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#ifndef ALIAS_SAMPLER_H_
#define ALIAS_SAMPLER_H_
#include <vector>
#include <limits>
// R. A. Kronmal and A. V. Peterson, Jr. (1977) On the alias method for
// generating random variables from a discrete distribution. In The American
// Statistician, Vol. 33, No. 4. Pages 214--218.
//
// Intuition: a multinomial with N outcomes can be rewritten as a uniform
// mixture of N Bernoulli distributions. The ith Bernoulli returns i with
// probability F[i], otherwise it returns an "alias" value L[i]. The
// constructor computes the F's and L's given an arbitrary multionimial p in
// O(n) time and Draw returns samples in O(1) time.
struct AliasSampler {
AliasSampler() {}
explicit AliasSampler(const std::vector<double>& p) { Init(p); }
void Init(const std::vector<double>& p) {
const unsigned N = p.size();
cutoffs_.resize(p.size());
aliases_.clear();
aliases_.resize(p.size(), std::numeric_limits<unsigned>::max());
std::vector<unsigned> s,g;
for (unsigned i = 0; i < N; ++i) {
const double cutoff = cutoffs_[i] = N * p[i];
if (cutoff >= 1.0) g.push_back(i); else s.push_back(i);
}
while(!s.empty() && !g.empty()) {
const unsigned k = g.back();
const unsigned j = s.back();
aliases_[j] = k;
cutoffs_[k] -= 1.0 - cutoffs_[j];
s.pop_back();
if (cutoffs_[k] < 1.0) {
g.pop_back();
s.push_back(k);
}
}
}
template <typename Uniform01Generator>
unsigned Draw(Uniform01Generator& u01) const {
const unsigned n = u01() * cutoffs_.size();
if (u01() > cutoffs_[n]) return aliases_[n]; else return n;
}
std::vector<double> cutoffs_; // F
std::vector<unsigned> aliases_; // L
};
#endif
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