cpython/Doc/library/heapq.rst

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:mod:`heapq` --- Heap queue algorithm
=====================================
.. module:: heapq
:synopsis: Heap queue algorithm (a.k.a. priority queue).
.. moduleauthor:: Kevin O'Connor
.. sectionauthor:: Guido van Rossum <guido@python.org>
.. sectionauthor:: François Pinard
.. sectionauthor:: Raymond Hettinger
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**Source code:** :source:`Lib/heapq.py`
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--------------
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This module provides an implementation of the heap queue algorithm, also known
as the priority queue algorithm.
Heaps are binary trees for which every parent node has a value less than or
equal to any of its children. This implementation uses arrays for which
``heap[k] <= heap[2*k+1]`` and ``heap[k] <= heap[2*k+2]`` for all *k*, counting
elements from zero. For the sake of comparison, non-existing elements are
considered to be infinite. The interesting property of a heap is that its
smallest element is always the root, ``heap[0]``.
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The API below differs from textbook heap algorithms in two aspects: (a) We use
zero-based indexing. This makes the relationship between the index for a node
and the indexes for its children slightly less obvious, but is more suitable
since Python uses zero-based indexing. (b) Our pop method returns the smallest
item, not the largest (called a "min heap" in textbooks; a "max heap" is more
common in texts because of its suitability for in-place sorting).
These two make it possible to view the heap as a regular Python list without
surprises: ``heap[0]`` is the smallest item, and ``heap.sort()`` maintains the
heap invariant!
To create a heap, use a list initialized to ``[]``, or you can transform a
populated list into a heap via function :func:`heapify`.
The following functions are provided:
.. function:: heappush(heap, item)
Push the value *item* onto the *heap*, maintaining the heap invariant.
.. function:: heappop(heap)
Pop and return the smallest item from the *heap*, maintaining the heap
invariant. If the heap is empty, :exc:`IndexError` is raised.
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Patch from Trent Nelson. Also simplified removing a file by using test_support. ........ r61242 | neal.norwitz | 2008-03-05 06:14:18 +0100 (Wed, 05 Mar 2008) | 3 lines Get this test to pass even when there is no sound card in the system. Patch from Trent Nelson. (I can't test this.) ........ r61243 | neal.norwitz | 2008-03-05 06:20:44 +0100 (Wed, 05 Mar 2008) | 3 lines Catch OSError when trying to remove a file in case removal fails. This should prevent a failure in tearDown masking any real test failure. ........ r61244 | neal.norwitz | 2008-03-05 06:38:06 +0100 (Wed, 05 Mar 2008) | 5 lines Make the timeout longer to give slow machines a chance to pass the test before timing out. This doesn't change the duration of the test under normal circumstances. This is targetted at fixing the spurious failures on the FreeBSD buildbot primarily. ........ r61245 | neal.norwitz | 2008-03-05 06:49:03 +0100 (Wed, 05 Mar 2008) | 1 line Tabs -> spaces ........ r61246 | neal.norwitz | 2008-03-05 06:50:20 +0100 (Wed, 05 Mar 2008) | 1 line Use -u urlfetch to run more tests ........ r61247 | neal.norwitz | 2008-03-05 06:51:20 +0100 (Wed, 05 Mar 2008) | 1 line test_smtplib sometimes reports leaks too, suppress it ........ r61248 | jeffrey.yasskin | 2008-03-05 07:19:56 +0100 (Wed, 05 Mar 2008) | 5 lines Fix test_socketserver on Windows after r61099 added several signal.alarm() calls (which don't exist on non-Unix platforms). Thanks to Trent Nelson for the report and patch. ........ r61249 | georg.brandl | 2008-03-05 08:10:35 +0100 (Wed, 05 Mar 2008) | 2 lines Fix some rst. ........ r61252 | thomas.heller | 2008-03-05 15:53:39 +0100 (Wed, 05 Mar 2008) | 2 lines News entry for yesterdays commit. ........ r61253 | thomas.heller | 2008-03-05 16:34:29 +0100 (Wed, 05 Mar 2008) | 3 lines Issue 1872: Changed the struct module typecode from 't' to '?', for compatibility with PEP3118. ........ r61254 | skip.montanaro | 2008-03-05 17:41:09 +0100 (Wed, 05 Mar 2008) | 4 lines Elaborate on the role of the altinstall target when installing multiple versions. ........ r61255 | georg.brandl | 2008-03-05 20:31:44 +0100 (Wed, 05 Mar 2008) | 2 lines #2239: PYTHONPATH delimiter is os.pathsep. ........ r61256 | raymond.hettinger | 2008-03-05 21:59:58 +0100 (Wed, 05 Mar 2008) | 1 line C implementation of itertools.permutations(). ........ r61257 | raymond.hettinger | 2008-03-05 22:04:32 +0100 (Wed, 05 Mar 2008) | 1 line Small code cleanup. ........ r61260 | martin.v.loewis | 2008-03-05 23:24:31 +0100 (Wed, 05 Mar 2008) | 2 lines cd PCbuild only after deleting all pyc files. ........ r61261 | raymond.hettinger | 2008-03-06 02:15:52 +0100 (Thu, 06 Mar 2008) | 1 line Add examples. ........ r61262 | andrew.kuchling | 2008-03-06 02:36:27 +0100 (Thu, 06 Mar 2008) | 1 line Add two items ........ r61263 | georg.brandl | 2008-03-06 07:47:18 +0100 (Thu, 06 Mar 2008) | 2 lines #1725737: ignore other VC directories other than CVS and SVN's too. ........ r61264 | martin.v.loewis | 2008-03-06 07:55:22 +0100 (Thu, 06 Mar 2008) | 4 lines Patch #2232: os.tmpfile might fail on Windows if the user has no permission to create files in the root directory. 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The core of the patch was written by Pedro Werneck, but any bugs are mine. 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Commits GHOP 237. Thanks Benjamin Peterson for the patch. ........ r61372 | brett.cannon | 2008-03-13 21:33:10 +0100 (Thu, 13 Mar 2008) | 4 lines Move test_tokenize to doctest. Done as GHOP 238 by Josip Dzolonga. ........ r61373 | brett.cannon | 2008-03-13 21:47:41 +0100 (Thu, 13 Mar 2008) | 4 lines Convert test_contains, test_crypt, and test_select to unittest. Patch from GHOP 294 by David Marek. ........ r61374 | brett.cannon | 2008-03-13 22:02:16 +0100 (Thu, 13 Mar 2008) | 4 lines Move test_gdbm to use unittest. Closes issue #1960. Thanks Giampaolo Rodola. ........ r61375 | brett.cannon | 2008-03-13 22:09:28 +0100 (Thu, 13 Mar 2008) | 4 lines Convert test_fcntl to unittest. Closes issue #2055. Thanks Giampaolo Rodola. ........ r61376 | raymond.hettinger | 2008-03-14 06:03:44 +0100 (Fri, 14 Mar 2008) | 1 line Leave heapreplace() unchanged. ........ r61378 | martin.v.loewis | 2008-03-14 14:56:09 +0100 (Fri, 14 Mar 2008) | 2 lines Patch #2284: add -x64 option to rt.bat. ........ r61379 | martin.v.loewis | 2008-03-14 14:57:59 +0100 (Fri, 14 Mar 2008) | 2 lines Use -x64 flag. ........ r61382 | brett.cannon | 2008-03-14 15:03:10 +0100 (Fri, 14 Mar 2008) | 2 lines Remove a bad test. ........ r61383 | mark.dickinson | 2008-03-14 15:23:37 +0100 (Fri, 14 Mar 2008) | 9 lines Issue 705836: Fix struct.pack(">f", 1e40) to behave consistently across platforms: it should now raise OverflowError on all platforms. (Previously it raised OverflowError only on non IEEE 754 platforms.) 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.. function:: heappushpop(heap, item)
Push *item* on the heap, then pop and return the smallest item from the
*heap*. The combined action runs more efficiently than :func:`heappush`
followed by a separate call to :func:`heappop`.
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.. function:: heapify(x)
Transform list *x* into a heap, in-place, in linear time.
.. function:: heapreplace(heap, item)
Pop and return the smallest item from the *heap*, and also push the new *item*.
The heap size doesn't change. If the heap is empty, :exc:`IndexError` is raised.
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This one step operation is more efficient than a :func:`heappop` followed by
:func:`heappush` and can be more appropriate when using a fixed-size heap.
The pop/push combination always returns an element from the heap and replaces
it with *item*.
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The value returned may be larger than the *item* added. If that isn't
desired, consider using :func:`heappushpop` instead. Its push/pop
combination returns the smaller of the two values, leaving the larger value
on the heap.
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The module also offers three general purpose functions based on heaps.
.. function:: merge(*iterables)
Merge multiple sorted inputs into a single sorted output (for example, merge
#1370: Finish the merge r58749, log below, by resolving all conflicts in Doc/. Merged revisions 58221-58741 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r58221 | georg.brandl | 2007-09-20 10:57:59 -0700 (Thu, 20 Sep 2007) | 2 lines Patch #1181: add os.environ.clear() method. ........ r58225 | sean.reifschneider | 2007-09-20 23:33:28 -0700 (Thu, 20 Sep 2007) | 3 lines Issue1704287: "make install" fails unless you do "make" first. Make oldsharedmods and sharedmods in "libinstall". ........ r58232 | guido.van.rossum | 2007-09-22 13:18:03 -0700 (Sat, 22 Sep 2007) | 4 lines Patch # 188 by Philip Jenvey. Make tell() mark CRLF as a newline. 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Note that archaic use of type(x) == types.DictType is because of keeping 1.5.2 compatibility. While this is much less relevant these days, there probably needs to be a separate commit for removing all archaic constructs at the same time. ........ r58288 | brett.cannon | 2007-09-30 12:45:10 -0700 (Sun, 30 Sep 2007) | 9 lines tuple.__repr__ did not consider a reference loop as it is not possible from Python code; but it is possible from C. object.__str__ had the issue of not expecting a type to doing something within it's tp_str implementation that could trigger an infinite recursion, but it could in C code.. Both found thanks to BaseException and how it handles its repr. Closes issue #1686386. Thanks to Thomas Herve for taking an initial stab at coming up with a solution. ........ r58289 | brett.cannon | 2007-09-30 13:37:19 -0700 (Sun, 30 Sep 2007) | 3 lines Fix error introduced by r58288; if a tuple is length 0 return its repr and don't worry about any self-referring tuples. ........ r58294 | facundo.batista | 2007-10-02 10:01:24 -0700 (Tue, 02 Oct 2007) | 11 lines Made the various is_* operations return booleans. This was discussed with Cawlishaw by mail, and he basically confirmed that to these is_* operations, there's no need to return Decimal(0) and Decimal(1) if the language supports the False and True booleans. Also added a few tests for the these functions in extra.decTest, since they are mostly untested (apart from the doctests). Thanks Mark Dickinson ........ r58295 | facundo.batista | 2007-10-02 11:21:18 -0700 (Tue, 02 Oct 2007) | 4 lines Added a class to store the digits of log(10), so that they can be made available when necessary without recomputing. 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M idlelib/EditorWindow.py M idlelib/aboutDialog.py M idlelib/textView.py M idlelib/NEWS.txt ........ r58310 | kurt.kaiser | 2007-10-03 20:11:12 -0700 (Wed, 03 Oct 2007) | 3 lines configDialog cleanup. Patch 1730217 Tal Einat. ........ r58311 | neal.norwitz | 2007-10-03 23:00:48 -0700 (Wed, 03 Oct 2007) | 4 lines Coverity #151: Remove deadcode. All this code already exists above starting at line 653. ........ r58325 | fred.drake | 2007-10-04 19:46:12 -0700 (Thu, 04 Oct 2007) | 1 line wrap lines to <80 characters before fixing errors ........ r58326 | raymond.hettinger | 2007-10-04 19:47:07 -0700 (Thu, 04 Oct 2007) | 6 lines Add __asdict__() to NamedTuple and refine the docs. Add maxlen support to deque() and fixup docs. Partially fix __reduce__(). The None as a third arg was no longer supported. Still needs work on __reduce__() to handle recursive inputs. ........ r58327 | fred.drake | 2007-10-04 19:48:32 -0700 (Thu, 04 Oct 2007) | 3 lines move descriptions of ac_(in|out)_buffer_size to the right place http://bugs.python.org/issue1053 ........ r58329 | neal.norwitz | 2007-10-04 20:39:17 -0700 (Thu, 04 Oct 2007) | 3 lines dict could be NULL, so we need to XDECREF. Fix a compiler warning about passing a PyTypeObject* instead of PyObject*. ........ r58330 | neal.norwitz | 2007-10-04 20:41:19 -0700 (Thu, 04 Oct 2007) | 2 lines Fix Coverity #158: Check the correct variable. ........ r58332 | neal.norwitz | 2007-10-04 22:01:38 -0700 (Thu, 04 Oct 2007) | 7 lines Fix Coverity #159. This code was broken if save() returned a negative number since i contained a boolean value and then we compared i < 0 which should never be true. Will backport (assuming it's necessary) ........ r58334 | neal.norwitz | 2007-10-04 22:29:17 -0700 (Thu, 04 Oct 2007) | 1 line Add a note about fixing some more warnings found by Coverity. ........ r58338 | raymond.hettinger | 2007-10-05 12:07:31 -0700 (Fri, 05 Oct 2007) | 1 line Restore BEGIN/END THREADS macros which were squashed in the previous checkin ........ r58343 | gregory.p.smith | 2007-10-06 00:48:10 -0700 (Sat, 06 Oct 2007) | 3 lines Stab in the dark attempt to fix the test_bsddb3 failure on sparc and S-390 ubuntu buildbots. ........ r58344 | gregory.p.smith | 2007-10-06 00:51:59 -0700 (Sat, 06 Oct 2007) | 2 lines Allows BerkeleyDB 4.6.x >= 4.6.21 for the bsddb module. ........ r58348 | gregory.p.smith | 2007-10-06 08:47:37 -0700 (Sat, 06 Oct 2007) | 3 lines Use the host the author likely meant in the first place. pop.gmail.com is reliable. gmail.org is someones personal domain. ........ r58351 | neal.norwitz | 2007-10-06 12:16:28 -0700 (Sat, 06 Oct 2007) | 3 lines Ensure that this test will pass even if another test left an unwritable TESTFN. Also use the safe unlink in test_support instead of rolling our own here. ........ r58368 | georg.brandl | 2007-10-08 00:50:24 -0700 (Mon, 08 Oct 2007) | 3 lines #1123: fix the docs for the str.split(None, sep) case. Also expand a few other methods' docs, which had more info in the deprecated string module docs. ........ r58369 | georg.brandl | 2007-10-08 01:06:05 -0700 (Mon, 08 Oct 2007) | 2 lines Update docstring of sched, also remove an unused assignment. ........ r58370 | raymond.hettinger | 2007-10-08 02:14:28 -0700 (Mon, 08 Oct 2007) | 5 lines Add comments to NamedTuple code. Let the field spec be either a string or a non-string sequence (suggested by Martin Blais with use cases). Improve the error message in the case of a SyntaxError (caused by a duplicate field name). ........ r58371 | raymond.hettinger | 2007-10-08 02:56:29 -0700 (Mon, 08 Oct 2007) | 1 line Missed a line in the docs ........ r58372 | raymond.hettinger | 2007-10-08 03:11:51 -0700 (Mon, 08 Oct 2007) | 1 line Better variable names ........ r58376 | georg.brandl | 2007-10-08 07:12:47 -0700 (Mon, 08 Oct 2007) | 3 lines #1199: docs for tp_as_{number,sequence,mapping}, by Amaury Forgeot d'Arc. No need to merge this to py3k! ........ r58380 | raymond.hettinger | 2007-10-08 14:26:58 -0700 (Mon, 08 Oct 2007) | 1 line Eliminate camelcase function name ........ r58381 | andrew.kuchling | 2007-10-08 16:23:03 -0700 (Mon, 08 Oct 2007) | 1 line Eliminate camelcase function name ........ r58382 | raymond.hettinger | 2007-10-08 18:36:23 -0700 (Mon, 08 Oct 2007) | 1 line Make the error messages more specific ........ r58384 | gregory.p.smith | 2007-10-08 23:02:21 -0700 (Mon, 08 Oct 2007) | 10 lines Splits Modules/_bsddb.c up into bsddb.h and _bsddb.c and adds a C API object available as bsddb.db.api. This is based on the patch submitted by Duncan Grisby here: http://sourceforge.net/tracker/index.php?func=detail&aid=1551895&group_id=13900&atid=313900 See this thread for additional info: http://sourceforge.net/mailarchive/forum.php?thread_name=E1GAVDK-0002rk-Iw%40apasphere.com&forum_name=pybsddb-users It also cleans up the code a little by removing some ifdef/endifs for python prior to 2.1 and for unsupported Berkeley DB <= 3.2. ........ r58385 | gregory.p.smith | 2007-10-08 23:50:43 -0700 (Mon, 08 Oct 2007) | 5 lines Fix a double free when positioning a database cursor to a non-existant string key (and probably a few other situations with string keys). This was reported with a patch as pybsddb sourceforge bug 1708868 by jjjhhhlll at gmail. ........ r58386 | gregory.p.smith | 2007-10-09 00:19:11 -0700 (Tue, 09 Oct 2007) | 3 lines Use the highest cPickle protocol in bsddb.dbshelve. This comes from sourceforge pybsddb patch 1551443 by w_barnes. ........ r58394 | gregory.p.smith | 2007-10-09 11:26:02 -0700 (Tue, 09 Oct 2007) | 2 lines remove another sleepycat reference ........ r58396 | kurt.kaiser | 2007-10-09 12:31:30 -0700 (Tue, 09 Oct 2007) | 3 lines Allow interrupt only when executing user code in subprocess Patch 1225 Tal Einat modified from IDLE-Spoon. ........ r58399 | brett.cannon | 2007-10-09 17:07:50 -0700 (Tue, 09 Oct 2007) | 5 lines Remove file-level typedefs that were inconsistently used throughout the file. Just move over to the public API names. Closes issue1238. ........ r58401 | raymond.hettinger | 2007-10-09 17:26:46 -0700 (Tue, 09 Oct 2007) | 1 line Accept Jim Jewett's api suggestion to use None instead of -1 to indicate unbounded deques. ........ r58403 | kurt.kaiser | 2007-10-09 17:55:40 -0700 (Tue, 09 Oct 2007) | 2 lines Allow cursor color change w/o restart. Patch 1725576 Tal Einat. ........ r58404 | kurt.kaiser | 2007-10-09 18:06:47 -0700 (Tue, 09 Oct 2007) | 2 lines show paste if > 80 columns. Patch 1659326 Tal Einat. ........ r58415 | thomas.heller | 2007-10-11 12:51:32 -0700 (Thu, 11 Oct 2007) | 5 lines On OS X, use os.uname() instead of gestalt.sysv(...) to get the operating system version. This allows to use ctypes when Python was configured with --disable-toolbox-glue. ........ r58419 | neal.norwitz | 2007-10-11 20:01:01 -0700 (Thu, 11 Oct 2007) | 1 line Get rid of warning about not being able to create an existing directory. ........ r58420 | neal.norwitz | 2007-10-11 20:01:30 -0700 (Thu, 11 Oct 2007) | 1 line Get rid of warnings on a bunch of platforms by using a proper prototype. ........ r58421 | neal.norwitz | 2007-10-11 20:01:54 -0700 (Thu, 11 Oct 2007) | 4 lines Get rid of compiler warning about retval being used (returned) without being initialized. (gcc warning and Coverity 202) ........ r58422 | neal.norwitz | 2007-10-11 20:03:23 -0700 (Thu, 11 Oct 2007) | 1 line Fix Coverity 168: Close the file before returning (exiting). ........ r58423 | neal.norwitz | 2007-10-11 20:04:18 -0700 (Thu, 11 Oct 2007) | 4 lines Fix Coverity 180: Don't overallocate. We don't need structs, but pointers. Also fix a memory leak. ........ r58424 | neal.norwitz | 2007-10-11 20:05:19 -0700 (Thu, 11 Oct 2007) | 5 lines Fix Coverity 185-186: If the passed in FILE is NULL, uninitialized memory would be accessed. Will backport. ........ r58425 | neal.norwitz | 2007-10-11 20:52:34 -0700 (Thu, 11 Oct 2007) | 1 line Get this module to compile with bsddb versions prior to 4.3 ........ r58430 | martin.v.loewis | 2007-10-12 01:56:52 -0700 (Fri, 12 Oct 2007) | 3 lines Bug #1216: Restore support for Visual Studio 2002. Will backport to 2.5. ........ r58433 | raymond.hettinger | 2007-10-12 10:53:11 -0700 (Fri, 12 Oct 2007) | 1 line Fix test of count.__repr__() to ignore the 'L' if the count is a long ........ r58434 | gregory.p.smith | 2007-10-12 11:44:06 -0700 (Fri, 12 Oct 2007) | 4 lines Fixes http://bugs.python.org/issue1233 - bsddb.dbshelve.DBShelf.append was useless due to inverted logic. Also adds a test case for RECNO dbs to test_dbshelve. ........ r58445 | georg.brandl | 2007-10-13 06:20:03 -0700 (Sat, 13 Oct 2007) | 2 lines Fix email example. ........ r58450 | gregory.p.smith | 2007-10-13 16:02:05 -0700 (Sat, 13 Oct 2007) | 2 lines Fix an uncollectable reference leak in bsddb.db.DBShelf.append ........ r58453 | neal.norwitz | 2007-10-13 17:18:40 -0700 (Sat, 13 Oct 2007) | 8 lines Let the O/S supply a port if none of the default ports can be used. This should make the tests more robust at the expense of allowing tests to be sloppier by not requiring them to cleanup after themselves. (It will legitamitely help when running two test suites simultaneously or if another process is already using one of the predefined ports.) Also simplifies (slightLy) the exception handling elsewhere. ........ r58459 | neal.norwitz | 2007-10-14 11:30:21 -0700 (Sun, 14 Oct 2007) | 2 lines Don't raise a string exception, they don't work anymore. ........ r58460 | neal.norwitz | 2007-10-14 11:40:37 -0700 (Sun, 14 Oct 2007) | 1 line Use unittest for assertions ........ r58468 | armin.rigo | 2007-10-15 00:48:35 -0700 (Mon, 15 Oct 2007) | 2 lines test_bigbits was not testing what it seemed to. ........ r58471 | guido.van.rossum | 2007-10-15 08:54:11 -0700 (Mon, 15 Oct 2007) | 3 lines Change a PyErr_Print() into a PyErr_Clear(), per discussion in issue 1031213. ........ r58500 | raymond.hettinger | 2007-10-16 12:18:30 -0700 (Tue, 16 Oct 2007) | 1 line Improve error messages ........ r58506 | raymond.hettinger | 2007-10-16 14:28:32 -0700 (Tue, 16 Oct 2007) | 1 line More docs, error messages, and tests ........ r58507 | andrew.kuchling | 2007-10-16 15:58:03 -0700 (Tue, 16 Oct 2007) | 1 line Add items ........ r58508 | brett.cannon | 2007-10-16 16:24:06 -0700 (Tue, 16 Oct 2007) | 3 lines Remove ``:const:`` notation on None in parameter list. Since the markup is not rendered for parameters it just showed up as ``:const:`None` `` in the output. ........ r58509 | brett.cannon | 2007-10-16 16:26:45 -0700 (Tue, 16 Oct 2007) | 3 lines Re-order some functions whose parameters differ between PyObject and const char * so that they are next to each other. ........ r58522 | armin.rigo | 2007-10-17 11:46:37 -0700 (Wed, 17 Oct 2007) | 5 lines Fix the overflow checking of list_repeat. Introduce overflow checking into list_inplace_repeat. Backport candidate, possibly. ........ r58530 | facundo.batista | 2007-10-17 20:16:03 -0700 (Wed, 17 Oct 2007) | 7 lines Issue #1580738. When HTTPConnection reads the whole stream with read(), it closes itself. When the stream is read in several calls to read(n), it should behave in the same way if HTTPConnection knows where the end of the stream is (through self.length). Added a test case for this behaviour. ........ r58531 | facundo.batista | 2007-10-17 20:44:48 -0700 (Wed, 17 Oct 2007) | 3 lines Issue 1289, just a typo. ........ r58532 | gregory.p.smith | 2007-10-18 00:56:54 -0700 (Thu, 18 Oct 2007) | 4 lines cleanup test_dbtables to use mkdtemp. cleanup dbtables to pass txn as a keyword argument whenever possible to avoid bugs and confusion. (dbtables.py line 447 self.db.get using txn as a non-keyword was an actual bug due to this) ........ r58533 | gregory.p.smith | 2007-10-18 01:34:20 -0700 (Thu, 18 Oct 2007) | 4 lines Fix a weird bug in dbtables: if it chose a random rowid string that contained NULL bytes it would cause the database all sorts of problems in the future leading to very strange random failures and corrupt dbtables.bsdTableDb dbs. ........ r58534 | gregory.p.smith | 2007-10-18 09:32:02 -0700 (Thu, 18 Oct 2007) | 3 lines A cleaner fix than the one committed last night. Generate random rowids that do not contain null bytes. ........ r58537 | gregory.p.smith | 2007-10-18 10:17:57 -0700 (Thu, 18 Oct 2007) | 2 lines mention bsddb fixes. ........ r58538 | raymond.hettinger | 2007-10-18 14:13:06 -0700 (Thu, 18 Oct 2007) | 1 line Remove useless warning ........ r58539 | gregory.p.smith | 2007-10-19 00:31:20 -0700 (Fri, 19 Oct 2007) | 2 lines squelch the warning that this test is supposed to trigger. ........ r58542 | georg.brandl | 2007-10-19 05:32:39 -0700 (Fri, 19 Oct 2007) | 2 lines Clarify wording for apply(). ........ r58544 | mark.summerfield | 2007-10-19 05:48:17 -0700 (Fri, 19 Oct 2007) | 3 lines Added a cross-ref to each other. ........ r58545 | georg.brandl | 2007-10-19 10:38:49 -0700 (Fri, 19 Oct 2007) | 2 lines #1284: "S" means "seen", not unread. ........ r58548 | thomas.heller | 2007-10-19 11:11:41 -0700 (Fri, 19 Oct 2007) | 4 lines Fix ctypes on 32-bit systems when Python is configured --with-system-ffi. See also https://bugs.launchpad.net/bugs/72505. Ported from release25-maint branch. ........ r58550 | facundo.batista | 2007-10-19 12:25:57 -0700 (Fri, 19 Oct 2007) | 8 lines The constructor from tuple was way too permissive: it allowed bad coefficient numbers, floats in the sign, and other details that generated directly the wrong number in the best case, or triggered misfunctionality in the alorithms. Test cases added for these issues. Thanks Mark Dickinson. ........ r58559 | georg.brandl | 2007-10-20 06:22:53 -0700 (Sat, 20 Oct 2007) | 2 lines Fix code being interpreted as a target. ........ r58561 | georg.brandl | 2007-10-20 06:36:24 -0700 (Sat, 20 Oct 2007) | 2 lines Document new "cmdoption" directive. ........ r58562 | georg.brandl | 2007-10-20 08:21:22 -0700 (Sat, 20 Oct 2007) | 2 lines Make a path more Unix-standardy. ........ r58564 | georg.brandl | 2007-10-20 10:51:39 -0700 (Sat, 20 Oct 2007) | 2 lines Document new directive "envvar". ........ r58567 | georg.brandl | 2007-10-20 11:08:14 -0700 (Sat, 20 Oct 2007) | 6 lines * Add new toplevel chapter, "Using Python." (how to install, configure and setup python on different platforms -- at least in theory.) * Move the Python on Mac docs in that chapter. * Add a new chapter about the command line invocation, by stargaming. ........ r58568 | georg.brandl | 2007-10-20 11:33:20 -0700 (Sat, 20 Oct 2007) | 2 lines Change title, for now. ........ r58569 | georg.brandl | 2007-10-20 11:39:25 -0700 (Sat, 20 Oct 2007) | 2 lines Add entry to ACKS. ........ r58570 | georg.brandl | 2007-10-20 12:05:45 -0700 (Sat, 20 Oct 2007) | 2 lines Clarify -E docs. ........ r58571 | georg.brandl | 2007-10-20 12:08:36 -0700 (Sat, 20 Oct 2007) | 2 lines Even more clarification. ........ r58572 | andrew.kuchling | 2007-10-20 12:25:37 -0700 (Sat, 20 Oct 2007) | 1 line Fix protocol name ........ r58573 | andrew.kuchling | 2007-10-20 12:35:18 -0700 (Sat, 20 Oct 2007) | 1 line Various items ........ r58574 | andrew.kuchling | 2007-10-20 12:39:35 -0700 (Sat, 20 Oct 2007) | 1 line Use correct header line ........ r58576 | armin.rigo | 2007-10-21 02:14:15 -0700 (Sun, 21 Oct 2007) | 3 lines Add a crasher for the long-standing issue with closing a file while another thread uses it. ........ r58577 | georg.brandl | 2007-10-21 03:01:56 -0700 (Sun, 21 Oct 2007) | 2 lines Remove duplicate crasher. ........ r58578 | georg.brandl | 2007-10-21 03:24:20 -0700 (Sun, 21 Oct 2007) | 2 lines Unify "byte code" to "bytecode". Also sprinkle :term: markup for it. ........ r58579 | georg.brandl | 2007-10-21 03:32:54 -0700 (Sun, 21 Oct 2007) | 2 lines Add markup to new function descriptions. ........ r58580 | georg.brandl | 2007-10-21 03:45:46 -0700 (Sun, 21 Oct 2007) | 2 lines Add :term:s for descriptors. ........ r58581 | georg.brandl | 2007-10-21 03:46:24 -0700 (Sun, 21 Oct 2007) | 2 lines Unify "file-descriptor" to "file descriptor". ........ r58582 | georg.brandl | 2007-10-21 03:52:38 -0700 (Sun, 21 Oct 2007) | 2 lines Add :term: for generators. ........ r58583 | georg.brandl | 2007-10-21 05:10:28 -0700 (Sun, 21 Oct 2007) | 2 lines Add :term:s for iterator. ........ r58584 | georg.brandl | 2007-10-21 05:15:05 -0700 (Sun, 21 Oct 2007) | 2 lines Add :term:s for "new-style class". ........ r58588 | neal.norwitz | 2007-10-21 21:47:54 -0700 (Sun, 21 Oct 2007) | 1 line Add Chris Monson so he can edit PEPs. ........ r58594 | guido.van.rossum | 2007-10-22 09:27:19 -0700 (Mon, 22 Oct 2007) | 4 lines Issue #1307, patch by Derek Shockey. When "MAIL" is received without args, an exception happens instead of sending a 501 syntax error response. ........ r58598 | travis.oliphant | 2007-10-22 19:40:56 -0700 (Mon, 22 Oct 2007) | 1 line Add phuang patch from Issue 708374 which adds offset parameter to mmap module. ........ r58601 | neal.norwitz | 2007-10-22 22:44:27 -0700 (Mon, 22 Oct 2007) | 2 lines Bug #1313, fix typo (wrong variable name) in example. ........ r58609 | georg.brandl | 2007-10-23 11:21:35 -0700 (Tue, 23 Oct 2007) | 2 lines Update Pygments version from externals. ........ r58618 | guido.van.rossum | 2007-10-23 12:25:41 -0700 (Tue, 23 Oct 2007) | 3 lines Issue 1307 by Derek Shockey, fox the same bug for RCPT. Neal: please backport! ........ r58620 | raymond.hettinger | 2007-10-23 13:37:41 -0700 (Tue, 23 Oct 2007) | 1 line Shorter name for namedtuple() ........ r58621 | andrew.kuchling | 2007-10-23 13:55:47 -0700 (Tue, 23 Oct 2007) | 1 line Update name ........ r58622 | raymond.hettinger | 2007-10-23 14:23:07 -0700 (Tue, 23 Oct 2007) | 1 line Fixup news entry ........ r58623 | raymond.hettinger | 2007-10-23 18:28:33 -0700 (Tue, 23 Oct 2007) | 1 line Optimize sum() for integer and float inputs. ........ r58624 | raymond.hettinger | 2007-10-23 19:05:51 -0700 (Tue, 23 Oct 2007) | 1 line Fixup error return and add support for intermixed ints and floats/ ........ r58628 | vinay.sajip | 2007-10-24 03:47:06 -0700 (Wed, 24 Oct 2007) | 1 line Bug #1321: Fixed logic error in TimedRotatingFileHandler.__init__() ........ r58641 | facundo.batista | 2007-10-24 12:11:08 -0700 (Wed, 24 Oct 2007) | 4 lines Issue 1290. CharacterData.__repr__ was constructing a string in response that keeped having a non-ascii character. ........ r58643 | thomas.heller | 2007-10-24 12:50:45 -0700 (Wed, 24 Oct 2007) | 1 line Added unittest for calling a function with paramflags (backport from py3k branch). ........ r58645 | matthias.klose | 2007-10-24 13:00:44 -0700 (Wed, 24 Oct 2007) | 2 lines - Build using system ffi library on arm*-linux*. ........ r58651 | georg.brandl | 2007-10-24 14:40:38 -0700 (Wed, 24 Oct 2007) | 2 lines Bug #1287: make os.environ.pop() work as expected. ........ r58652 | raymond.hettinger | 2007-10-24 19:26:58 -0700 (Wed, 24 Oct 2007) | 1 line Missing DECREFs ........ r58653 | matthias.klose | 2007-10-24 23:37:24 -0700 (Wed, 24 Oct 2007) | 2 lines - Build using system ffi library on arm*-linux*, pass --with-system-ffi to CONFIG_ARGS ........ r58655 | thomas.heller | 2007-10-25 12:47:32 -0700 (Thu, 25 Oct 2007) | 2 lines ffi_type_longdouble may be already #defined. See issue 1324. ........ r58656 | kurt.kaiser | 2007-10-25 15:43:45 -0700 (Thu, 25 Oct 2007) | 3 lines Correct an ancient bug in an unused path by removing that path: register() is now idempotent. ........ r58660 | kurt.kaiser | 2007-10-25 17:10:09 -0700 (Thu, 25 Oct 2007) | 4 lines 1. Add comments to provide top-level documentation. 2. Refactor to use more descriptive names. 3. Enhance tests in main(). ........ r58675 | georg.brandl | 2007-10-26 11:30:41 -0700 (Fri, 26 Oct 2007) | 2 lines Fix new pop() method on os.environ on ignorecase-platforms. ........ r58696 | neal.norwitz | 2007-10-27 15:32:21 -0700 (Sat, 27 Oct 2007) | 1 line Update URL for Pygments. 0.8.1 is no longer available ........ r58697 | hyeshik.chang | 2007-10-28 04:19:02 -0700 (Sun, 28 Oct 2007) | 3 lines - Add support for FreeBSD 8 which is recently forked from FreeBSD 7. - Regenerate IN module for most recent maintenance tree of FreeBSD 6 and 7. ........ r58698 | hyeshik.chang | 2007-10-28 05:38:09 -0700 (Sun, 28 Oct 2007) | 2 lines Enable platform-specific tweaks for FreeBSD 8 (exactly same to FreeBSD 7's yet) ........ r58700 | kurt.kaiser | 2007-10-28 12:03:59 -0700 (Sun, 28 Oct 2007) | 2 lines Add confirmation dialog before printing. Patch 1717170 Tal Einat. ........ r58706 | guido.van.rossum | 2007-10-29 13:52:45 -0700 (Mon, 29 Oct 2007) | 3 lines Patch 1353 by Jacob Winther. Add mp4 mapping to mimetypes.py. ........ r58709 | guido.van.rossum | 2007-10-29 15:15:05 -0700 (Mon, 29 Oct 2007) | 6 lines Backport fixes for the code that decodes octal escapes (and for PyString also hex escapes) -- this was reaching beyond the end of the input string buffer, even though it is not supposed to be \0-terminated. This has no visible effect but is clearly the correct thing to do. (In 3.0 it had a visible effect after removing ob_sstate from PyString.) ........ r58710 | kurt.kaiser | 2007-10-29 19:38:54 -0700 (Mon, 29 Oct 2007) | 7 lines check in Tal Einat's update to tabpage.py Patch 1612746 M configDialog.py M NEWS.txt AM tabbedpages.py ........ r58715 | georg.brandl | 2007-10-30 10:51:18 -0700 (Tue, 30 Oct 2007) | 2 lines Use correct markup. ........ r58716 | georg.brandl | 2007-10-30 10:57:12 -0700 (Tue, 30 Oct 2007) | 2 lines Make example about hiding None return values at the prompt clearer. ........ r58728 | neal.norwitz | 2007-10-30 23:33:20 -0700 (Tue, 30 Oct 2007) | 1 line Fix some compiler warnings for signed comparisons on Unix and Windows. ........ r58731 | martin.v.loewis | 2007-10-31 10:19:33 -0700 (Wed, 31 Oct 2007) | 2 lines Adding Christian Heimes. ........ r58737 | raymond.hettinger | 2007-10-31 14:57:58 -0700 (Wed, 31 Oct 2007) | 1 line Clarify the reasons why pickle is almost always better than marshal ........ r58739 | raymond.hettinger | 2007-10-31 15:15:49 -0700 (Wed, 31 Oct 2007) | 1 line Sets are marshalable. ........
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timestamped entries from multiple log files). Returns an :term:`iterator`
Merged revisions 66887,66891,66902-66903,66905-66906,66911-66913,66922,66927-66928,66936,66939-66940,66962,66964,66973 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ................ r66887 | benjamin.peterson | 2008-10-13 16:51:40 -0500 (Mon, 13 Oct 2008) | 1 line document how to disable fixers ................ r66891 | amaury.forgeotdarc | 2008-10-14 16:47:22 -0500 (Tue, 14 Oct 2008) | 5 lines #4122: On Windows, Py_UNICODE_ISSPACE cannot be used in an extension module: compilation fails with "undefined reference to _Py_ascii_whitespace" Will backport to 2.6. ................ r66902 | skip.montanaro | 2008-10-15 06:49:10 -0500 (Wed, 15 Oct 2008) | 1 line easter egg ................ r66903 | benjamin.peterson | 2008-10-15 15:34:09 -0500 (Wed, 15 Oct 2008) | 1 line don't recurse into directories that start with '.' ................ r66905 | benjamin.peterson | 2008-10-15 16:05:55 -0500 (Wed, 15 Oct 2008) | 1 line support the optional line argument for idle ................ r66906 | benjamin.peterson | 2008-10-15 16:58:46 -0500 (Wed, 15 Oct 2008) | 1 line add a much requested newline ................ r66911 | benjamin.peterson | 2008-10-15 18:10:28 -0500 (Wed, 15 Oct 2008) | 41 lines Merged revisions 66805,66841,66860,66884-66886,66893,66907,66910 via svnmerge from svn+ssh://pythondev@svn.python.org/sandbox/trunk/2to3/lib2to3 ........ r66805 | benjamin.peterson | 2008-10-04 20:11:02 -0500 (Sat, 04 Oct 2008) | 1 line mention what the fixes directory is for ........ r66841 | benjamin.peterson | 2008-10-07 17:48:12 -0500 (Tue, 07 Oct 2008) | 1 line use assertFalse and assertTrue ........ r66860 | benjamin.peterson | 2008-10-08 16:05:07 -0500 (Wed, 08 Oct 2008) | 1 line instead of abusing the pattern matcher, use start_tree to find a next binding ........ r66884 | benjamin.peterson | 2008-10-13 15:50:30 -0500 (Mon, 13 Oct 2008) | 1 line don't print tokens to stdout when -v is given ........ r66885 | benjamin.peterson | 2008-10-13 16:28:57 -0500 (Mon, 13 Oct 2008) | 1 line add the -x option to disable fixers ........ r66886 | benjamin.peterson | 2008-10-13 16:33:53 -0500 (Mon, 13 Oct 2008) | 1 line cut down on some crud ........ r66893 | benjamin.peterson | 2008-10-14 17:16:54 -0500 (Tue, 14 Oct 2008) | 1 line add an optional set literal fixer ........ r66907 | benjamin.peterson | 2008-10-15 16:59:41 -0500 (Wed, 15 Oct 2008) | 1 line don't write backup files by default ........ r66910 | benjamin.peterson | 2008-10-15 17:43:10 -0500 (Wed, 15 Oct 2008) | 1 line add the -n option; it stops backupfiles from being written ........ ................ r66912 | hirokazu.yamamoto | 2008-10-16 01:25:25 -0500 (Thu, 16 Oct 2008) | 2 lines removed unused _PyUnicode_FromFileSystemEncodedObject. made win32_chdir, win32_wchdir static. ................ r66913 | benjamin.peterson | 2008-10-16 13:52:14 -0500 (Thu, 16 Oct 2008) | 1 line document that deque indexing is O(n) #4123 ................ r66922 | benjamin.peterson | 2008-10-16 14:40:14 -0500 (Thu, 16 Oct 2008) | 1 line use new showwarnings signature for idle #3391 ................ r66927 | andrew.kuchling | 2008-10-16 15:15:47 -0500 (Thu, 16 Oct 2008) | 1 line Fix wording (2.6.1 backport candidate) ................ r66928 | georg.brandl | 2008-10-16 15:20:56 -0500 (Thu, 16 Oct 2008) | 2 lines Add more TOC to the whatsnew index page. ................ r66936 | georg.brandl | 2008-10-16 16:20:15 -0500 (Thu, 16 Oct 2008) | 2 lines #4131: FF3 doesn't write cookies.txt files. ................ r66939 | georg.brandl | 2008-10-16 16:36:39 -0500 (Thu, 16 Oct 2008) | 2 lines part of #4012: kill off old name "processing". ................ r66940 | georg.brandl | 2008-10-16 16:38:48 -0500 (Thu, 16 Oct 2008) | 2 lines #4083: add "as" to except handler grammar as per PEP 3110. ................ r66962 | benjamin.peterson | 2008-10-17 15:01:01 -0500 (Fri, 17 Oct 2008) | 1 line clarify CALL_FUNCTION #4141 ................ r66964 | georg.brandl | 2008-10-17 16:41:49 -0500 (Fri, 17 Oct 2008) | 2 lines Fix duplicate word. ................ r66973 | armin.ronacher | 2008-10-19 03:27:43 -0500 (Sun, 19 Oct 2008) | 3 lines Fixed #4067 by implementing _attributes and _fields for the AST root node. ................
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over the sorted values.
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Similar to ``sorted(itertools.chain(*iterables))`` but returns an iterable, does
not pull the data into memory all at once, and assumes that each of the input
streams is already sorted (smallest to largest).
.. function:: nlargest(n, iterable, key=None)
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Return a list with the *n* largest elements from the dataset defined by
*iterable*. *key*, if provided, specifies a function of one argument that is
used to extract a comparison key from each element in the iterable:
``key=str.lower`` Equivalent to: ``sorted(iterable, key=key,
reverse=True)[:n]``
.. function:: nsmallest(n, iterable, key=None)
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Return a list with the *n* smallest elements from the dataset defined by
*iterable*. *key*, if provided, specifies a function of one argument that is
used to extract a comparison key from each element in the iterable:
``key=str.lower`` Equivalent to: ``sorted(iterable, key=key)[:n]``
The latter two functions perform best for smaller values of *n*. For larger
values, it is more efficient to use the :func:`sorted` function. Also, when
``n==1``, it is more efficient to use the built-in :func:`min` and :func:`max`
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functions.
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Basic Examples
--------------
A `heapsort <http://en.wikipedia.org/wiki/Heapsort>`_ can be implemented by
pushing all values onto a heap and then popping off the smallest values one at a
time::
>>> def heapsort(iterable):
... 'Equivalent to sorted(iterable)'
... h = []
... for value in iterable:
... heappush(h, value)
... return [heappop(h) for i in range(len(h))]
...
>>> heapsort([1, 3, 5, 7, 9, 2, 4, 6, 8, 0])
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Heap elements can be tuples. This is useful for assigning comparison values
(such as task priorities) alongside the main record being tracked::
>>> h = []
>>> heappush(h, (5, 'write code'))
>>> heappush(h, (7, 'release product'))
>>> heappush(h, (1, 'write spec'))
>>> heappush(h, (3, 'create tests'))
>>> heappop(h)
(1, 'write spec')
Priority Queue Implementation Notes
-----------------------------------
A `priority queue <http://en.wikipedia.org/wiki/Priority_queue>`_ is common use
for a heap, and it presents several implementation challenges:
* Sort stability: how do you get two tasks with equal priorities to be returned
in the order they were originally added?
* Tuple comparison breaks for (priority, task) pairs if the priorities are equal
and the tasks do not have a default comparison order.
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* If the priority of a task changes, how do you move it to a new position in
the heap?
* Or if a pending task needs to be deleted, how do you find it and remove it
from the queue?
A solution to the first two challenges is to store entries as 3-element list
including the priority, an entry count, and the task. The entry count serves as
a tie-breaker so that two tasks with the same priority are returned in the order
they were added. And since no two entry counts are the same, the tuple
comparison will never attempt to directly compare two tasks.
The remaining challenges revolve around finding a pending task and making
changes to its priority or removing it entirely. Finding a task can be done
with a dictionary pointing to an entry in the queue.
Removing the entry or changing its priority is more difficult because it would
break the heap structure invariants. So, a possible solution is to mark an
entry as invalid and optionally add a new entry with the revised priority::
pq = [] # the priority queue list
counter = itertools.count(1) # unique sequence count
task_finder = {} # mapping of tasks to entries
INVALID = 0 # mark an entry as deleted
def add_task(priority, task, count=None):
if count is None:
count = next(counter)
entry = [priority, count, task]
task_finder[task] = entry
heappush(pq, entry)
def get_top_priority():
while True:
priority, count, task = heappop(pq)
del task_finder[task]
if count is not INVALID:
return task
def delete_task(task):
entry = task_finder[task]
entry[1] = INVALID
def reprioritize(priority, task):
entry = task_finder[task]
add_task(priority, task, entry[1])
entry[1] = INVALID
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Theory
------
Heaps are arrays for which ``a[k] <= a[2*k+1]`` and ``a[k] <= a[2*k+2]`` for all
*k*, counting elements from 0. For the sake of comparison, non-existing
elements are considered to be infinite. The interesting property of a heap is
that ``a[0]`` is always its smallest element.
The strange invariant above is meant to be an efficient memory representation
for a tournament. The numbers below are *k*, not ``a[k]``::
0
1 2
3 4 5 6
7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
In the tree above, each cell *k* is topping ``2*k+1`` and ``2*k+2``. In an usual
binary tournament we see in sports, each cell is the winner over the two cells
it tops, and we can trace the winner down the tree to see all opponents s/he
had. However, in many computer applications of such tournaments, we do not need
to trace the history of a winner. To be more memory efficient, when a winner is
promoted, we try to replace it by something else at a lower level, and the rule
becomes that a cell and the two cells it tops contain three different items, but
the top cell "wins" over the two topped cells.
If this heap invariant is protected at all time, index 0 is clearly the overall
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.
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
last 0'th element you extracted. This is especially useful in simulation
contexts, where the tree holds all incoming events, and the "win" condition
means the smallest scheduled time. When an event schedule other events for
execution, they are scheduled into the future, so they can easily go into the
heap. So, a heap is a good structure for implementing schedulers (this is what
I used for my MIDI sequencer :-).
Various structures for implementing schedulers have been extensively studied,
and heaps are good for this, as they are reasonably speedy, the speed is almost
constant, and the worst case is not much different than the average case.
However, there are other representations which are more efficient overall, yet
the worst cases might be terrible.
Heaps are also very useful in big disk sorts. You most probably all know that a
big sort implies producing "runs" (which are pre-sorted sequences, which size is
usually related to the amount of CPU memory), followed by a merging passes for
these runs, which merging is often very cleverly organised [#]_. It is very
important that the initial sort produces the longest runs possible. Tournaments
are a good way to that. If, using all the memory available to hold a
tournament, you replace and percolate items that happen to fit the current run,
you'll produce runs which are twice the size of the memory for random input, and
much better for input fuzzily ordered.
Moreover, if you output the 0'th item on disk and get an input which may not fit
in the current tournament (because the value "wins" over the last output value),
it cannot fit in the heap, so the size of the heap decreases. The freed memory
could be cleverly reused immediately for progressively building a second heap,
which grows at exactly the same rate the first heap is melting. When the first
heap completely vanishes, you switch heaps and start a new run. Clever and
quite effective!
In a word, heaps are useful memory structures to know. I use them in a few
applications, and I think it is good to keep a 'heap' module around. :-)
.. rubric:: Footnotes
.. [#] The disk balancing algorithms which are current, nowadays, are more annoying
than clever, and this is a consequence of the seeking capabilities of the disks.
On devices which cannot seek, like big tape drives, the story was quite
different, and one had to be very clever to ensure (far in advance) that each
tape movement will be the most effective possible (that is, will best
participate at "progressing" the merge). Some tapes were even able to read
backwards, and this was also used to avoid the rewinding time. Believe me, real
good tape sorts were quite spectacular to watch! From all times, sorting has
always been a Great Art! :-)