# HG changeset patch
# User Balazs Dezso <deba@inf.elte.hu>
# Date 2008-10-17 23:55:18
# Node ID 4f7224faf3bd0bf460965b685cd503a838251df9
# Parent  6dbd5184c6a99e936a7de899e64c114e30c0f94f

Porting radix sorts from SVN #3509

diff --git a/lemon/Makefile.am b/lemon/Makefile.am
--- a/lemon/Makefile.am
+++ b/lemon/Makefile.am
@@ -36,6 +36,7 @@
 	lemon/maps.h \
 	lemon/math.h \
 	lemon/path.h \
+	lemon/radix_sort.h \
         lemon/random.h \
 	lemon/smart_graph.h \
         lemon/time_measure.h \
diff --git a/lemon/radix_sort.h b/lemon/radix_sort.h
new file mode 100644
--- /dev/null
+++ b/lemon/radix_sort.h
@@ -0,0 +1,484 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef RADIX_SORT_H
+#define RADIX_SORT_H
+
+/// \ingroup auxalg
+/// \file
+/// \brief Radix sort
+///
+/// Linear time sorting algorithms
+
+#include <vector>
+#include <limits>
+#include <iterator>
+#include <algorithm>
+
+namespace lemon {
+
+  namespace _radix_sort_bits {
+
+    template <typename Value>
+    struct Identity {
+      const Value& operator()(const Value& val) {
+	return val;
+      }
+    };
+
+
+    template <typename Value, typename Iterator, typename Functor>
+    Iterator radixSortPartition(Iterator first, Iterator last, 
+				Functor functor, Value mask) {
+      while (first != last && !(functor(*first) & mask)) {
+	++first;
+      }
+      if (first == last) {
+	return first;
+      }
+      --last;
+      while (first != last && (functor(*last) & mask)) {
+	--last;
+      }
+      if (first == last) {
+	return first;
+      }
+      std::iter_swap(first, last);
+      ++first;
+      if (!(first < last)) {
+	return first;
+      }
+      while (true) {
+	while (!(functor(*first) & mask)) {
+	  ++first;
+	}
+	--last;
+	while (functor(*last) & mask) {
+	  --last;
+	}
+	if (!(first < last)) {
+	  return first;
+	}
+	std::iter_swap(first, last);
+	++first;
+      }
+    }
+
+    template <typename Iterator, typename Functor>
+    Iterator radixSortSignPartition(Iterator first, Iterator last, 
+				    Functor functor) {
+      while (first != last && functor(*first) < 0) {
+	++first;
+      }
+      if (first == last) {
+	return first;
+      }
+      --last;
+      while (first != last && functor(*last) >= 0) {
+	--last;
+      }
+      if (first == last) {
+	return first;
+      }
+      std::iter_swap(first, last);
+      ++first;
+      if (!(first < last)) {
+	return first;
+      }
+      while (true) {
+	while (functor(*first) < 0) {
+	  ++first;
+	}
+	--last;
+	while (functor(*last) >= 0) {
+	  --last;
+	}
+	if (!(first < last)) {
+	  return first;
+	}
+	std::iter_swap(first, last);
+	++first;
+      }
+    }
+
+    template <typename Value, typename Iterator, typename Functor>
+    void radixIntroSort(Iterator first, Iterator last, 
+			Functor functor, Value mask) {
+      while (mask != 0 && last - first > 1) {
+	Iterator cut = radixSortPartition(first, last, functor, mask);
+	mask >>= 1;
+	radixIntroSort(first, cut, functor, mask);
+	first = cut;
+      }
+    }
+
+    template <typename Value, typename Iterator, typename Functor>
+    void radixSignedSort(Iterator first, Iterator last, Functor functor) {
+
+      Iterator cut = radixSortSignPartition(first, last, functor);
+
+      Value mask;
+      int max_digit;
+      Iterator it;
+
+      mask = ~0; max_digit = 0;
+      for (it = first; it != cut; ++it) {
+	while ((mask & functor(*it)) != mask) {
+	  ++max_digit;
+	  mask <<= 1;
+	}
+      }
+      radixIntroSort(first, cut, functor, 1 << max_digit);
+
+      mask = 0; max_digit = 0;
+      for (it = cut; it != last; ++it) {
+	while ((mask | functor(*it)) != mask) {
+	  ++max_digit;
+	  mask <<= 1; mask |= 1;
+	}
+      }
+      radixIntroSort(cut, last, functor, 1 << max_digit);
+    }
+
+    template <typename Value, typename Iterator, typename Functor>
+    void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
+
+      Value mask = 0;
+      int max_digit = 0;
+
+      Iterator it;
+      for (it = first; it != last; ++it) {
+	while ((mask | functor(*it)) != mask) {
+	  ++max_digit;
+	  mask <<= 1; mask |= 1;
+	}
+      }
+      radixIntroSort(first, last, functor, 1 << max_digit);
+    }
+
+
+    template <typename Value, 
+	      bool sign = std::numeric_limits<Value>::is_signed >
+    struct RadixSortSelector {
+      template <typename Iterator, typename Functor>
+      static void sort(Iterator first, Iterator last, Functor functor) {
+	radixSignedSort<Value>(first, last, functor);
+      }
+    };
+
+    template <typename Value>
+    struct RadixSortSelector<Value, false> {
+      template <typename Iterator, typename Functor>
+      static void sort(Iterator first, Iterator last, Functor functor) {
+	radixUnsignedSort<Value>(first, last, functor);
+      }
+    };
+
+  }
+
+  /// \ingroup auxalg
+  ///
+  /// \brief Sorts the STL compatible range into ascending order.
+  ///
+  /// The \c radixSort sorts the STL compatible range into ascending
+  /// order.  The radix sort algorithm can sort the items which mapped
+  /// to an integer with an adaptable unary function \c functor and the
+  /// order will be ascending by these mapped values. As function
+  /// specialization it is possible to use a normal function instead
+  /// of the functor object or if the functor is not given it will use
+  /// an identity function instead.
+  ///
+  /// This implemented radix sort is a special quick sort which pivot
+  /// value is choosen to partite the items on the next
+  /// bit. Therefore, let be \c c the maximal capacity and \c n the
+  /// number of the items in the container, the time complexity of the
+  /// algorithm is \f$ O(\log(c)n) \f$ and the additional space
+  /// complexity is \f$ O(\log(c)) \f$.
+  ///
+  /// \param first The begin of the given range.
+  /// \param last The end of the given range.
+  /// \param functor An adaptible unary function or a normal function
+  /// which maps the items to any integer type which can be either
+  /// signed or unsigned.
+  template <typename Iterator, typename Functor>
+  void radixSort(Iterator first, Iterator last, Functor functor) {
+    using namespace _radix_sort_bits;
+    typedef typename Functor::result_type Value;
+    RadixSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
+    using namespace _radix_sort_bits;
+    RadixSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
+    using namespace _radix_sort_bits;
+    RadixSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
+    using namespace _radix_sort_bits;
+    RadixSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
+    using namespace _radix_sort_bits;
+    RadixSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator>
+  void radixSort(Iterator first, Iterator last) {
+    using namespace _radix_sort_bits;
+    typedef typename std::iterator_traits<Iterator>::value_type Value;
+    RadixSortSelector<Value>::sort(first, last, Identity<Value>());
+  }
+
+  namespace _radix_sort_bits {
+
+    template <typename Value>
+    unsigned char valueByte(Value value, int byte) {
+      return value >> (std::numeric_limits<unsigned char>::digits * byte);
+    }
+
+    template <typename Functor, typename Key>
+    void counterIntroSort(Key *first, Key *last, Key *target, 
+			  int byte, Functor functor) {
+      const int size = 
+	unsigned(std::numeric_limits<unsigned char>::max()) + 1;
+      std::vector<int> counter(size);
+      for (int i = 0; i < size; ++i) {
+	counter[i] = 0;
+      }
+      Key *it = first;
+      while (first != last) {
+	++counter[valueByte(functor(*first), byte)]; 
+	++first;
+      }
+      int prev, num = 0;
+      for (int i = 0; i < size; ++i) {
+	prev = num;
+	num += counter[i];
+	counter[i] = prev;
+      }
+      while (it != last) {
+	target[counter[valueByte(functor(*it), byte)]++] = *it;
+	++it;
+      }
+    }
+
+    template <typename Functor, typename Key>
+    void signedCounterIntroSort(Key *first, Key *last, Key *target, 
+				int byte, Functor functor) {
+      const int size = 
+	unsigned(std::numeric_limits<unsigned char>::max()) + 1;
+      std::vector<int> counter(size);
+      for (int i = 0; i < size; ++i) {
+	counter[i] = 0;
+      }
+      Key *it = first;
+      while (first != last) {
+	counter[valueByte(functor(*first), byte)]++;
+	++first;
+      }
+      int prev, num = 0;
+      for (int i = size / 2; i < size; ++i) {
+	prev = num;
+	num += counter[i];
+	counter[i] = prev;
+      }
+      for (int i = 0; i < size / 2; ++i) {
+	prev = num;
+	num += counter[i];
+	counter[i] = prev;
+      }
+      while (it != last) {
+	target[counter[valueByte(functor(*it), byte)]++] = *it;
+	++it;
+      }
+    }
+
+  
+    template <typename Value, typename Iterator, typename Functor>
+    void counterSignedSort(Iterator first, Iterator last, Functor functor) {
+      if (first == last) return;
+      typedef typename std::iterator_traits<Iterator>::value_type Key;
+      typedef std::allocator<Key> Allocator;
+      Allocator allocator;
+
+      int length = std::distance(first, last);
+      Key* buffer = allocator.allocate(2 * length);
+      try {
+	bool dir = true;
+	std::copy(first, last, buffer);
+	for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
+	  if (dir) {
+	    counterIntroSort(buffer, buffer + length, buffer + length, 
+			     i, functor);
+	  } else {
+	    counterIntroSort(buffer + length, buffer + 2 * length, buffer, 
+			     i, functor);
+	  }
+	  dir = !dir;
+	}
+	if (dir) {
+	  signedCounterIntroSort(buffer, buffer + length, buffer + length, 
+				 sizeof(Value) - 1, functor);
+	  std::copy(buffer + length, buffer + 2 * length, first);
+	}	else {
+	  signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer, 
+				 sizeof(Value) - 1, functor);
+	  std::copy(buffer, buffer + length, first);
+	}
+      } catch (...) {
+	allocator.deallocate(buffer, 2 * length);
+	throw;
+      }
+      allocator.deallocate(buffer, 2 * length);
+    }
+
+    template <typename Value, typename Iterator, typename Functor>
+    void counterUnsignedSort(Iterator first, Iterator last, Functor functor) {
+      if (first == last) return;
+      typedef typename std::iterator_traits<Iterator>::value_type Key;
+      typedef std::allocator<Key> Allocator;
+      Allocator allocator;
+
+      int length = std::distance(first, last);
+      Key *buffer = allocator.allocate(2 * length);
+      try {
+	bool dir = true;
+	std::copy(first, last, buffer);
+	for (int i = 0; i < int(sizeof(Value)); ++i) {
+	  if (dir) {
+	    counterIntroSort(buffer, buffer + length, 
+			     buffer + length, i, functor);
+	  } else {
+	    counterIntroSort(buffer + length, buffer + 2 * length, 
+			     buffer, i, functor);
+	  }
+	  dir = !dir;
+	}
+	if (dir) {
+	  std::copy(buffer, buffer + length, first);
+	}	else {
+	  std::copy(buffer + length, buffer + 2 * length, first);
+	}
+      } catch (...) {
+	allocator.deallocate(buffer, 2 * length);
+	throw;
+      }
+      allocator.deallocate(buffer, 2 * length);
+    }
+
+
+
+    template <typename Value, 
+	      bool sign = std::numeric_limits<Value>::is_signed >
+    struct CounterSortSelector {
+      template <typename Iterator, typename Functor>
+      static void sort(Iterator first, Iterator last, Functor functor) {
+	counterSignedSort<Value>(first, last, functor);
+      }
+    };
+
+    template <typename Value>
+    struct CounterSortSelector<Value, false> {
+      template <typename Iterator, typename Functor>
+      static void sort(Iterator first, Iterator last, Functor functor) {
+	counterUnsignedSort<Value>(first, last, functor);
+      }
+    };
+
+  }
+
+  /// \ingroup auxalg
+  ///
+  /// \brief Sorts stable the STL compatible range into ascending order.
+  ///
+  /// The \c counterSort sorts the STL compatible range into ascending
+  /// order.  The counter sort algorithm can sort the items which
+  /// mapped to an integer with an adaptable unary function \c functor
+  /// and the order will be ascending by these mapped values. As
+  /// function specialization it is possible to use a normal function
+  /// instead of the functor object or if the functor is not given it
+  /// will use an identity function instead.
+  ///
+  /// The implemented counter sort use a radix forward sort on the
+  /// bytes of the integer number. The algorithm sorts the items
+  /// byte-by-byte, first it counts how many times occurs a byte value
+  /// in the containerm, and with the occurence number the container
+  /// can be copied to an other in asceding order in \c O(n) time.
+  /// Let be \c c the maximal capacity of the integer type and \c n
+  /// the number of the items in the container, the time complexity of
+  /// the algorithm is \f$ O(\log(c)n) \f$ and the additional space
+  /// complexity is \f$ O(n) \f$.
+  ///
+  /// The sorting algorithm is stable, i.e. the order of two equal
+  /// element remains the same.
+  ///
+  /// \param first The begin of the given range.
+  /// \param last The end of the given range.
+  /// \param functor An adaptible unary function or a normal function
+  /// which maps the items to any integer type which can be either
+  /// signed or unsigned.
+  template <typename Iterator, typename Functor>
+  void counterSort(Iterator first, Iterator last, Functor functor) {
+    using namespace _radix_sort_bits;
+    typedef typename Functor::result_type Value;
+    CounterSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {
+    using namespace _radix_sort_bits;
+    CounterSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
+    using namespace _radix_sort_bits;
+    CounterSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
+    using namespace _radix_sort_bits;
+    CounterSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator, typename Value, typename Key>
+  void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
+    using namespace _radix_sort_bits;
+    CounterSortSelector<Value>::sort(first, last, functor);
+  }
+
+  template <typename Iterator>
+  void counterSort(Iterator first, Iterator last) {
+    using namespace _radix_sort_bits;
+    typedef typename std::iterator_traits<Iterator>::value_type Value;
+    CounterSortSelector<Value>::sort(first, last, Identity<Value>());
+  }
+
+}
+
+#endif
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -16,6 +16,7 @@
   heap_test
   kruskal_test
   maps_test
+  radix_sort_test
   random_test
   path_test
   time_measure_test
diff --git a/test/Makefile.am b/test/Makefile.am
--- a/test/Makefile.am
+++ b/test/Makefile.am
@@ -19,6 +19,7 @@
 	test/heap_test \
 	test/kruskal_test \
         test/maps_test \
+	test/radix_sort_test \
         test/random_test \
         test/path_test \
         test/test_tools_fail \
@@ -43,6 +44,7 @@
 test_kruskal_test_SOURCES = test/kruskal_test.cc
 test_maps_test_SOURCES = test/maps_test.cc
 test_path_test_SOURCES = test/path_test.cc
+test_radix_sort_test_SOURCES = test/radix_sort_test.cc
 test_random_test_SOURCES = test/random_test.cc
 test_test_tools_fail_SOURCES = test/test_tools_fail.cc
 test_test_tools_pass_SOURCES = test/test_tools_pass.cc
diff --git a/test/radix_sort_test.cc b/test/radix_sort_test.cc
new file mode 100644
--- /dev/null
+++ b/test/radix_sort_test.cc
@@ -0,0 +1,147 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <lemon/time_measure.h>
+#include <lemon/smart_graph.h>
+#include <lemon/maps.h>
+#include <lemon/radix_sort.h>
+#include <lemon/math.h>
+
+#include "test_tools.h"
+
+#include <vector>
+#include <algorithm>
+
+using namespace lemon;
+
+static const int n = 10000;
+
+struct Negate {
+  typedef int argument_type;
+  typedef int result_type;
+  int operator()(int a) { return - a; }
+};
+
+int negate(int a) { return - a; }
+
+
+void generateIntSequence(int n, std::vector<int>& data) {
+  int prime = 9973;
+  int root = 136, value = 1;
+  for (int i = 0; i < n; ++i) {
+    data.push_back(value - prime / 2);
+    value = (value * root) % prime;
+  }
+}
+
+void generateCharSequence(int n, std::vector<unsigned char>& data) {
+  int prime = 251;
+  int root = 3, value = root;
+  for (int i = 0; i < n; ++i) {
+    data.push_back(static_cast<unsigned char>(value));
+    value = (value * root) % prime;
+  }
+}
+
+void checkRadixSort() {
+  {
+    std::vector<int> data1;
+    generateIntSequence(n, data1);
+
+    std::vector<int> data2(data1);
+    std::sort(data1.begin(), data1.end());
+
+    radixSort(data2.begin(), data2.end());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[i], "Test failed");
+    }
+
+    radixSort(data2.begin(), data2.end(), Negate());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[n - 1 - i], "Test failed");
+    }
+
+    radixSort(data2.begin(), data2.end(), negate);
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[n - 1 - i], "Test failed");
+    }
+
+  } 
+  
+  {
+    std::vector<unsigned char> data1(n);
+    generateCharSequence(n, data1);
+
+    std::vector<unsigned char> data2(data1);
+    std::sort(data1.begin(), data1.end());
+
+    radixSort(data2.begin(), data2.end());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[i], "Test failed");
+    }
+
+  }
+}
+
+
+void checkCounterSort() {
+  {
+    std::vector<int> data1;
+    generateIntSequence(n, data1);
+
+    std::vector<int> data2(data1);
+    std::sort(data1.begin(), data1.end());
+
+    counterSort(data2.begin(), data2.end());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[i], "Test failed");
+    }
+
+    counterSort(data2.begin(), data2.end(), Negate());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[n - 1 - i], "Test failed");
+    }
+
+    counterSort(data2.begin(), data2.end(), negate);
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[n - 1 - i], "Test failed");
+    }
+  } 
+
+  {
+    std::vector<unsigned char> data1(n);
+    generateCharSequence(n, data1);
+
+    std::vector<unsigned char> data2(data1);
+    std::sort(data1.begin(), data1.end());
+
+    radixSort(data2.begin(), data2.end());
+    for (int i = 0; i < n; ++i) {
+      check(data1[i] == data2[i], "Test failed");
+    }
+
+  }
+}
+
+int main() {
+
+  checkRadixSort();  
+  checkCounterSort();
+
+  return 0;
+}