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Re: sort_heap complexity guarantee


On 05/10/2014 22:54, Marc Glisse wrote:
On Sun, 5 Oct 2014, FranÃois Dumont wrote:

I took a look at PR 61217 regarding pop_heap complexity guarantee. Looks like we have no test to check complexity of our algos so I start writing some starting with the heap operations. I found no issue with make_heap, push_heap and pop_heap despite what the bug report is saying however the attached testcase for sort_heap is failing.

Standard is saying std::sort_heap shall use less than N * log(N) comparisons but with my test using 1000 random values the test is showing:

8687 comparisons on 6907.76 max allowed

Is this a known issue of sort_heap ? Do you confirm that the test is valid ?

I would first look for confirmation that the standard didn't just forget a big-O or something. I would expect an implementation as n calls to pop_heap to be legal, and if pop_heap makes 2*log(n) comparisons, that naively sums to too much. And I don't expect the standard to contain an advanced amortized analysis or anything like that...

Good point, with n calls to pop_heap it means that limit must be 2*log(1) + 2*log(2) +... + 2*log(n) which is 2*log(n!) and which is also necessarily < 2*n*log(n). I guess Standard comittee has forgotten the factor 2 in the limit so this is what I am using as limit in the final test, unless someone prefer the stricter 2*log(n!) ?

Ok to commit those new tests ?

2014-10-06  FranÃois Dumont  <fdumont@gcc.gnu.org>

    * testsuite/util/testsuite_counter_type.h
    (counter_type::operator<(const counter_type&)): Update
    less_compare_count when called.
    * testsuite/25_algorithms/make_heap/complexity.cc: New.
    * testsuite/25_algorithms/pop_heap/complexity.cc: New.
    * testsuite/25_algorithms/push_heap/complexity.cc: New.
    * testsuite/25_algorithms/sort_heap/complexity.cc: New.


Tested under Linux x86_64.

FranÃois
Index: testsuite/25_algorithms/make_heap/complexity.cc
===================================================================
--- testsuite/25_algorithms/make_heap/complexity.cc	(revision 0)
+++ testsuite/25_algorithms/make_heap/complexity.cc	(working copy)
@@ -0,0 +1,50 @@
+// Copyright (C) 2014 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-options "-std=gnu++11" }
+
+#include <random>
+#include <vector>
+#include <algorithm>
+
+#include <testsuite_counter_type.h>
+#include <testsuite_hooks.h>
+
+void test01()
+{
+  using __gnu_test::counter_type;
+  const std::size_t nb_values = 1000;
+
+  std::random_device dev;
+  std::uniform_int_distribution<int> dist;
+  std::vector<counter_type> values;
+  values.reserve(nb_values);
+  for (std::size_t i = 0; i != nb_values; ++i)
+    values.push_back(dist(dev));
+
+  counter_type::reset();
+
+  std::make_heap(values.begin(), values.end());
+
+  VERIFY( counter_type::less_compare_count <= 3.0 * nb_values );
+}
+
+int main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/25_algorithms/pop_heap/complexity.cc
===================================================================
--- testsuite/25_algorithms/pop_heap/complexity.cc	(revision 0)
+++ testsuite/25_algorithms/pop_heap/complexity.cc	(working copy)
@@ -0,0 +1,53 @@
+// Copyright (C) 2014 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-options "-std=gnu++11" }
+
+#include <cmath>
+#include <random>
+#include <vector>
+#include <algorithm>
+
+#include <testsuite_counter_type.h>
+#include <testsuite_hooks.h>
+
+void test01()
+{
+  using __gnu_test::counter_type;
+  const std::size_t nb_values = 1000;
+
+  std::random_device dev;
+  std::uniform_int_distribution<int> dist;
+  std::vector<counter_type> values;
+  values.reserve(nb_values);
+  for (std::size_t i = 0; i != nb_values; ++i)
+    values.push_back(dist(dev));
+
+  std::make_heap(values.begin(), values.end());
+
+  counter_type::reset();
+
+  std::pop_heap(values.begin(), values.end());
+
+  VERIFY( counter_type::less_compare_count <= 2.0 * std::log(nb_values) );
+}
+
+int main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/25_algorithms/push_heap/complexity.cc
===================================================================
--- testsuite/25_algorithms/push_heap/complexity.cc	(revision 0)
+++ testsuite/25_algorithms/push_heap/complexity.cc	(working copy)
@@ -0,0 +1,54 @@
+// Copyright (C) 2014 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-options "-std=gnu++11" }
+
+#include <cmath>
+#include <random>
+#include <vector>
+#include <algorithm>
+
+#include <testsuite_counter_type.h>
+#include <testsuite_hooks.h>
+
+void test01()
+{
+  using __gnu_test::counter_type;
+  const std::size_t nb_values = 1000;
+
+  std::random_device dev;
+  std::uniform_int_distribution<int> dist;
+  std::vector<counter_type> values;
+  values.reserve(nb_values);
+  for (std::size_t i = 0; i != nb_values; ++i)
+    values.push_back(dist(dev));
+
+  std::make_heap(values.begin(), values.end());
+  values.push_back(dist(dev));
+
+  counter_type::reset();
+
+  std::push_heap(values.begin(), values.end());
+
+  VERIFY( counter_type::less_compare_count <= std::log(values.size()) );
+}
+
+int main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/25_algorithms/sort_heap/complexity.cc
===================================================================
--- testsuite/25_algorithms/sort_heap/complexity.cc	(revision 0)
+++ testsuite/25_algorithms/sort_heap/complexity.cc	(working copy)
@@ -0,0 +1,53 @@
+// Copyright (C) 2014 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-options "-std=gnu++11" }
+
+#include <cmath>
+#include <random>
+#include <vector>
+#include <algorithm>
+
+#include <testsuite_counter_type.h>
+#include <testsuite_hooks.h>
+
+void test01()
+{
+  using __gnu_test::counter_type;
+  const std::size_t nb_values = 1000;
+
+  std::random_device dev;
+  std::uniform_int_distribution<int> dist;
+  std::vector<counter_type> values;
+  values.reserve(nb_values);
+  for (std::size_t i = 0; i != nb_values; ++i)
+    values.push_back(dist(dev));
+
+  std::make_heap(values.begin(), values.end());
+
+  counter_type::reset();
+
+  std::sort_heap(values.begin(), values.end());
+
+  VERIFY( counter_type::less_compare_count <= 2.0 * nb_values * std::log(nb_values) );
+}
+
+int main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/util/testsuite_counter_type.h
===================================================================
--- testsuite/util/testsuite_counter_type.h	(revision 215958)
+++ testsuite/util/testsuite_counter_type.h	(working copy)
@@ -95,7 +95,10 @@
     { return val == rhs.val; }
 
     bool operator<(const counter_type& rhs) const
-    { return val < rhs.val; }
+    {
+      ++less_compare_count;
+      return val < rhs.val;
+    }
   };
 
   int counter_type::default_count = 0;

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