Add 'indirect_sort'

doc/algorithm.qbk

@@ -233,6 +233,8 @@ Convert a sequence of hexadecimal characters into a sequence of integers or char
 Convert a sequence of integral types into a lower case hexadecimal sequence of characters
 [endsect:hex_lower]
 
+[include indirect_sort.qbk]
+
 [include is_palindrome.qbk]
 
 [include is_partitioned_until.qbk]

doc/indirect_sort.qbk

@@ -0,0 +1,111 @@
+[/ File indirect_sort.qbk]
+
+[section:indirect_sort indirect_sort ]
+
+[/license
+Copyright (c) 2023 Marshall Clow
+
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+]
+
+There are times that you want a sorted version of a sequence, but for some reason you don't want to modify it.  Maybe the elements in the sequence can't be moved/copied, e.g. the sequence is const, or they're just really expensive to move around.   An example of this might be a sequence of records from a database.
+
+That's where indirect sorting comes in.  In a "normal" sort, the elements of the sequence to be sorted are shuffled in place.  In indirect sorting, the elements are unchanged, but the sort algorithm returns a "permutation" of the elements that, when applied, will put the elements in the sequence in a sorted order.
+
+Assume have a sequence `[first, last)` of 1000 items that are expensive to swap:
+```
+	std::sort(first, last);  // ['O(N ln N)] comparisons and ['O(N ln N)] swaps (of the element type).
+```
+
+On the other hand, using indirect sorting:
+```
+	auto perm = indirect_sort(first, last);  // ['O(N lg N)] comparisons and ['O(N lg N)] swaps (of size_t).
+	apply_permutation(first, last, perm.begin(), perm.end()); // ['O(N)] swaps (of the element type)
+```
+
+If the element type is sufficiently expensive to swap, then 10,000 swaps of size_t + 1000 swaps of the element_type could be cheaper than 10,000 swaps of the element_type.
+
+Or maybe you don't need the elements to actually be sorted - you just want to traverse them in a sorted order:
+```
+	auto permutation = indirect_sort(first, last);
+	for (size_t idx: permutation)
+		std::cout << first[idx] << std::endl;
+```
+
+
+Assume that instead of an "array of structures", you have a "struct of arrays".
+```
+struct AType {
+	Type0 key;
+	Type1 value1;
+	Type1 value2;
+	};
+
+std::array<AType, 1000> arrayOfStruct;
+```
+
+versus:
+
+```
+template <size_t N>
+struct AType {
+	std::array<Type0, N> key;
+	std::array<Type1, N> value1;
+	std::array<Type2, N> value2;
+	};
+
+AType<1000> structOfArrays;
+```
+
+Sorting the first one is easy, because each set of fields (`key`, `value1`, `value2`) are part of the same struct.  But with indirect sorting, the second one is easy to sort as well - just sort the keys, then apply the permutation to the keys and the values:
+```
+	auto perm = indirect_sort(std::begin(structOfArrays.key), std::end(structOfArrays.key));
+	apply_permutation(structOfArrays.key.begin(),    structOfArrays.key.end(),    perm.begin(), perm.end());
+	apply_permutation(structOfArrays.value1.begin(), structOfArrays.value1.end(), perm.begin(), perm.end());
+	apply_permutation(structOfArrays.value2.begin(), structOfArrays.value2.end(), perm.begin(), perm.end());
+```
+
+[heading interface]
+
+The function `indirect_sort` returns a `vector<size_t>` containing the permutation necessary to put the input sequence into a sorted order. One version uses `std::less` to do the comparisons; the other lets the caller pass predicate to do the comparisons. 
+
+There is also a variant called `indirect_stable_sort`; it bears the same relation to `indirect_sort` that `std::stable_sort` does to `std::sort`.
+
+```
+template <typename RAIterator>
+std::vector<size_t> indirect_sort (RAIterator first, RAIterator last);
+
+template <typename RAIterator, typename BinaryPredicate>
+std::vector<size_t> indirect_sort (RAIterator first, RAIterator last, BinaryPredicate pred);
+
+template <typename RAIterator>
+std::vector<size_t> indirect_stable_sort (RAIterator first, RAIterator last);
+
+template <typename RAIterator, typename BinaryPredicate>
+std::vector<size_t> indirect_stable_sort (RAIterator first, RAIterator last, BinaryPredicate pred);
+```
+
+[heading Examples]
+
+[heading Iterator Requirements]
+
+`indirect_sort` requires random-access iterators.
+
+[heading Complexity]
+
+Both of the variants of `indirect_sort` run in ['O(N lg N)] time; they are not more (or less) efficient than `std::sort`. There is an extra layer of indirection on each comparison, but all of the swaps are done on values of type `size_t`
+
+[heading Exception Safety]
+
+[heading Notes]
+
+In numpy, this algorithm is known as `argsort`.
+
+[endsect]
+
+[/ File indirect_sort.qbk
+Copyright 2023 Marshall Clow
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt).
+]

include/boost/algorithm/indirect_sort.hpp

@@ -0,0 +1,192 @@
+/* 
+   Copyright (c) Marshall Clow 2023.
+
+   Distributed under the Boost Software License, Version 1.0. (See accompanying
+   file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+*/
+
+/// \file indirect_sort.hpp
+/// \brief indirect sorting algorithms
+/// \author Marshall Clow
+///
+
+#ifndef BOOST_ALGORITHM_INDIRECT_SORT
+#define BOOST_ALGORITHM_INDIRECT_SORT
+
+#include <algorithm>        // for std::sort (and others)
+#include <functional>       // for std::less
+#include <vector>           // for std::vector
+
+#include <boost/algorithm/cxx11/iota.hpp>
+
+namespace boost { namespace algorithm {
+
+namespace detail {
+
+	template <class Predicate, class Iter>
+	struct indirect_predicate {
+		indirect_predicate (Predicate pred, Iter iter)
+		: pred_(pred), iter_(iter) {}
+
+		bool operator ()(size_t a, size_t b) const {
+			 return pred_(iter_[a], iter_[b]);
+		}
+
+		Predicate pred_;
+		Iter      iter_;
+	};
+
+}
+
+typedef std::vector<size_t> Permutation;
+
+                    // ===== sort =====
+
+/// \fn indirect_sort (RAIterator first, RAIterator last, Predicate p)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted according to the predicate pred.
+///
+/// \param first  The start of the input sequence
+/// \param last   The end of the input sequence
+/// \param pred   The predicate to compare elements with
+///
+template <typename RAIterator, typename Pred>
+Permutation indirect_sort (RAIterator first, RAIterator last, Pred pred) {
+	Permutation ret(std::distance(first, last));
+	boost::algorithm::iota(ret.begin(), ret.end(), size_t(0));
+	std::sort(ret.begin(), ret.end(), 
+	                  detail::indirect_predicate<Pred, RAIterator>(pred, first));
+	return ret;
+}
+
+/// \fn indirect_sort (RAIterator first, RAIterator last)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted in non-descending order.
+///
+/// \param first  The start of the input sequence
+/// \param last   The end of the input sequence
+///
+template <typename RAIterator>
+Permutation indirect_sort (RAIterator first, RAIterator last) {
+    return indirect_sort(first, last, 
+                    std::less<typename std::iterator_traits<RAIterator>::value_type>());
+}
+
+                    // ===== stable_sort =====
+
+/// \fn indirect_stable_sort (RAIterator first, RAIterator last, Predicate p)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted according to the predicate pred.
+///
+/// \param first  The start of the input sequence
+/// \param last   The end of the input sequence
+/// \param pred   The predicate to compare elements with
+///
+template <typename RAIterator, typename Pred>
+Permutation indirect_stable_sort (RAIterator first, RAIterator last, Pred pred) {
+	Permutation ret(std::distance(first, last));
+	boost::algorithm::iota(ret.begin(), ret.end(), size_t(0));
+	std::stable_sort(ret.begin(), ret.end(), 
+	                  detail::indirect_predicate<Pred, RAIterator>(pred, first));
+	return ret;
+}
+
+/// \fn indirect_stable_sort (RAIterator first, RAIterator last)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted in non-descending order.
+///
+/// \param first  The start of the input sequence
+/// \param last   The end of the input sequence
+///
+template <typename RAIterator>
+Permutation indirect_stable_sort (RAIterator first, RAIterator last) {
+    return indirect_stable_sort(first, last, 
+                    std::less<typename std::iterator_traits<RAIterator>::value_type>());
+}
+
+                    // ===== partial_sort =====
+
+/// \fn indirect_partial_sort (RAIterator first, RAIterator last, Predicate p)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the resulting range [first, middle) is sorted and the range [middle,last)
+///     consists of elements that are "larger" than then ones in [first, middle),
+///     according to the predicate pred.
+///
+/// \param first  The start of the input sequence
+/// \param middle The end of the range to be sorted
+/// \param last   The end of the input sequence
+/// \param pred   The predicate to compare elements with
+///
+template <typename RAIterator, typename Pred>
+Permutation indirect_partial_sort (RAIterator first, RAIterator middle, 
+                                   RAIterator last, Pred pred) {
+	Permutation ret(std::distance(first, last));
+
+	boost::algorithm::iota(ret.begin(), ret.end(), size_t(0));
+	std::partial_sort(ret.begin(), ret.begin() + std::distance(first, middle), ret.end(), 
+	                  detail::indirect_predicate<Pred, RAIterator>(pred, first));
+	return ret;
+}
+
+/// \fn indirect_partial_sort (RAIterator first, RAIterator last)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the resulting range [first, middle) is sorted in non-descending order,
+///     and the range [middle,last) consists of elements that are larger than
+///     then ones in [first, middle).
+///
+/// \param first  The start of the input sequence
+/// \param last   The end of the input sequence
+///
+template <typename RAIterator>
+Permutation indirect_partial_sort (RAIterator first, RAIterator middle, RAIterator last) {
+    return indirect_partial_sort(first, middle, last, 
+                    std::less<typename std::iterator_traits<RAIterator>::value_type>());
+}
+
+                    // ===== nth_element =====
+
+/// \fn indirect_nth_element (RAIterator first, RAIterator last, Predicate p)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted according to the predicate pred.
+///
+/// \param first  The start of the input sequence
+/// \param nth    The sort partition point in the input sequence
+/// \param last   The end of the input sequence
+/// \param pred   The predicate to compare elements with
+///
+template <typename RAIterator, typename Pred>
+Permutation indirect_nth_element (RAIterator first, RAIterator nth,
+                                  RAIterator last, Pred pred) {
+	Permutation ret(std::distance(first, last));
+	boost::algorithm::iota(ret.begin(), ret.end(), size_t(0));
+	std::nth_element(ret.begin(), ret.begin() + std::distance(first, nth), ret.end(), 
+	                  detail::indirect_predicate<Pred, RAIterator>(pred, first));
+	return ret;
+}
+
+/// \fn indirect_nth_element (RAIterator first, RAIterator last)
+/// \returns a permutation of the elements in the range [first, last)
+///     such that when the permutation is applied to the sequence,
+///     the result is sorted in non-descending order.
+///
+/// \param first  The start of the input sequence
+/// \param nth    The sort partition point in the input sequence
+/// \param last   The end of the input sequence
+///
+template <typename RAIterator>
+Permutation indirect_nth_element (RAIterator first, RAIterator nth, RAIterator last) {
+    return indirect_nth_element(first, nth, last, 
+                    std::less<typename std::iterator_traits<RAIterator>::value_type>());
+}
+
+}}
+
+#endif // BOOST_ALGORITHM_INDIRECT_SORT

test/Jamfile.v2

@@ -88,6 +88,10 @@ alias unit_test_framework
 
 # Apply_permutation tests
      [ run apply_permutation_test.cpp unit_test_framework    : : : : apply_permutation_test ]
+
+# Indirect_sort tests
+     [ run indirect_sort_test.cpp unit_test_framework    : : : : indirect_sort_test ]
+
 # Find tests
      [ run find_not_test.cpp unit_test_framework   : : : : find_not_test ]
      [ run find_backward_test.cpp unit_test_framework   : : : : find_backward_test ]