c143c340b 100644 --- a/Doc/whatsnew/2.7.rst +++ b/Doc/whatsnew/2.7.rst @@ -282,7 +282,7 @@ How does the :class:`~collections.OrderedDict` work? It maintains a doubly linked list of keys, appending new keys to the list as they're inserted. A secondary dictionary maps keys to their corresponding list node, so deletion doesn't have to traverse the entire linked list and therefore -remains O(1). +remains *O*\ (1). The standard library now supports use of ordered dictionaries in several modules. diff --git a/Doc/whatsnew/3.3.rst b/Doc/whatsnew/3.3.rst index 3bc3d2f7c3740e..608a8b54c10ffd 100644 --- a/Doc/whatsnew/3.3.rst +++ b/Doc/whatsnew/3.3.rst @@ -174,7 +174,7 @@ Features b or c are now hashable. (Contributed by Antoine Pitrou in :issue:`13411`.) * Arbitrary slicing of any 1-D arrays type is supported. For example, it - is now possible to reverse a memoryview in O(1) by using a negative step. + is now possible to reverse a memoryview in *O*\ (1) by using a negative step. API changes ----------- diff --git a/Misc/NEWS.d/3.5.0a1.rst b/Misc/NEWS.d/3.5.0a1.rst index 96e59206cb1291..f793323f217070 100644 --- a/Misc/NEWS.d/3.5.0a1.rst +++ b/Misc/NEWS.d/3.5.0a1.rst @@ -2648,7 +2648,7 @@ module. .. nonce: THJSYB .. section: Library -Changed FeedParser feed() to avoid O(N\ :sup:`2`) behavior when parsing long line. +Changed FeedParser feed() to avoid *O*\ (*n*\ :sup:`2`) behavior when parsing long line. Original patch by Raymond Hettinger. ..