You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@spark.apache.org by gu...@apache.org on 2020/07/27 11:12:42 UTC

[spark] branch master updated: [SPARK-32435][PYTHON] Remove heapq3 port from Python 3

This is an automated email from the ASF dual-hosted git repository.

gurwls223 pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/spark.git


The following commit(s) were added to refs/heads/master by this push:
     new a82aee0  [SPARK-32435][PYTHON] Remove heapq3 port from Python 3
a82aee0 is described below

commit a82aee044127825ffefa0ed09b0ae5b987b9dd21
Author: HyukjinKwon <gu...@apache.org>
AuthorDate: Mon Jul 27 20:10:13 2020 +0900

    [SPARK-32435][PYTHON] Remove heapq3 port from Python 3
    
    ### What changes were proposed in this pull request?
    
    This PR removes the manual port of `heapq3.py` introduced from SPARK-3073. The main reason of this was to support Python 2.6 and 2.7 because Python 2's `heapq.merge()` doesn't not support `key` and `reverse`.
    
    See
    - https://docs.python.org/2/library/heapq.html#heapq.merge in Python 2
    - https://docs.python.org/3.8/library/heapq.html#heapq.merge in Python 3
    
    Since we dropped the Python 2 at SPARK-32138, we can remove this away.
    
    ### Why are the changes needed?
    
    To remove unnecessary codes. Also, we can leverage bug fixes made in Python 3.x at `heapq`.
    
    ### Does this PR introduce _any_ user-facing change?
    
    No, dev-only.
    
    ### How was this patch tested?
    
    Existing tests should cover. I locally ran and verified:
    
    ```bash
    ./python/run-tests --python-executable=python3 --testname="pyspark.tests.test_shuffle"
    ./python/run-tests --python-executable=python3 --testname="pyspark.shuffle ExternalSorter"
    ./python/run-tests --python-executable=python3 --testname="pyspark.tests.test_rdd RDDTests.test_external_group_by_key"
    ```
    
    Closes #29229 from HyukjinKwon/SPARK-32435.
    
    Authored-by: HyukjinKwon <gu...@apache.org>
    Signed-off-by: HyukjinKwon <gu...@apache.org>
---
 LICENSE                           |   1 -
 LICENSE-binary                    |   6 -
 dev/.rat-excludes                 |   1 -
 dev/tox.ini                       |   2 +-
 licenses-binary/LICENSE-heapq.txt | 280 ------------
 licenses/LICENSE-heapq.txt        |  49 ---
 python/pylintrc                   |   2 +-
 python/pyspark/heapq3.py          | 890 --------------------------------------
 python/pyspark/shuffle.py         |   6 +-
 9 files changed, 5 insertions(+), 1232 deletions(-)

diff --git a/LICENSE b/LICENSE
index 8cec4f5..df6bed1 100644
--- a/LICENSE
+++ b/LICENSE
@@ -222,7 +222,6 @@ external/spark-ganglia-lgpl/src/main/java/com/codahale/metrics/ganglia/GangliaRe
 Python Software Foundation License
 ----------------------------------
 
-pyspark/heapq3.py
 python/docs/source/_static/copybutton.js
 
 BSD 3-Clause
diff --git a/LICENSE-binary b/LICENSE-binary
index b50da6b..d363661 100644
--- a/LICENSE-binary
+++ b/LICENSE-binary
@@ -557,12 +557,6 @@ jakarta.ws.rs:jakarta.ws.rs-api https://github.com/eclipse-ee4j/jaxrs-api
 org.glassfish.hk2.external:jakarta.inject
 
 
-Python Software Foundation License
-----------------------------------
-
-pyspark/heapq3.py
-
-
 Public Domain
 -------------
 
diff --git a/dev/.rat-excludes b/dev/.rat-excludes
index db6a4ce..3889dc9 100644
--- a/dev/.rat-excludes
+++ b/dev/.rat-excludes
@@ -49,7 +49,6 @@ jsonFormatter.min.js
 .*log
 pyspark-coverage-site/*
 cloudpickle/*
-heapq3.py
 join.py
 SparkExprTyper.scala
 SparkILoop.scala
diff --git a/dev/tox.ini b/dev/tox.ini
index e25595a..5bf27d1 100644
--- a/dev/tox.ini
+++ b/dev/tox.ini
@@ -16,4 +16,4 @@
 [pycodestyle]
 ignore=E226,E241,E305,E402,E722,E731,E741,W503,W504
 max-line-length=100
-exclude=python/pyspark/cloudpickle/*.py,heapq3.py,shared.py,python/docs/source/conf.py,work/*/*.py,python/.eggs/*,dist/*,.git/*
+exclude=python/pyspark/cloudpickle/*.py,shared.py,python/docs/source/conf.py,work/*/*.py,python/.eggs/*,dist/*,.git/*
diff --git a/licenses-binary/LICENSE-heapq.txt b/licenses-binary/LICENSE-heapq.txt
deleted file mode 100644
index 0c4c4b9..0000000
--- a/licenses-binary/LICENSE-heapq.txt
+++ /dev/null
@@ -1,280 +0,0 @@
-
-# A. HISTORY OF THE SOFTWARE
-# ==========================
-#
-# Python was created in the early 1990s by Guido van Rossum at Stichting
-# Mathematisch Centrum (CWI, see http://www.cwi.nl) in the Netherlands
-# as a successor of a language called ABC.  Guido remains Python's
-# principal author, although it includes many contributions from others.
-#
-# In 1995, Guido continued his work on Python at the Corporation for
-#     National Research Initiatives (CNRI, see http://www.cnri.reston.va.us)
-# in Reston, Virginia where he released several versions of the
-# software.
-#
-# In May 2000, Guido and the Python core development team moved to
-# BeOpen.com to form the BeOpen PythonLabs team.  In October of the same
-# year, the PythonLabs team moved to Digital Creations (now Zope
-# Corporation, see http://www.zope.com).  In 2001, the Python Software
-# Foundation (PSF, see http://www.python.org/psf/) was formed, a
-# non-profit organization created specifically to own Python-related
-# Intellectual Property.  Zope Corporation is a sponsoring member of
-# the PSF.
-#
-# All Python releases are Open Source (see http://www.opensource.org for
-# the Open Source Definition).  Historically, most, but not all, Python
-# releases have also been GPL-compatible; the table below summarizes
-# the various releases.
-#
-# Release         Derived     Year        Owner       GPL-
-# from                                compatible? (1)
-#
-# 0.9.0 thru 1.2              1991-1995   CWI         yes
-# 1.3 thru 1.5.2  1.2         1995-1999   CNRI        yes
-# 1.6             1.5.2       2000        CNRI        no
-# 2.0             1.6         2000        BeOpen.com  no
-# 1.6.1           1.6         2001        CNRI        yes (2)
-# 2.1             2.0+1.6.1   2001        PSF         no
-# 2.0.1           2.0+1.6.1   2001        PSF         yes
-# 2.1.1           2.1+2.0.1   2001        PSF         yes
-# 2.2             2.1.1       2001        PSF         yes
-# 2.1.2           2.1.1       2002        PSF         yes
-# 2.1.3           2.1.2       2002        PSF         yes
-# 2.2.1           2.2         2002        PSF         yes
-# 2.2.2           2.2.1       2002        PSF         yes
-# 2.2.3           2.2.2       2003        PSF         yes
-# 2.3             2.2.2       2002-2003   PSF         yes
-# 2.3.1           2.3         2002-2003   PSF         yes
-# 2.3.2           2.3.1       2002-2003   PSF         yes
-# 2.3.3           2.3.2       2002-2003   PSF         yes
-# 2.3.4           2.3.3       2004        PSF         yes
-# 2.3.5           2.3.4       2005        PSF         yes
-# 2.4             2.3         2004        PSF         yes
-# 2.4.1           2.4         2005        PSF         yes
-# 2.4.2           2.4.1       2005        PSF         yes
-# 2.4.3           2.4.2       2006        PSF         yes
-# 2.4.4           2.4.3       2006        PSF         yes
-# 2.5             2.4         2006        PSF         yes
-# 2.5.1           2.5         2007        PSF         yes
-# 2.5.2           2.5.1       2008        PSF         yes
-# 2.5.3           2.5.2       2008        PSF         yes
-# 2.6             2.5         2008        PSF         yes
-# 2.6.1           2.6         2008        PSF         yes
-# 2.6.2           2.6.1       2009        PSF         yes
-# 2.6.3           2.6.2       2009        PSF         yes
-# 2.6.4           2.6.3       2009        PSF         yes
-# 2.6.5           2.6.4       2010        PSF         yes
-# 2.7             2.6         2010        PSF         yes
-#
-# Footnotes:
-#
-# (1) GPL-compatible doesn't mean that we're distributing Python under
-# the GPL.  All Python licenses, unlike the GPL, let you distribute
-# a modified version without making your changes open source.  The
-# GPL-compatible licenses make it possible to combine Python with
-#     other software that is released under the GPL; the others don't.
-#
-# (2) According to Richard Stallman, 1.6.1 is not GPL-compatible,
-# because its license has a choice of law clause.  According to
-# CNRI, however, Stallman's lawyer has told CNRI's lawyer that 1.6.1
-# is "not incompatible" with the GPL.
-#
-# Thanks to the many outside volunteers who have worked under Guido's
-# direction to make these releases possible.
-#
-#
-# B. TERMS AND CONDITIONS FOR ACCESSING OR OTHERWISE USING PYTHON
-# ===============================================================
-#
-# PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
-# --------------------------------------------
-#
-# 1. This LICENSE AGREEMENT is between the Python Software Foundation
-# ("PSF"), and the Individual or Organization ("Licensee") accessing and
-# otherwise using this software ("Python") in source or binary form and
-# its associated documentation.
-#
-# 2. Subject to the terms and conditions of this License Agreement, PSF hereby
-# grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
-# analyze, test, perform and/or display publicly, prepare derivative works,
-# distribute, and otherwise use Python alone or in any derivative version,
-# provided, however, that PSF's License Agreement and PSF's notice of copyright,
-# i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
-# 2011, 2012, 2013 Python Software Foundation; All Rights Reserved" are retained
-# in Python alone or in any derivative version prepared by Licensee.
-#
-# 3. In the event Licensee prepares a derivative work that is based on
-# or incorporates Python or any part thereof, and wants to make
-# the derivative work available to others as provided herein, then
-# Licensee hereby agrees to include in any such work a brief summary of
-# the changes made to Python.
-#
-# 4. PSF is making Python available to Licensee on an "AS IS"
-# basis.  PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
-# FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
-# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
-# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 6. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 7. Nothing in this License Agreement shall be deemed to create any
-# relationship of agency, partnership, or joint venture between PSF and
-# Licensee.  This License Agreement does not grant permission to use PSF
-# trademarks or trade name in a trademark sense to endorse or promote
-# products or services of Licensee, or any third party.
-#
-# 8. By copying, installing or otherwise using Python, Licensee
-# agrees to be bound by the terms and conditions of this License
-# Agreement.
-#
-#
-# BEOPEN.COM LICENSE AGREEMENT FOR PYTHON 2.0
-# -------------------------------------------
-#
-# BEOPEN PYTHON OPEN SOURCE LICENSE AGREEMENT VERSION 1
-#
-# 1. This LICENSE AGREEMENT is between BeOpen.com ("BeOpen"), having an
-# office at 160 Saratoga Avenue, Santa Clara, CA 95051, and the
-# Individual or Organization ("Licensee") accessing and otherwise using
-# this software in source or binary form and its associated
-# documentation ("the Software").
-#
-# 2. Subject to the terms and conditions of this BeOpen Python License
-# Agreement, BeOpen hereby grants Licensee a non-exclusive,
-# royalty-free, world-wide license to reproduce, analyze, test, perform
-# and/or display publicly, prepare derivative works, distribute, and
-# otherwise use the Software alone or in any derivative version,
-# provided, however, that the BeOpen Python License is retained in the
-# Software, alone or in any derivative version prepared by Licensee.
-#
-# 3. BeOpen is making the Software available to Licensee on an "AS IS"
-# basis.  BEOPEN MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, BEOPEN MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF THE SOFTWARE WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 4. BEOPEN SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF THE
-# SOFTWARE FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS
-# AS A RESULT OF USING, MODIFYING OR DISTRIBUTING THE SOFTWARE, OR ANY
-# DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 5. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 6. This License Agreement shall be governed by and interpreted in all
-# respects by the law of the State of California, excluding conflict of
-# law provisions.  Nothing in this License Agreement shall be deemed to
-# create any relationship of agency, partnership, or joint venture
-# between BeOpen and Licensee.  This License Agreement does not grant
-# permission to use BeOpen trademarks or trade names in a trademark
-# sense to endorse or promote products or services of Licensee, or any
-# third party.  As an exception, the "BeOpen Python" logos available at
-# http://www.pythonlabs.com/logos.html may be used according to the
-# permissions granted on that web page.
-#
-# 7. By copying, installing or otherwise using the software, Licensee
-# agrees to be bound by the terms and conditions of this License
-# Agreement.
-#
-#
-# CNRI LICENSE AGREEMENT FOR PYTHON 1.6.1
-# ---------------------------------------
-#
-# 1. This LICENSE AGREEMENT is between the Corporation for National
-#     Research Initiatives, having an office at 1895 Preston White Drive,
-# Reston, VA 20191 ("CNRI"), and the Individual or Organization
-# ("Licensee") accessing and otherwise using Python 1.6.1 software in
-# source or binary form and its associated documentation.
-#
-# 2. Subject to the terms and conditions of this License Agreement, CNRI
-# hereby grants Licensee a nonexclusive, royalty-free, world-wide
-# license to reproduce, analyze, test, perform and/or display publicly,
-# prepare derivative works, distribute, and otherwise use Python 1.6.1
-# alone or in any derivative version, provided, however, that CNRI's
-# License Agreement and CNRI's notice of copyright, i.e., "Copyright (c)
-# 1995-2001 Corporation for National Research Initiatives; All Rights
-# Reserved" are retained in Python 1.6.1 alone or in any derivative
-# version prepared by Licensee.  Alternately, in lieu of CNRI's License
-# Agreement, Licensee may substitute the following text (omitting the
-# quotes): "Python 1.6.1 is made available subject to the terms and
-# conditions in CNRI's License Agreement.  This Agreement together with
-# Python 1.6.1 may be located on the Internet using the following
-# unique, persistent identifier (known as a handle): 1895.22/1013.  This
-# Agreement may also be obtained from a proxy server on the Internet
-# using the following URL: http://hdl.handle.net/1895.22/1013".
-#
-# 3. In the event Licensee prepares a derivative work that is based on
-# or incorporates Python 1.6.1 or any part thereof, and wants to make
-# the derivative work available to others as provided herein, then
-# Licensee hereby agrees to include in any such work a brief summary of
-# the changes made to Python 1.6.1.
-#
-# 4. CNRI is making Python 1.6.1 available to Licensee on an "AS IS"
-# basis.  CNRI MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, CNRI MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON 1.6.1 WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 5. CNRI SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
-# 1.6.1 FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
-# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON 1.6.1,
-# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 6. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 7. This License Agreement shall be governed by the federal
-# intellectual property law of the United States, including without
-# limitation the federal copyright law, and, to the extent such
-# U.S. federal law does not apply, by the law of the Commonwealth of
-# Virginia, excluding Virginia's conflict of law provisions.
-# Notwithstanding the foregoing, with regard to derivative works based
-# on Python 1.6.1 that incorporate non-separable material that was
-# previously distributed under the GNU General Public License (GPL), the
-# law of the Commonwealth of Virginia shall govern this License
-# Agreement only as to issues arising under or with respect to
-# Paragraphs 4, 5, and 7 of this License Agreement.  Nothing in this
-# License Agreement shall be deemed to create any relationship of
-# agency, partnership, or joint venture between CNRI and Licensee.  This
-# License Agreement does not grant permission to use CNRI trademarks or
-# trade name in a trademark sense to endorse or promote products or
-# services of Licensee, or any third party.
-#
-# 8. By clicking on the "ACCEPT" button where indicated, or by copying,
-# installing or otherwise using Python 1.6.1, Licensee agrees to be
-# bound by the terms and conditions of this License Agreement.
-#
-# ACCEPT
-#
-#
-# CWI LICENSE AGREEMENT FOR PYTHON 0.9.0 THROUGH 1.2
-# --------------------------------------------------
-#
-# Copyright (c) 1991 - 1995, Stichting Mathematisch Centrum Amsterdam,
-# The Netherlands.  All rights reserved.
-#
-# Permission to use, copy, modify, and distribute this software and its
-# documentation for any purpose and without fee is hereby granted,
-# provided that the above copyright notice appear in all copies and that
-# both that copyright notice and this permission notice appear in
-# supporting documentation, and that the name of Stichting Mathematisch
-# Centrum or CWI not be used in advertising or publicity pertaining to
-# distribution of the software without specific, written prior
-# permission.
-#
-# STICHTING MATHEMATISCH CENTRUM DISCLAIMS ALL WARRANTIES WITH REGARD TO
-# THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
-# FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH CENTRUM BE LIABLE
-# FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
-# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT
-# OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
\ No newline at end of file
diff --git a/licenses/LICENSE-heapq.txt b/licenses/LICENSE-heapq.txt
deleted file mode 100644
index 45be6b8..0000000
--- a/licenses/LICENSE-heapq.txt
+++ /dev/null
@@ -1,49 +0,0 @@
-PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
---------------------------------------------
-
-1. This LICENSE AGREEMENT is between the Python Software Foundation
-("PSF"), and the Individual or Organization ("Licensee") accessing and
-otherwise using this software ("Python") in source or binary form and
-its associated documentation.
-
-2. Subject to the terms and conditions of this License Agreement, PSF hereby
-grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
-analyze, test, perform and/or display publicly, prepare derivative works,
-distribute, and otherwise use Python alone or in any derivative version,
-provided, however, that PSF's License Agreement and PSF's notice of copyright,
-i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
-2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Python Software Foundation;
-All Rights Reserved" are retained in Python alone or in any derivative version
-prepared by Licensee.
-
-3. In the event Licensee prepares a derivative work that is based on
-or incorporates Python or any part thereof, and wants to make
-the derivative work available to others as provided herein, then
-Licensee hereby agrees to include in any such work a brief summary of
-the changes made to Python.
-
-4. PSF is making Python available to Licensee on an "AS IS"
-basis.  PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
-DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
-INFRINGE ANY THIRD PARTY RIGHTS.
-
-5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
-FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
-A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
-OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-
-6. This License Agreement will automatically terminate upon a material
-breach of its terms and conditions.
-
-7. Nothing in this License Agreement shall be deemed to create any
-relationship of agency, partnership, or joint venture between PSF and
-Licensee.  This License Agreement does not grant permission to use PSF
-trademarks or trade name in a trademark sense to endorse or promote
-products or services of Licensee, or any third party.
-
-8. By copying, installing or otherwise using Python, Licensee
-agrees to be bound by the terms and conditions of this License
-Agreement.
-
diff --git a/python/pylintrc b/python/pylintrc
index 26d2741..5483774 100644
--- a/python/pylintrc
+++ b/python/pylintrc
@@ -29,7 +29,7 @@ profile=no
 
 # Add files or directories to the ignoreList. They should be base names, not
 # paths.
-ignore=pyspark.heapq3
+#ignore=
 
 # Pickle collected data for later comparisons.
 persistent=yes
diff --git a/python/pyspark/heapq3.py b/python/pyspark/heapq3.py
deleted file mode 100644
index 37a2914..0000000
--- a/python/pyspark/heapq3.py
+++ /dev/null
@@ -1,890 +0,0 @@
-# -*- encoding: utf-8 -*-
-#  back ported from CPython 3
-# A. HISTORY OF THE SOFTWARE
-# ==========================
-#
-# Python was created in the early 1990s by Guido van Rossum at Stichting
-# Mathematisch Centrum (CWI, see http://www.cwi.nl) in the Netherlands
-# as a successor of a language called ABC.  Guido remains Python's
-# principal author, although it includes many contributions from others.
-#
-# In 1995, Guido continued his work on Python at the Corporation for
-#     National Research Initiatives (CNRI, see http://www.cnri.reston.va.us)
-# in Reston, Virginia where he released several versions of the
-# software.
-#
-# In May 2000, Guido and the Python core development team moved to
-# BeOpen.com to form the BeOpen PythonLabs team.  In October of the same
-# year, the PythonLabs team moved to Digital Creations (now Zope
-# Corporation, see http://www.zope.com).  In 2001, the Python Software
-# Foundation (PSF, see http://www.python.org/psf/) was formed, a
-# non-profit organization created specifically to own Python-related
-# Intellectual Property.  Zope Corporation is a sponsoring member of
-# the PSF.
-#
-# All Python releases are Open Source (see http://www.opensource.org for
-# the Open Source Definition).  Historically, most, but not all, Python
-# releases have also been GPL-compatible; the table below summarizes
-# the various releases.
-#
-# Release         Derived     Year        Owner       GPL-
-# from                                compatible? (1)
-#
-# 0.9.0 thru 1.2              1991-1995   CWI         yes
-# 1.3 thru 1.5.2  1.2         1995-1999   CNRI        yes
-# 1.6             1.5.2       2000        CNRI        no
-# 2.0             1.6         2000        BeOpen.com  no
-# 1.6.1           1.6         2001        CNRI        yes (2)
-# 2.1             2.0+1.6.1   2001        PSF         no
-# 2.0.1           2.0+1.6.1   2001        PSF         yes
-# 2.1.1           2.1+2.0.1   2001        PSF         yes
-# 2.2             2.1.1       2001        PSF         yes
-# 2.1.2           2.1.1       2002        PSF         yes
-# 2.1.3           2.1.2       2002        PSF         yes
-# 2.2.1           2.2         2002        PSF         yes
-# 2.2.2           2.2.1       2002        PSF         yes
-# 2.2.3           2.2.2       2003        PSF         yes
-# 2.3             2.2.2       2002-2003   PSF         yes
-# 2.3.1           2.3         2002-2003   PSF         yes
-# 2.3.2           2.3.1       2002-2003   PSF         yes
-# 2.3.3           2.3.2       2002-2003   PSF         yes
-# 2.3.4           2.3.3       2004        PSF         yes
-# 2.3.5           2.3.4       2005        PSF         yes
-# 2.4             2.3         2004        PSF         yes
-# 2.4.1           2.4         2005        PSF         yes
-# 2.4.2           2.4.1       2005        PSF         yes
-# 2.4.3           2.4.2       2006        PSF         yes
-# 2.4.4           2.4.3       2006        PSF         yes
-# 2.5             2.4         2006        PSF         yes
-# 2.5.1           2.5         2007        PSF         yes
-# 2.5.2           2.5.1       2008        PSF         yes
-# 2.5.3           2.5.2       2008        PSF         yes
-# 2.6             2.5         2008        PSF         yes
-# 2.6.1           2.6         2008        PSF         yes
-# 2.6.2           2.6.1       2009        PSF         yes
-# 2.6.3           2.6.2       2009        PSF         yes
-# 2.6.4           2.6.3       2009        PSF         yes
-# 2.6.5           2.6.4       2010        PSF         yes
-# 2.7             2.6         2010        PSF         yes
-#
-# Footnotes:
-#
-# (1) GPL-compatible doesn't mean that we're distributing Python under
-# the GPL.  All Python licenses, unlike the GPL, let you distribute
-# a modified version without making your changes open source.  The
-# GPL-compatible licenses make it possible to combine Python with
-#     other software that is released under the GPL; the others don't.
-#
-# (2) According to Richard Stallman, 1.6.1 is not GPL-compatible,
-# because its license has a choice of law clause.  According to
-# CNRI, however, Stallman's lawyer has told CNRI's lawyer that 1.6.1
-# is "not incompatible" with the GPL.
-#
-# Thanks to the many outside volunteers who have worked under Guido's
-# direction to make these releases possible.
-#
-#
-# B. TERMS AND CONDITIONS FOR ACCESSING OR OTHERWISE USING PYTHON
-# ===============================================================
-#
-# PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
-# --------------------------------------------
-#
-# 1. This LICENSE AGREEMENT is between the Python Software Foundation
-# ("PSF"), and the Individual or Organization ("Licensee") accessing and
-# otherwise using this software ("Python") in source or binary form and
-# its associated documentation.
-#
-# 2. Subject to the terms and conditions of this License Agreement, PSF hereby
-# grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
-# analyze, test, perform and/or display publicly, prepare derivative works,
-# distribute, and otherwise use Python alone or in any derivative version,
-# provided, however, that PSF's License Agreement and PSF's notice of copyright,
-# i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
-# 2011, 2012, 2013 Python Software Foundation; All Rights Reserved" are retained
-# in Python alone or in any derivative version prepared by Licensee.
-#
-# 3. In the event Licensee prepares a derivative work that is based on
-# or incorporates Python or any part thereof, and wants to make
-# the derivative work available to others as provided herein, then
-# Licensee hereby agrees to include in any such work a brief summary of
-# the changes made to Python.
-#
-# 4. PSF is making Python available to Licensee on an "AS IS"
-# basis.  PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
-# FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
-# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
-# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 6. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 7. Nothing in this License Agreement shall be deemed to create any
-# relationship of agency, partnership, or joint venture between PSF and
-# Licensee.  This License Agreement does not grant permission to use PSF
-# trademarks or trade name in a trademark sense to endorse or promote
-# products or services of Licensee, or any third party.
-#
-# 8. By copying, installing or otherwise using Python, Licensee
-# agrees to be bound by the terms and conditions of this License
-# Agreement.
-#
-#
-# BEOPEN.COM LICENSE AGREEMENT FOR PYTHON 2.0
-# -------------------------------------------
-#
-# BEOPEN PYTHON OPEN SOURCE LICENSE AGREEMENT VERSION 1
-#
-# 1. This LICENSE AGREEMENT is between BeOpen.com ("BeOpen"), having an
-# office at 160 Saratoga Avenue, Santa Clara, CA 95051, and the
-# Individual or Organization ("Licensee") accessing and otherwise using
-# this software in source or binary form and its associated
-# documentation ("the Software").
-#
-# 2. Subject to the terms and conditions of this BeOpen Python License
-# Agreement, BeOpen hereby grants Licensee a non-exclusive,
-# royalty-free, world-wide license to reproduce, analyze, test, perform
-# and/or display publicly, prepare derivative works, distribute, and
-# otherwise use the Software alone or in any derivative version,
-# provided, however, that the BeOpen Python License is retained in the
-# Software, alone or in any derivative version prepared by Licensee.
-#
-# 3. BeOpen is making the Software available to Licensee on an "AS IS"
-# basis.  BEOPEN MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, BEOPEN MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF THE SOFTWARE WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 4. BEOPEN SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF THE
-# SOFTWARE FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS
-# AS A RESULT OF USING, MODIFYING OR DISTRIBUTING THE SOFTWARE, OR ANY
-# DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 5. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 6. This License Agreement shall be governed by and interpreted in all
-# respects by the law of the State of California, excluding conflict of
-# law provisions.  Nothing in this License Agreement shall be deemed to
-# create any relationship of agency, partnership, or joint venture
-# between BeOpen and Licensee.  This License Agreement does not grant
-# permission to use BeOpen trademarks or trade names in a trademark
-# sense to endorse or promote products or services of Licensee, or any
-# third party.  As an exception, the "BeOpen Python" logos available at
-# http://www.pythonlabs.com/logos.html may be used according to the
-# permissions granted on that web page.
-#
-# 7. By copying, installing or otherwise using the software, Licensee
-# agrees to be bound by the terms and conditions of this License
-# Agreement.
-#
-#
-# CNRI LICENSE AGREEMENT FOR PYTHON 1.6.1
-# ---------------------------------------
-#
-# 1. This LICENSE AGREEMENT is between the Corporation for National
-#     Research Initiatives, having an office at 1895 Preston White Drive,
-# Reston, VA 20191 ("CNRI"), and the Individual or Organization
-# ("Licensee") accessing and otherwise using Python 1.6.1 software in
-# source or binary form and its associated documentation.
-#
-# 2. Subject to the terms and conditions of this License Agreement, CNRI
-# hereby grants Licensee a nonexclusive, royalty-free, world-wide
-# license to reproduce, analyze, test, perform and/or display publicly,
-# prepare derivative works, distribute, and otherwise use Python 1.6.1
-# alone or in any derivative version, provided, however, that CNRI's
-# License Agreement and CNRI's notice of copyright, i.e., "Copyright (c)
-# 1995-2001 Corporation for National Research Initiatives; All Rights
-# Reserved" are retained in Python 1.6.1 alone or in any derivative
-# version prepared by Licensee.  Alternately, in lieu of CNRI's License
-# Agreement, Licensee may substitute the following text (omitting the
-# quotes): "Python 1.6.1 is made available subject to the terms and
-# conditions in CNRI's License Agreement.  This Agreement together with
-# Python 1.6.1 may be located on the Internet using the following
-# unique, persistent identifier (known as a handle): 1895.22/1013.  This
-# Agreement may also be obtained from a proxy server on the Internet
-# using the following URL: http://hdl.handle.net/1895.22/1013".
-#
-# 3. In the event Licensee prepares a derivative work that is based on
-# or incorporates Python 1.6.1 or any part thereof, and wants to make
-# the derivative work available to others as provided herein, then
-# Licensee hereby agrees to include in any such work a brief summary of
-# the changes made to Python 1.6.1.
-#
-# 4. CNRI is making Python 1.6.1 available to Licensee on an "AS IS"
-# basis.  CNRI MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
-# IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, CNRI MAKES NO AND
-# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
-# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON 1.6.1 WILL NOT
-# INFRINGE ANY THIRD PARTY RIGHTS.
-#
-# 5. CNRI SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
-# 1.6.1 FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
-# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON 1.6.1,
-# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
-#
-# 6. This License Agreement will automatically terminate upon a material
-# breach of its terms and conditions.
-#
-# 7. This License Agreement shall be governed by the federal
-# intellectual property law of the United States, including without
-# limitation the federal copyright law, and, to the extent such
-# U.S. federal law does not apply, by the law of the Commonwealth of
-# Virginia, excluding Virginia's conflict of law provisions.
-# Notwithstanding the foregoing, with regard to derivative works based
-# on Python 1.6.1 that incorporate non-separable material that was
-# previously distributed under the GNU General Public License (GPL), the
-# law of the Commonwealth of Virginia shall govern this License
-# Agreement only as to issues arising under or with respect to
-# Paragraphs 4, 5, and 7 of this License Agreement.  Nothing in this
-# License Agreement shall be deemed to create any relationship of
-# agency, partnership, or joint venture between CNRI and Licensee.  This
-# License Agreement does not grant permission to use CNRI trademarks or
-# trade name in a trademark sense to endorse or promote products or
-# services of Licensee, or any third party.
-#
-# 8. By clicking on the "ACCEPT" button where indicated, or by copying,
-# installing or otherwise using Python 1.6.1, Licensee agrees to be
-# bound by the terms and conditions of this License Agreement.
-#
-# ACCEPT
-#
-#
-# CWI LICENSE AGREEMENT FOR PYTHON 0.9.0 THROUGH 1.2
-# --------------------------------------------------
-#
-# Copyright (c) 1991 - 1995, Stichting Mathematisch Centrum Amsterdam,
-# The Netherlands.  All rights reserved.
-#
-# Permission to use, copy, modify, and distribute this software and its
-# documentation for any purpose and without fee is hereby granted,
-# provided that the above copyright notice appear in all copies and that
-# both that copyright notice and this permission notice appear in
-# supporting documentation, and that the name of Stichting Mathematisch
-# Centrum or CWI not be used in advertising or publicity pertaining to
-# distribution of the software without specific, written prior
-# permission.
-#
-# STICHTING MATHEMATISCH CENTRUM DISCLAIMS ALL WARRANTIES WITH REGARD TO
-# THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
-# FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH CENTRUM BE LIABLE
-# FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
-# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT
-# OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
-"""Heap queue algorithm (a.k.a. priority queue).
-
-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.
-
-Usage:
-
-heap = []            # creates an empty heap
-heappush(heap, item) # pushes a new item on the heap
-item = heappop(heap) # pops the smallest item from the heap
-item = heap[0]       # smallest item on the heap without popping it
-heapify(x)           # transforms list into a heap, in-place, in linear time
-item = heapreplace(heap, item) # pops and returns smallest item, and adds
-                               # new item; the heap size is unchanged
-
-Our API differs from textbook heap algorithms as follows:
-
-- We use 0-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 0-based indexing.
-
-- Our heappop() method returns the smallest item, not the largest.
-
-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!
-"""
-
-# Original code by Kevin O'Connor, augmented by Tim Peters and Raymond Hettinger
-
-__about__ = """Heap queues
-
-[explanation by François Pinard]
-
-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 ln 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[1].  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. :-)
-
---------------------
-[1] 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! :-)
-"""
-
-__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace', 'merge',
-           'nlargest', 'nsmallest', 'heappushpop']
-
-def heappush(heap, item):
-    """Push item onto heap, maintaining the heap invariant."""
-    heap.append(item)
-    _siftdown(heap, 0, len(heap)-1)
-
-def heappop(heap):
-    """Pop the smallest item off the heap, maintaining the heap invariant."""
-    lastelt = heap.pop()    # raises appropriate IndexError if heap is empty
-    if heap:
-        returnitem = heap[0]
-        heap[0] = lastelt
-        _siftup(heap, 0)
-        return returnitem
-    return lastelt
-
-def heapreplace(heap, item):
-    """Pop and return the current smallest value, and add the new item.
-
-    This is more efficient than heappop() followed by heappush(), and can be
-    more appropriate when using a fixed-size heap.  Note that the value
-    returned may be larger than item!  That constrains reasonable uses of
-    this routine unless written as part of a conditional replacement:
-
-        if item > heap[0]:
-            item = heapreplace(heap, item)
-    """
-    returnitem = heap[0]    # raises appropriate IndexError if heap is empty
-    heap[0] = item
-    _siftup(heap, 0)
-    return returnitem
-
-def heappushpop(heap, item):
-    """Fast version of a heappush followed by a heappop."""
-    if heap and heap[0] < item:
-        item, heap[0] = heap[0], item
-        _siftup(heap, 0)
-    return item
-
-def heapify(x):
-    """Transform list into a heap, in-place, in O(len(x)) time."""
-    n = len(x)
-    # Transform bottom-up.  The largest index there's any point to looking at
-    # is the largest with a child index in-range, so must have 2*i + 1 < n,
-    # or i < (n-1)/2.  If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so
-    # j-1 is the largest, which is n//2 - 1.  If n is odd = 2*j+1, this is
-    # (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.
-    for i in reversed(range(n//2)):
-        _siftup(x, i)
-
-def _heappop_max(heap):
-    """Maxheap version of a heappop."""
-    lastelt = heap.pop()    # raises appropriate IndexError if heap is empty
-    if heap:
-        returnitem = heap[0]
-        heap[0] = lastelt
-        _siftup_max(heap, 0)
-        return returnitem
-    return lastelt
-
-def _heapreplace_max(heap, item):
-    """Maxheap version of a heappop followed by a heappush."""
-    returnitem = heap[0]    # raises appropriate IndexError if heap is empty
-    heap[0] = item
-    _siftup_max(heap, 0)
-    return returnitem
-
-def _heapify_max(x):
-    """Transform list into a maxheap, in-place, in O(len(x)) time."""
-    n = len(x)
-    for i in reversed(range(n//2)):
-        _siftup_max(x, i)
-
-# 'heap' is a heap at all indices >= startpos, except possibly for pos.  pos
-# is the index of a leaf with a possibly out-of-order value.  Restore the
-# heap invariant.
-def _siftdown(heap, startpos, pos):
-    newitem = heap[pos]
-    # Follow the path to the root, moving parents down until finding a place
-    # newitem fits.
-    while pos > startpos:
-        parentpos = (pos - 1) >> 1
-        parent = heap[parentpos]
-        if newitem < parent:
-            heap[pos] = parent
-            pos = parentpos
-            continue
-        break
-    heap[pos] = newitem
-
-# The child indices of heap index pos are already heaps, and we want to make
-# a heap at index pos too.  We do this by bubbling the smaller child of
-# pos up (and so on with that child's children, etc) until hitting a leaf,
-# then using _siftdown to move the oddball originally at index pos into place.
-#
-# We *could* break out of the loop as soon as we find a pos where newitem <=
-# both its children, but turns out that's not a good idea, and despite that
-# many books write the algorithm that way.  During a heap pop, the last array
-# element is sifted in, and that tends to be large, so that comparing it
-# against values starting from the root usually doesn't pay (= usually doesn't
-# get us out of the loop early).  See Knuth, Volume 3, where this is
-# explained and quantified in an exercise.
-#
-# Cutting the # of comparisons is important, since these routines have no
-# way to extract "the priority" from an array element, so that intelligence
-# is likely to be hiding in custom comparison methods, or in array elements
-# storing (priority, record) tuples.  Comparisons are thus potentially
-# expensive.
-#
-# On random arrays of length 1000, making this change cut the number of
-# comparisons made by heapify() a little, and those made by exhaustive
-# heappop() a lot, in accord with theory.  Here are typical results from 3
-# runs (3 just to demonstrate how small the variance is):
-#
-# Compares needed by heapify     Compares needed by 1000 heappops
-# --------------------------     --------------------------------
-# 1837 cut to 1663               14996 cut to 8680
-# 1855 cut to 1659               14966 cut to 8678
-# 1847 cut to 1660               15024 cut to 8703
-#
-# Building the heap by using heappush() 1000 times instead required
-# 2198, 2148, and 2219 compares:  heapify() is more efficient, when
-# you can use it.
-#
-# The total compares needed by list.sort() on the same lists were 8627,
-# 8627, and 8632 (this should be compared to the sum of heapify() and
-# heappop() compares):  list.sort() is (unsurprisingly!) more efficient
-# for sorting.
-
-def _siftup(heap, pos):
-    endpos = len(heap)
-    startpos = pos
-    newitem = heap[pos]
-    # Bubble up the smaller child until hitting a leaf.
-    childpos = 2*pos + 1    # leftmost child position
-    while childpos < endpos:
-        # Set childpos to index of smaller child.
-        rightpos = childpos + 1
-        if rightpos < endpos and not heap[childpos] < heap[rightpos]:
-            childpos = rightpos
-        # Move the smaller child up.
-        heap[pos] = heap[childpos]
-        pos = childpos
-        childpos = 2*pos + 1
-    # The leaf at pos is empty now.  Put newitem there, and bubble it up
-    # to its final resting place (by sifting its parents down).
-    heap[pos] = newitem
-    _siftdown(heap, startpos, pos)
-
-def _siftdown_max(heap, startpos, pos):
-    'Maxheap variant of _siftdown'
-    newitem = heap[pos]
-    # Follow the path to the root, moving parents down until finding a place
-    # newitem fits.
-    while pos > startpos:
-        parentpos = (pos - 1) >> 1
-        parent = heap[parentpos]
-        if parent < newitem:
-            heap[pos] = parent
-            pos = parentpos
-            continue
-        break
-    heap[pos] = newitem
-
-def _siftup_max(heap, pos):
-    'Maxheap variant of _siftup'
-    endpos = len(heap)
-    startpos = pos
-    newitem = heap[pos]
-    # Bubble up the larger child until hitting a leaf.
-    childpos = 2*pos + 1    # leftmost child position
-    while childpos < endpos:
-        # Set childpos to index of larger child.
-        rightpos = childpos + 1
-        if rightpos < endpos and not heap[rightpos] < heap[childpos]:
-            childpos = rightpos
-        # Move the larger child up.
-        heap[pos] = heap[childpos]
-        pos = childpos
-        childpos = 2*pos + 1
-    # The leaf at pos is empty now.  Put newitem there, and bubble it up
-    # to its final resting place (by sifting its parents down).
-    heap[pos] = newitem
-    _siftdown_max(heap, startpos, pos)
-
-def merge(iterables, key=None, reverse=False):
-    '''Merge multiple sorted inputs into a single sorted output.
-
-    Similar to sorted(itertools.chain(*iterables)) but returns a generator,
-    does not pull the data into memory all at once, and assumes that each of
-    the input streams is already sorted (smallest to largest).
-
-    >>> list(merge([1,3,5,7], [0,2,4,8], [5,10,15,20], [], [25]))
-    [0, 1, 2, 3, 4, 5, 5, 7, 8, 10, 15, 20, 25]
-
-    If *key* is not None, applies a key function to each element to determine
-    its sort order.
-
-    >>> list(merge(['dog', 'horse'], ['cat', 'fish', 'kangaroo'], key=len))
-    ['dog', 'cat', 'fish', 'horse', 'kangaroo']
-
-    '''
-
-    h = []
-    h_append = h.append
-
-    if reverse:
-        _heapify = _heapify_max
-        _heappop = _heappop_max
-        _heapreplace = _heapreplace_max
-        direction = -1
-    else:
-        _heapify = heapify
-        _heappop = heappop
-        _heapreplace = heapreplace
-        direction = 1
-
-    if key is None:
-        for order, it in enumerate(map(iter, iterables)):
-            try:
-                h_append([next(it), order * direction, it])
-            except StopIteration:
-                pass
-        _heapify(h)
-        while len(h) > 1:
-            try:
-                while True:
-                    value, order, it = s = h[0]
-                    yield value
-                    s[0] = next(it)           # raises StopIteration when exhausted
-                    _heapreplace(h, s)      # restore heap condition
-            except StopIteration:
-                _heappop(h)                 # remove empty iterator
-        if h:
-            # fast case when only a single iterator remains
-            value, order, it = h[0]
-            yield value
-            for value in it:
-                yield value
-        return
-
-    for order, it in enumerate(map(iter, iterables)):
-        try:
-            value = next(it)
-            h_append([key(value), order * direction, value, it])
-        except StopIteration:
-            pass
-    _heapify(h)
-    while len(h) > 1:
-        try:
-            while True:
-                key_value, order, value, it = s = h[0]
-                yield value
-                value = next(it)
-                s[0] = key(value)
-                s[2] = value
-                _heapreplace(h, s)
-        except StopIteration:
-            _heappop(h)
-    if h:
-        key_value, order, value, it = h[0]
-        yield value
-        for value in it:
-            yield value
-
-
-# Algorithm notes for nlargest() and nsmallest()
-# ==============================================
-#
-# Make a single pass over the data while keeping the k most extreme values
-# in a heap.  Memory consumption is limited to keeping k values in a list.
-#
-# Measured performance for random inputs:
-#
-#                                   number of comparisons
-#    n inputs     k-extreme values  (average of 5 trials)   % more than min()
-# -------------   ----------------  ---------------------   -----------------
-#      1,000           100                  3,317               231.7%
-#     10,000           100                 14,046                40.5%
-#    100,000           100                105,749                 5.7%
-#  1,000,000           100              1,007,751                 0.8%
-# 10,000,000           100             10,009,401                 0.1%
-#
-# Theoretical number of comparisons for k smallest of n random inputs:
-#
-# Step   Comparisons                  Action
-# ----   --------------------------   ---------------------------
-#  1     1.66 * k                     heapify the first k-inputs
-#  2     n - k                        compare remaining elements to top of heap
-#  3     k * (1 + lg2(k)) * ln(n/k)   replace the topmost value on the heap
-#  4     k * lg2(k) - (k/2)           final sort of the k most extreme values
-#
-# Combining and simplifying for a rough estimate gives:
-#
-#        comparisons = n + k * (log(k, 2) * log(n/k) + log(k, 2) + log(n/k))
-#
-# Computing the number of comparisons for step 3:
-# -----------------------------------------------
-# * For the i-th new value from the iterable, the probability of being in the
-#   k most extreme values is k/i.  For example, the probability of the 101st
-#   value seen being in the 100 most extreme values is 100/101.
-# * If the value is a new extreme value, the cost of inserting it into the
-#   heap is 1 + log(k, 2).
-# * The probability times the cost gives:
-#            (k/i) * (1 + log(k, 2))
-# * Summing across the remaining n-k elements gives:
-#            sum((k/i) * (1 + log(k, 2)) for i in range(k+1, n+1))
-# * This reduces to:
-#            (H(n) - H(k)) * k * (1 + log(k, 2))
-# * Where H(n) is the n-th harmonic number estimated by:
-#            gamma = 0.5772156649
-#            H(n) = log(n, e) + gamma + 1 / (2 * n)
-#   http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#Rate_of_divergence
-# * Substituting the H(n) formula:
-#            comparisons = k * (1 + log(k, 2)) * (log(n/k, e) + (1/n - 1/k) / 2)
-#
-# Worst-case for step 3:
-# ----------------------
-# In the worst case, the input data is reversed sorted so that every new element
-# must be inserted in the heap:
-#
-#             comparisons = 1.66 * k + log(k, 2) * (n - k)
-#
-# Alternative Algorithms
-# ----------------------
-# Other algorithms were not used because they:
-# 1) Took much more auxiliary memory,
-# 2) Made multiple passes over the data.
-# 3) Made more comparisons in common cases (small k, large n, semi-random input).
-# See the more detailed comparison of approach at:
-# http://code.activestate.com/recipes/577573-compare-algorithms-for-heapqsmallest
-
-def nsmallest(n, iterable, key=None):
-    """Find the n smallest elements in a dataset.
-
-    Equivalent to:  sorted(iterable, key=key)[:n]
-    """
-
-    # Short-cut for n==1 is to use min()
-    if n == 1:
-        it = iter(iterable)
-        sentinel = object()
-        if key is None:
-            result = min(it, default=sentinel)
-        else:
-            result = min(it, default=sentinel, key=key)
-        return [] if result is sentinel else [result]
-
-    # When n>=size, it's faster to use sorted()
-    try:
-        size = len(iterable)
-    except (TypeError, AttributeError):
-        pass
-    else:
-        if n >= size:
-            return sorted(iterable, key=key)[:n]
-
-    # When key is none, use simpler decoration
-    if key is None:
-        it = iter(iterable)
-        # put the range(n) first so that zip() doesn't
-        # consume one too many elements from the iterator
-        result = [(elem, i) for i, elem in zip(range(n), it)]
-        if not result:
-            return result
-        _heapify_max(result)
-        top = result[0][0]
-        order = n
-        _heapreplace = _heapreplace_max
-        for elem in it:
-            if elem < top:
-                _heapreplace(result, (elem, order))
-                top = result[0][0]
-                order += 1
-        result.sort()
-        return [r[0] for r in result]
-
-    # General case, slowest method
-    it = iter(iterable)
-    result = [(key(elem), i, elem) for i, elem in zip(range(n), it)]
-    if not result:
-        return result
-    _heapify_max(result)
-    top = result[0][0]
-    order = n
-    _heapreplace = _heapreplace_max
-    for elem in it:
-        k = key(elem)
-        if k < top:
-            _heapreplace(result, (k, order, elem))
-            top = result[0][0]
-            order += 1
-    result.sort()
-    return [r[2] for r in result]
-
-def nlargest(n, iterable, key=None):
-    """Find the n largest elements in a dataset.
-
-    Equivalent to:  sorted(iterable, key=key, reverse=True)[:n]
-    """
-
-    # Short-cut for n==1 is to use max()
-    if n == 1:
-        it = iter(iterable)
-        sentinel = object()
-        if key is None:
-            result = max(it, default=sentinel)
-        else:
-            result = max(it, default=sentinel, key=key)
-        return [] if result is sentinel else [result]
-
-    # When n>=size, it's faster to use sorted()
-    try:
-        size = len(iterable)
-    except (TypeError, AttributeError):
-        pass
-    else:
-        if n >= size:
-            return sorted(iterable, key=key, reverse=True)[:n]
-
-    # When key is none, use simpler decoration
-    if key is None:
-        it = iter(iterable)
-        result = [(elem, i) for i, elem in zip(range(0, -n, -1), it)]
-        if not result:
-            return result
-        heapify(result)
-        top = result[0][0]
-        order = -n
-        _heapreplace = heapreplace
-        for elem in it:
-            if top < elem:
-                _heapreplace(result, (elem, order))
-                top = result[0][0]
-                order -= 1
-        result.sort(reverse=True)
-        return [r[0] for r in result]
-
-    # General case, slowest method
-    it = iter(iterable)
-    result = [(key(elem), i, elem) for i, elem in zip(range(0, -n, -1), it)]
-    if not result:
-        return result
-    heapify(result)
-    top = result[0][0]
-    order = -n
-    _heapreplace = heapreplace
-    for elem in it:
-        k = key(elem)
-        if top < k:
-            _heapreplace(result, (k, order, elem))
-            top = result[0][0]
-            order -= 1
-    result.sort(reverse=True)
-    return [r[2] for r in result]
-
-# If available, use C implementation
-try:
-    from _heapq import *
-except ImportError:
-    pass
-try:
-    from _heapq import _heapreplace_max
-except ImportError:
-    pass
-try:
-    from _heapq import _heapify_max
-except ImportError:
-    pass
-try:
-    from _heapq import _heappop_max
-except ImportError:
-    pass
-
-
-if __name__ == "__main__":
-    import doctest
-    import sys
-    (failure_count, test_count) = doctest.testmod()
-    if failure_count:
-        sys.exit(-1)
diff --git a/python/pyspark/shuffle.py b/python/pyspark/shuffle.py
index 5d2d638..308305e 100644
--- a/python/pyspark/shuffle.py
+++ b/python/pyspark/shuffle.py
@@ -25,7 +25,7 @@ import operator
 import random
 import sys
 
-import pyspark.heapq3 as heapq
+import heapq
 from pyspark.serializers import BatchedSerializer, PickleSerializer, FlattenedValuesSerializer, \
     CompressedSerializer, AutoBatchedSerializer
 from pyspark.util import fail_on_stopiteration
@@ -498,7 +498,7 @@ class ExternalSorter(object):
         if current_chunk:
             chunks.append(iter(current_chunk))
 
-        return heapq.merge(chunks, key=key, reverse=reverse)
+        return heapq.merge(*chunks, key=key, reverse=reverse)
 
 
 class ExternalList(object):
@@ -796,7 +796,7 @@ class ExternalGroupBy(ExternalMerger):
 
         if self._sorted:
             # all the partitions are already sorted
-            sorted_items = heapq.merge(disk_items, key=operator.itemgetter(0))
+            sorted_items = heapq.merge(*disk_items, key=operator.itemgetter(0))
 
         else:
             # Flatten the combined values, so it will not consume huge


---------------------------------------------------------------------
To unsubscribe, e-mail: commits-unsubscribe@spark.apache.org
For additional commands, e-mail: commits-help@spark.apache.org