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 /* boost random/discrete_distribution.hpp header file
  *
  * Copyright Steven Watanabe 2009-2011
  * 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)
  *
  * See http://www.boost.org for most recent version including documentation.
  *
  * $Id$
  */
 
 #ifndef BOOST_RANDOM_DISCRETE_DISTRIBUTION_HPP_INCLUDED
 #define BOOST_RANDOM_DISCRETE_DISTRIBUTION_HPP_INCLUDED
 
 #include <vector>
 #include <limits>
 #include <numeric>
 #include <utility>
 #include <iterator>
 #include <boost/assert.hpp>
 #include <boost/random/uniform_01.hpp>
 #include <boost/random/uniform_int_distribution.hpp>
 #include <boost/random/detail/config.hpp>
 #include <boost/random/detail/operators.hpp>
 #include <boost/random/detail/vector_io.hpp>
 
 #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
 #include <initializer_list>
 #endif
 
 #include <boost/range/begin.hpp>
 #include <boost/range/end.hpp>
 
 #include <boost/random/detail/disable_warnings.hpp>
 
 namespace boost {
 namespace random {
 namespace detail {
 
 template<class IntType, class WeightType>
 struct integer_alias_table {
     WeightType get_weight(IntType bin) const {
         WeightType result = _average;
         if(bin < _excess) ++result;
         return result;
     }
     template<class Iter>
     WeightType init_average(Iter begin, Iter end) {
         WeightType weight_average = 0;
         IntType excess = 0;
         IntType n = 0;
         // weight_average * n + excess == current partial sum
         // This is a bit messy, but it's guaranteed not to overflow
         for(Iter iter = begin; iter != end; ++iter) {
             ++n;
             if(*iter < weight_average) {
                 WeightType diff = weight_average - *iter;
                 weight_average -= diff / n;
                 if(diff % n > excess) {
                     --weight_average;
                     excess += n - diff % n;
                 } else {
                     excess -= diff % n;
                 }
             } else {
                 WeightType diff = *iter - weight_average;
                 weight_average += diff / n;
                 if(diff % n < n - excess) {
                     excess += diff % n;
                 } else {
                     ++weight_average;
                     excess -= n - diff % n;
                 }
             }
         }
         _alias_table.resize(static_cast<std::size_t>(n));
         _average = weight_average;
         _excess = excess;
         return weight_average;
     }
     void init_empty()
     {
         _alias_table.clear();
         _alias_table.push_back(std::make_pair(static_cast<WeightType>(1),
                                               static_cast<IntType>(0)));
         _average = static_cast<WeightType>(1);
         _excess = static_cast<IntType>(0);
     }
     bool operator==(const integer_alias_table& other) const
     {
         return _alias_table == other._alias_table &&
             _average == other._average && _excess == other._excess;
     }
     static WeightType normalize(WeightType val, WeightType /* average */)
     {
         return val;
     }
     static void normalize(std::vector<WeightType>&) {}
     template<class URNG>
     WeightType test(URNG &urng) const
     {
         return uniform_int_distribution<WeightType>(0, _average)(urng);
     }
     bool accept(IntType result, WeightType val) const
     {
         return result < _excess || val < _average;
     }
     static WeightType try_get_sum(const std::vector<WeightType>& weights)
     {
         WeightType result = static_cast<WeightType>(0);
         for(typename std::vector<WeightType>::const_iterator
                 iter = weights.begin(), end = weights.end();
             iter != end; ++iter)
         {
             if((std::numeric_limits<WeightType>::max)() - result > *iter) {
                 return static_cast<WeightType>(0);
             }
             result += *iter;
         }
         return result;
     }
     template<class URNG>
     static WeightType generate_in_range(URNG &urng, WeightType max)
     {
         return uniform_int_distribution<WeightType>(
             static_cast<WeightType>(0), max-1)(urng);
     }
     typedef std::vector<std::pair<WeightType, IntType> > alias_table_t;
     alias_table_t _alias_table;
     WeightType _average;
     IntType _excess;
 };
 
 template<class IntType, class WeightType>
 struct real_alias_table {
     WeightType get_weight(IntType) const
     {
         return WeightType(1.0);
     }
     template<class Iter>
     WeightType init_average(Iter first, Iter last)
     {
         std::size_t size = std::distance(first, last);
         WeightType weight_sum =
             std::accumulate(first, last, static_cast<WeightType>(0));
         _alias_table.resize(size);
         return weight_sum / size;
     }
     void init_empty()
     {
         _alias_table.clear();
         _alias_table.push_back(std::make_pair(static_cast<WeightType>(1),
                                               static_cast<IntType>(0)));
     }
     bool operator==(const real_alias_table& other) const
     {
         return _alias_table == other._alias_table;
     }
     static WeightType normalize(WeightType val, WeightType average)
     {
         return val / average;
     }
     static void normalize(std::vector<WeightType>& weights)
     {
         WeightType sum =
             std::accumulate(weights.begin(), weights.end(),
                             static_cast<WeightType>(0));
         for(typename std::vector<WeightType>::iterator
                 iter = weights.begin(),
                 end = weights.end();
             iter != end; ++iter)
         {
             *iter /= sum;
         }
     }
     template<class URNG>
     WeightType test(URNG &urng) const
     {
         return uniform_01<WeightType>()(urng);
     }
     bool accept(IntType, WeightType) const
     {
         return true;
     }
     static WeightType try_get_sum(const std::vector<WeightType>& /* weights */)
     {
         return static_cast<WeightType>(1);
     }
     template<class URNG>
     static WeightType generate_in_range(URNG &urng, WeightType)
     {
         return uniform_01<WeightType>()(urng);
     }
     typedef std::vector<std::pair<WeightType, IntType> > alias_table_t;
     alias_table_t _alias_table;
 };
 
 template<bool IsIntegral>
 struct select_alias_table;
 
 template<>
 struct select_alias_table<true> {
     template<class IntType, class WeightType>
     struct apply {
         typedef integer_alias_table<IntType, WeightType> type;
     };
 };
 
 template<>
 struct select_alias_table<false> {
     template<class IntType, class WeightType>
     struct apply {
         typedef real_alias_table<IntType, WeightType> type;
     };
 };
 
 }
 
 /**
  * The class @c discrete_distribution models a \random_distribution.
  * It produces integers in the range [0, n) with the probability
  * of producing each value is specified by the parameters of the
  * distribution.
  */
 template<class IntType = int, class WeightType = double>
 class discrete_distribution {
 public:
     typedef WeightType input_type;
     typedef IntType result_type;
 
     class param_type {
     public:
 
         typedef discrete_distribution distribution_type;
 
         /**
          * Constructs a @c param_type object, representing a distribution
          * with \f$p(0) = 1\f$ and \f$p(k|k>0) = 0\f$.
          */
         param_type() : _probabilities(1, static_cast<WeightType>(1)) {}
         /**
          * If @c first == @c last, equivalent to the default constructor.
          * Otherwise, the values of the range represent weights for the
          * possible values of the distribution.
          */
         template<class Iter>
         param_type(Iter first, Iter last) : _probabilities(first, last)
         {
             normalize();
         }
 #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
         /**
          * If wl.size() == 0, equivalent to the default constructor.
          * Otherwise, the values of the @c initializer_list represent
          * weights for the possible values of the distribution.
          */
         param_type(const std::initializer_list<WeightType>& wl)
           : _probabilities(wl)
         {
             normalize();
         }
 #endif
         /**
          * If the range is empty, equivalent to the default constructor.
          * Otherwise, the elements of the range represent
          * weights for the possible values of the distribution.
          */
         template<class Range>
         explicit param_type(const Range& range)
           : _probabilities(boost::begin(range), boost::end(range))
         {
             normalize();
         }
 
         /**
          * If nw is zero, equivalent to the default constructor.
          * Otherwise, the range of the distribution is [0, nw),
          * and the weights are found by  calling fw with values
          * evenly distributed between \f$\mbox{xmin} + \delta/2\f$ and
          * \f$\mbox{xmax} - \delta/2\f$, where
          * \f$\delta = (\mbox{xmax} - \mbox{xmin})/\mbox{nw}\f$.
          */
         template<class Func>
         param_type(std::size_t nw, double xmin, double xmax, Func fw)
         {
             std::size_t n = (nw == 0) ? 1 : nw;
             double delta = (xmax - xmin) / n;
             BOOST_ASSERT(delta > 0);
             for(std::size_t k = 0; k < n; ++k) {
                 _probabilities.push_back(fw(xmin + k*delta + delta/2));
             }
             normalize();
         }
 
         /**
          * Returns a vector containing the probabilities of each possible
          * value of the distribution.
          */
         std::vector<WeightType> probabilities() const
         {
             return _probabilities;
         }
 
         /** Writes the parameters to a @c std::ostream. */
         BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
         {
             detail::print_vector(os, parm._probabilities);
             return os;
         }
         
         /** Reads the parameters from a @c std::istream. */
         BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
         {
             std::vector<WeightType> temp;
             detail::read_vector(is, temp);
             if(is) {
                 parm._probabilities.swap(temp);
             }
             return is;
         }
 
         /** Returns true if the two sets of parameters are the same. */
         BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
         {
             return lhs._probabilities == rhs._probabilities;
         }
         /** Returns true if the two sets of parameters are different. */
         BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
     private:
         /// @cond show_private
         friend class discrete_distribution;
         explicit param_type(const discrete_distribution& dist)
           : _probabilities(dist.probabilities())
         {}
         void normalize()
         {
             impl_type::normalize(_probabilities);
         }
         std::vector<WeightType> _probabilities;
         /// @endcond
     };
 
     /**
      * Creates a new @c discrete_distribution object that has
      * \f$p(0) = 1\f$ and \f$p(i|i>0) = 0\f$.
      */
     discrete_distribution()
     {
         _impl.init_empty();
     }
     /**
      * Constructs a discrete_distribution from an iterator range.
      * If @c first == @c last, equivalent to the default constructor.
      * Otherwise, the values of the range represent weights for the
      * possible values of the distribution.
      */
     template<class Iter>
     discrete_distribution(Iter first, Iter last)
     {
         init(first, last);
     }
 #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
     /**
      * Constructs a @c discrete_distribution from a @c std::initializer_list.
      * If the @c initializer_list is empty, equivalent to the default
      * constructor.  Otherwise, the values of the @c initializer_list
      * represent weights for the possible values of the distribution.
      * For example, given the distribution
      *
      * @code
      * discrete_distribution<> dist{1, 4, 5};
      * @endcode
      *
      * The probability of a 0 is 1/10, the probability of a 1 is 2/5,
      * the probability of a 2 is 1/2, and no other values are possible.
      */
     discrete_distribution(std::initializer_list<WeightType> wl)
     {
         init(wl.begin(), wl.end());
     }
 #endif
     /**
      * Constructs a discrete_distribution from a Boost.Range range.
      * If the range is empty, equivalent to the default constructor.
      * Otherwise, the values of the range represent weights for the
      * possible values of the distribution.
      */
     template<class Range>
     explicit discrete_distribution(const Range& range)
     {
         init(boost::begin(range), boost::end(range));
     }
     /**
      * Constructs a discrete_distribution that approximates a function.
      * If nw is zero, equivalent to the default constructor.
      * Otherwise, the range of the distribution is [0, nw),
      * and the weights are found by  calling fw with values
      * evenly distributed between \f$\mbox{xmin} + \delta/2\f$ and
      * \f$\mbox{xmax} - \delta/2\f$, where
      * \f$\delta = (\mbox{xmax} - \mbox{xmin})/\mbox{nw}\f$.
      */
     template<class Func>
     discrete_distribution(std::size_t nw, double xmin, double xmax, Func fw)
     {
         std::size_t n = (nw == 0) ? 1 : nw;
         double delta = (xmax - xmin) / n;
         BOOST_ASSERT(delta > 0);
         std::vector<WeightType> weights;
         for(std::size_t k = 0; k < n; ++k) {
             weights.push_back(fw(xmin + k*delta + delta/2));
         }
         init(weights.begin(), weights.end());
     }
     /**
      * Constructs a discrete_distribution from its parameters.
      */
     explicit discrete_distribution(const param_type& parm)
     {
         param(parm);
     }
 
     /**
      * Returns a value distributed according to the parameters of the
      * discrete_distribution.
      */
     template<class URNG>
     IntType operator()(URNG& urng) const
     {
         BOOST_ASSERT(!_impl._alias_table.empty());
         IntType result;
         WeightType test;
         do {
             result = uniform_int_distribution<IntType>((min)(), (max)())(urng);
             test = _impl.test(urng);
         } while(!_impl.accept(result, test));
         if(test < _impl._alias_table[static_cast<std::size_t>(result)].first) {
             return result;
         } else {
             return(_impl._alias_table[static_cast<std::size_t>(result)].second);
         }
     }
     
     /**
      * Returns a value distributed according to the parameters
      * specified by param.
      */
     template<class URNG>
     IntType operator()(URNG& urng, const param_type& parm) const
     {
         if(WeightType limit = impl_type::try_get_sum(parm._probabilities)) {
             WeightType val = impl_type::generate_in_range(urng, limit);
             WeightType sum = 0;
             std::size_t result = 0;
             for(typename std::vector<WeightType>::const_iterator
                     iter = parm._probabilities.begin(),
                     end = parm._probabilities.end();
                 iter != end; ++iter, ++result)
             {
                 sum += *iter;
                 if(sum > val) {
                     return result;
                 }
             }
             // This shouldn't be reachable, but round-off error
             // can prevent any match from being found when val is
             // very close to 1.
             return static_cast<IntType>(parm._probabilities.size() - 1);
         } else {
             // WeightType is integral and sum(parm._probabilities)
             // would overflow.  Just use the easy solution.
             return discrete_distribution(parm)(urng);
         }
     }
     
     /** Returns the smallest value that the distribution can produce. */
     result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return 0; }
     /** Returns the largest value that the distribution can produce. */
     result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
     { return static_cast<result_type>(_impl._alias_table.size() - 1); }
 
     /**
      * Returns a vector containing the probabilities of each
      * value of the distribution.  For example, given
      *
      * @code
      * discrete_distribution<> dist = { 1, 4, 5 };
      * std::vector<double> p = dist.param();
      * @endcode
      *
      * the vector, p will contain {0.1, 0.4, 0.5}.
      *
      * If @c WeightType is integral, then the weights
      * will be returned unchanged.
      */
     std::vector<WeightType> probabilities() const
     {
         std::vector<WeightType> result(_impl._alias_table.size(), static_cast<WeightType>(0));
         std::size_t i = 0;
         for(typename impl_type::alias_table_t::const_iterator
                 iter = _impl._alias_table.begin(),
                 end = _impl._alias_table.end();
                 iter != end; ++iter, ++i)
         {
             WeightType val = iter->first;
             result[i] += val;
             result[static_cast<std::size_t>(iter->second)] += _impl.get_weight(i) - val;
         }
         impl_type::normalize(result);
         return(result);
     }
 
     /** Returns the parameters of the distribution. */
     param_type param() const
     {
         return param_type(*this);
     }
     /** Sets the parameters of the distribution. */
     void param(const param_type& parm)
     {
         init(parm._probabilities.begin(), parm._probabilities.end());
     }
     
     /**
      * Effects: Subsequent uses of the distribution do not depend
      * on values produced by any engine prior to invoking reset.
      */
     void reset() {}
 
     /** Writes a distribution to a @c std::ostream. */
     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, discrete_distribution, dd)
     {
         os << dd.param();
         return os;
     }
 
     /** Reads a distribution from a @c std::istream */
     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, discrete_distribution, dd)
     {
         param_type parm;
         if(is >> parm) {
             dd.param(parm);
         }
         return is;
     }
 
     /**
      * Returns true if the two distributions will return the
      * same sequence of values, when passed equal generators.
      */
     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(discrete_distribution, lhs, rhs)
     {
         return lhs._impl == rhs._impl;
     }
     /**
      * Returns true if the two distributions may return different
      * sequences of values, when passed equal generators.
      */
     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(discrete_distribution)
 
 private:
 
     /// @cond show_private
 
     template<class Iter>
     void init(Iter first, Iter last, std::input_iterator_tag)
     {
         std::vector<WeightType> temp(first, last);
         init(temp.begin(), temp.end());
     }
     template<class Iter>
     void init(Iter first, Iter last, std::forward_iterator_tag)
     {
         size_t input_size = std::distance(first, last);
         std::vector<std::pair<WeightType, IntType> > below_average;
         std::vector<std::pair<WeightType, IntType> > above_average;
         below_average.reserve(input_size);
         above_average.reserve(input_size);
         
         WeightType weight_average = _impl.init_average(first, last);
         WeightType normalized_average = _impl.get_weight(0);
         std::size_t i = 0;
         for(; first != last; ++first, ++i) {
             WeightType val = impl_type::normalize(*first, weight_average);
             std::pair<WeightType, IntType> elem(val, static_cast<IntType>(i));
             if(val < normalized_average) {
                 below_average.push_back(elem);
             } else {
                 above_average.push_back(elem);
             }
         }
 
         typename impl_type::alias_table_t::iterator
             b_iter = below_average.begin(),
             b_end = below_average.end(),
             a_iter = above_average.begin(),
             a_end = above_average.end()
             ;
         while(b_iter != b_end && a_iter != a_end) {
             _impl._alias_table[static_cast<std::size_t>(b_iter->second)] =
                 std::make_pair(b_iter->first, a_iter->second);
             a_iter->first -= (_impl.get_weight(b_iter->second) - b_iter->first);
             if(a_iter->first < normalized_average) {
                 *b_iter = *a_iter++;
             } else {
                 ++b_iter;
             }
         }
         for(; b_iter != b_end; ++b_iter) {
             _impl._alias_table[static_cast<std::size_t>(b_iter->second)].first =
                 _impl.get_weight(b_iter->second);
         }
         for(; a_iter != a_end; ++a_iter) {
             _impl._alias_table[static_cast<std::size_t>(a_iter->second)].first =
                 _impl.get_weight(a_iter->second);
         }
     }
     template<class Iter>
     void init(Iter first, Iter last)
     {
         if(first == last) {
             _impl.init_empty();
         } else {
             typename std::iterator_traits<Iter>::iterator_category category;
             init(first, last, category);
         }
     }
     typedef typename detail::select_alias_table<
         (::boost::is_integral<WeightType>::value)
     >::template apply<IntType, WeightType>::type impl_type;
     impl_type _impl;
     /// @endcond
 };
 
 }
 }
 
 #include <boost/random/detail/enable_warnings.hpp>
 
 #endif

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