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+// Copyright 2017 The Abseil Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef ABSL_RANDOM_DISCRETE_DISTRIBUTION_H_
+#define ABSL_RANDOM_DISCRETE_DISTRIBUTION_H_
+
+#include <cassert>
+#include <cmath>
+#include <istream>
+#include <limits>
+#include <numeric>
+#include <type_traits>
+#include <utility>
+#include <vector>
+
+#include "absl/random/bernoulli_distribution.h"
+#include "absl/random/internal/iostream_state_saver.h"
+#include "absl/random/uniform_int_distribution.h"
+
+namespace absl {
+inline namespace lts_2019_08_08 {
+
+// absl::discrete_distribution
+//
+// A discrete distribution produces random integers i, where 0 <= i < n
+// distributed according to the discrete probability function:
+//
+//     P(i|p0,...,pn−1)=pi
+//
+// This class is an implementation of discrete_distribution (see
+// [rand.dist.samp.discrete]).
+//
+// The algorithm used is Walker's Aliasing algorithm, described in Knuth, Vol 2.
+// absl::discrete_distribution takes O(N) time to precompute the probabilities
+// (where N is the number of possible outcomes in the distribution) at
+// construction, and then takes O(1) time for each variate generation.  Many
+// other implementations also take O(N) time to construct an ordered sequence of
+// partial sums, plus O(log N) time per variate to binary search.
+//
+template <typename IntType = int>
+class discrete_distribution {
+ public:
+  using result_type = IntType;
+
+  class param_type {
+   public:
+    using distribution_type = discrete_distribution;
+
+    param_type() { init(); }
+
+    template <typename InputIterator>
+    explicit param_type(InputIterator begin, InputIterator end)
+        : p_(begin, end) {
+      init();
+    }
+
+    explicit param_type(std::initializer_list<double> weights) : p_(weights) {
+      init();
+    }
+
+    template <class UnaryOperation>
+    explicit param_type(size_t nw, double xmin, double xmax,
+                        UnaryOperation fw) {
+      if (nw > 0) {
+        p_.reserve(nw);
+        double delta = (xmax - xmin) / static_cast<double>(nw);
+        assert(delta > 0);
+        double t = delta * 0.5;
+        for (size_t i = 0; i < nw; ++i) {
+          p_.push_back(fw(xmin + i * delta + t));
+        }
+      }
+      init();
+    }
+
+    const std::vector<double>& probabilities() const { return p_; }
+    size_t n() const { return p_.size() - 1; }
+
+    friend bool operator==(const param_type& a, const param_type& b) {
+      return a.probabilities() == b.probabilities();
+    }
+
+    friend bool operator!=(const param_type& a, const param_type& b) {
+      return !(a == b);
+    }
+
+   private:
+    friend class discrete_distribution;
+
+    void init();
+
+    std::vector<double> p_;                     // normalized probabilities
+    std::vector<std::pair<double, size_t>> q_;  // (acceptance, alternate) pairs
+
+    static_assert(std::is_integral<result_type>::value,
+                  "Class-template absl::discrete_distribution<> must be "
+                  "parameterized using an integral type.");
+  };
+
+  discrete_distribution() : param_() {}
+
+  explicit discrete_distribution(const param_type& p) : param_(p) {}
+
+  template <typename InputIterator>
+  explicit discrete_distribution(InputIterator begin, InputIterator end)
+      : param_(begin, end) {}
+
+  explicit discrete_distribution(std::initializer_list<double> weights)
+      : param_(weights) {}
+
+  template <class UnaryOperation>
+  explicit discrete_distribution(size_t nw, double xmin, double xmax,
+                                 UnaryOperation fw)
+      : param_(nw, xmin, xmax, std::move(fw)) {}
+
+  void reset() {}
+
+  // generating functions
+  template <typename URBG>
+  result_type operator()(URBG& g) {  // NOLINT(runtime/references)
+    return (*this)(g, param_);
+  }
+
+  template <typename URBG>
+  result_type operator()(URBG& g,  // NOLINT(runtime/references)
+                         const param_type& p);
+
+  const param_type& param() const { return param_; }
+  void param(const param_type& p) { param_ = p; }
+
+  result_type(min)() const { return 0; }
+  result_type(max)() const {
+    return static_cast<result_type>(param_.n());
+  }  // inclusive
+
+  // NOTE [rand.dist.sample.discrete] returns a std::vector<double> not a
+  // const std::vector<double>&.
+  const std::vector<double>& probabilities() const {
+    return param_.probabilities();
+  }
+
+  friend bool operator==(const discrete_distribution& a,
+                         const discrete_distribution& b) {
+    return a.param_ == b.param_;
+  }
+  friend bool operator!=(const discrete_distribution& a,
+                         const discrete_distribution& b) {
+    return a.param_ != b.param_;
+  }
+
+ private:
+  param_type param_;
+};
+
+// --------------------------------------------------------------------------
+// Implementation details only below
+// --------------------------------------------------------------------------
+
+namespace random_internal {
+
+// Using the vector `*probabilities`, whose values are the weights or
+// probabilities of an element being selected, constructs the proportional
+// probabilities used by the discrete distribution.  `*probabilities` will be
+// scaled, if necessary, so that its entries sum to a value sufficiently close
+// to 1.0.
+std::vector<std::pair<double, size_t>> InitDiscreteDistribution(
+    std::vector<double>* probabilities);
+
+}  // namespace random_internal
+
+template <typename IntType>
+void discrete_distribution<IntType>::param_type::init() {
+  if (p_.empty()) {
+    p_.push_back(1.0);
+    q_.emplace_back(1.0, 0);
+  } else {
+    assert(n() <= (std::numeric_limits<IntType>::max)());
+    q_ = random_internal::InitDiscreteDistribution(&p_);
+  }
+}
+
+template <typename IntType>
+template <typename URBG>
+typename discrete_distribution<IntType>::result_type
+discrete_distribution<IntType>::operator()(
+    URBG& g,  // NOLINT(runtime/references)
+    const param_type& p) {
+  const auto idx = absl::uniform_int_distribution<result_type>(0, p.n())(g);
+  const auto& q = p.q_[idx];
+  const bool selected = absl::bernoulli_distribution(q.first)(g);
+  return selected ? idx : static_cast<result_type>(q.second);
+}
+
+template <typename CharT, typename Traits, typename IntType>
+std::basic_ostream<CharT, Traits>& operator<<(
+    std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references)
+    const discrete_distribution<IntType>& x) {
+  auto saver = random_internal::make_ostream_state_saver(os);
+  const auto& probabilities = x.param().probabilities();
+  os << probabilities.size();
+
+  os.precision(random_internal::stream_precision_helper<double>::kPrecision);
+  for (const auto& p : probabilities) {
+    os << os.fill() << p;
+  }
+  return os;
+}
+
+template <typename CharT, typename Traits, typename IntType>
+std::basic_istream<CharT, Traits>& operator>>(
+    std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references)
+    discrete_distribution<IntType>& x) {    // NOLINT(runtime/references)
+  using param_type = typename discrete_distribution<IntType>::param_type;
+  auto saver = random_internal::make_istream_state_saver(is);
+
+  size_t n;
+  std::vector<double> p;
+
+  is >> n;
+  if (is.fail()) return is;
+  if (n > 0) {
+    p.reserve(n);
+    for (IntType i = 0; i < n && !is.fail(); ++i) {
+      auto tmp = random_internal::read_floating_point<double>(is);
+      if (is.fail()) return is;
+      p.push_back(tmp);
+    }
+  }
+  x.param(param_type(p.begin(), p.end()));
+  return is;
+}
+
+}  // inline namespace lts_2019_08_08
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_DISCRETE_DISTRIBUTION_H_