DecisionTree-inl.h

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/* ----------------------------------------------------------------------------
 
 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
 
 * See LICENSE for the license information
 
 * -------------------------------------------------------------------------- */
 
#pragma once
 
#include <gtsam/discrete/DecisionTree.h>
 
#include <algorithm>
 
#include <cmath>
#include <fstream>
#include <list>
#include <map>
#include <set>
#include <sstream>
#include <string>
#include <vector>
#include <optional>
#include <cassert>
#include <iterator>
 
namespace gtsam {
 
  /****************************************************************************/
  // Node
  /****************************************************************************/
#ifdef DT_DEBUG_MEMORY
  template<typename L, typename Y>
  int DecisionTree<L, Y>::Node::nrNodes = 0;
#endif
 
  /****************************************************************************/
  // Leaf
  /****************************************************************************/
  template <typename L, typename Y>
  struct DecisionTree<L, Y>::Leaf : public DecisionTree<L, Y>::Node {
    Y constant_;
 
    Leaf() {}
 
    Leaf(const Y& constant) : constant_(constant) {}
 
    const Y& constant() const {
      return constant_;
    }
 
    bool sameLeaf(const Leaf& q) const override {
      return constant_ == q.constant_;
    }
 
    bool sameLeaf(const Node& q) const override {
      return (q.isLeaf() && q.sameLeaf(*this));
    }
 
    bool equals(const Node& q, const CompareFunc& compare) const override {
      const Leaf* other = dynamic_cast<const Leaf*>(&q);
      if (!other) return false;
      return compare(this->constant_, other->constant_);
    }
 
    void print(const std::string& s, const LabelFormatter& labelFormatter,
               const ValueFormatter& valueFormatter) const override {
      std::cout << s << " Leaf " << valueFormatter(constant_) << std::endl;
    }
 
    void dot(std::ostream& os, const LabelFormatter& labelFormatter,
             const ValueFormatter& valueFormatter,
             bool showZero) const override {
      std::string value = valueFormatter(constant_);
      if (showZero || value.compare("0"))
        os << "\"" << this->id() << "\" [label=\"" << value
           << "\", shape=box, rank=sink, height=0.35, fixedsize=true]\n";
    }
 
    const Y& operator()(const Assignment<L>& x) const override {
      return constant_;
    }
 
    NodePtr apply(const Unary& op) const override {
      NodePtr f(new Leaf(op(constant_)));
      return f;
    }
 
    NodePtr apply(const UnaryAssignment& op,
                  const Assignment<L>& assignment) const override {
      NodePtr f(new Leaf(op(assignment, constant_)));
      return f;
    }
 
    // Apply binary operator "h = f op g" on Leaf node
    // Note op is not assumed commutative so we need to keep track of order
    // Simply calls apply on argument to call correct virtual method:
    // fL.apply_f_op_g(gL) -> gL.apply_g_op_fL(fL) (below)
    // fL.apply_f_op_g(gC) -> gC.apply_g_op_fL(fL) (Choice)
    NodePtr apply_f_op_g(const Node& g, const Binary& op) const override {
      return g.apply_g_op_fL(*this, op);
    }
 
    // Applying binary operator to two leaves results in a leaf
    NodePtr apply_g_op_fL(const Leaf& fL, const Binary& op) const override {
      // fL op gL
      NodePtr h(new Leaf(op(fL.constant_, constant_)));
      return h;
    }
 
    // If second argument is a Choice node, call it's apply with leaf as second
    NodePtr apply_g_op_fC(const Choice& fC, const Binary& op) const override {
      return fC.apply_fC_op_gL(*this, op);  // operand order back to normal
    }
 
    NodePtr choose(const L& label, size_t index) const override {
      return NodePtr(new Leaf(constant()));
    }
 
    bool isLeaf() const override { return true; }
 
   private:
    using Base = DecisionTree<L, Y>::Node;
 
#ifdef GTSAM_ENABLE_BOOST_SERIALIZATION
 
    friend class boost::serialization::access;
    template <class ARCHIVE>
    void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
      ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
      ar& BOOST_SERIALIZATION_NVP(constant_);
    }
#endif
  };  // Leaf
 
  /****************************************************************************/
  // Choice
  /****************************************************************************/
  template<typename L, typename Y>
  struct DecisionTree<L, Y>::Choice: public DecisionTree<L, Y>::Node {
    L label_;
 
    std::vector<NodePtr> branches_;
 
   private:
    size_t allSame_;
 
    using ChoicePtr = std::shared_ptr<const Choice>;
 
   public:
    Choice() {}
 
    ~Choice() override {
#ifdef DT_DEBUG_MEMORY
      std::cout << Node::nrNodes << " destructing (Choice) " << this->id()
                     << std::endl;
#endif
    }
 
    static NodePtr Unique(const NodePtr& node) {
      if (auto choice = std::dynamic_pointer_cast<const Choice>(node)) {
        // Choice node, we recurse!
        // Make non-const copy so we can update
        auto f = std::make_shared<Choice>(choice->label(), choice->nrChoices());
 
        // Iterate over all the branches
        for (size_t i = 0; i < choice->nrChoices(); i++) {
          auto branch = choice->branches_[i];
          f->push_back(Unique(branch));
        }
 
#ifdef GTSAM_DT_MERGING
        // If all the branches are the same, we can merge them into one
        if (f->allSame_) {
          assert(f->branches().size() > 0);
          NodePtr f0 = f->branches_[0];
 
          NodePtr newLeaf(
              new Leaf(std::dynamic_pointer_cast<const Leaf>(f0)->constant()));
          return newLeaf;
        }
#endif
        return f;
      } else {
        // Leaf node, return as is
        return node;
      }
    }
 
    bool isLeaf() const override { return false; }
 
    Choice(const L& label, size_t count) :
      label_(label), allSame_(true) {
      branches_.reserve(count);
    }
 
    Choice(const Choice& f, const Choice& g, const Binary& op) :
      allSame_(true) {
      // Choose what to do based on label
      if (f.label() > g.label()) {
        // f higher than g
        label_ = f.label();
        size_t count = f.nrChoices();
        branches_.reserve(count);
        for (size_t i = 0; i < count; i++)
          push_back(f.branches_[i]->apply_f_op_g(g, op));
      } else if (g.label() > f.label()) {
        // f lower than g
        label_ = g.label();
        size_t count = g.nrChoices();
        branches_.reserve(count);
        for (size_t i = 0; i < count; i++)
          push_back(g.branches_[i]->apply_g_op_fC(f, op));
      } else {
        // f same level as g
        label_ = f.label();
        size_t count = f.nrChoices();
        branches_.reserve(count);
        for (size_t i = 0; i < count; i++)
          push_back(f.branches_[i]->apply_f_op_g(*g.branches_[i], op));
      }
    }
 
    const L& label() const {
      return label_;
    }
 
    size_t nrChoices() const {
      return branches_.size();
    }
 
    const std::vector<NodePtr>& branches() const {
      return branches_;
    }
 
    void push_back(const NodePtr& node) {
      // allSame_ is restricted to leaf nodes in a decision tree
      if (allSame_ && !branches_.empty()) {
        allSame_ = node->sameLeaf(*branches_.back());
      }
      branches_.push_back(node);
    }
 
    void print(const std::string& s, const LabelFormatter& labelFormatter,
               const ValueFormatter& valueFormatter) const override {
      std::cout << s << " Choice(";
      std::cout << labelFormatter(label_) << ") " << std::endl;
      for (size_t i = 0; i < branches_.size(); i++) {
        branches_[i]->print(s + " " + std::to_string(i), labelFormatter, valueFormatter);
      }
    }
 
    void dot(std::ostream& os, const LabelFormatter& labelFormatter,
             const ValueFormatter& valueFormatter,
             bool showZero) const override {
      os << "\"" << this->id() << "\" [shape=circle, label=\"" << label_
          << "\"]\n";
      size_t B = branches_.size();
      for (size_t i = 0; i < B; i++) {
        const NodePtr& branch = branches_[i];
 
        // Check if zero
        if (!showZero) {
          const Leaf* leaf = dynamic_cast<const Leaf*>(branch.get());
          if (leaf && valueFormatter(leaf->constant()).compare("0")) continue;
        }
 
        os << "\"" << this->id() << "\" -> \"" << branch->id() << "\"";
        if (B == 2 && i == 0) os << " [style=dashed]";
        os << std::endl;
        branch->dot(os, labelFormatter, valueFormatter, showZero);
      }
    }
 
    bool sameLeaf(const Leaf& q) const override {
      return false;
    }
 
    bool sameLeaf(const Node& q) const override {
      return (q.isLeaf() && q.sameLeaf(*this));
    }
 
    bool equals(const Node& q, const CompareFunc& compare) const override {
      const Choice* other = dynamic_cast<const Choice*>(&q);
      if (!other) return false;
      if (this->label_ != other->label_) return false;
      if (branches_.size() != other->branches_.size()) return false;
      // we don't care about shared pointers being equal here
      for (size_t i = 0; i < branches_.size(); i++)
        if (!(branches_[i]->equals(*(other->branches_[i]), compare)))
          return false;
      return true;
    }
 
    const Y& operator()(const Assignment<L>& x) const override {
#ifndef NDEBUG
      typename Assignment<L>::const_iterator it = x.find(label_);
      if (it == x.end()) {
        std::cout << "Trying to find value for " << label_ << std::endl;
        throw std::invalid_argument(
            "DecisionTree::operator(): value undefined for a label");
      }
#endif
      size_t index = x.at(label_);
      NodePtr child = branches_[index];
      return (*child)(x);
    }
 
    Choice(const L& label, const Choice& f, const Unary& op) :
      label_(label), allSame_(true) {
      branches_.reserve(f.branches_.size());  // reserve space
      for (const NodePtr& branch : f.branches_) {
        push_back(branch->apply(op));
      }
    }
 
    Choice(const L& label, const Choice& f, const UnaryAssignment& op,
           const Assignment<L>& assignment)
        : label_(label), allSame_(true) {
      branches_.reserve(f.branches_.size());  // reserve space
 
      Assignment<L> assignment_ = assignment;
 
      for (size_t i = 0; i < f.branches_.size(); i++) {
        assignment_[label_] = i;  // Set assignment for label to i
 
        const NodePtr branch = f.branches_[i];
        push_back(branch->apply(op, assignment_));
 
        // Remove the assignment so we are backtracking
        auto assignment_it = assignment_.find(label_);
        assignment_.erase(assignment_it);
      }
    }
 
    NodePtr apply(const Unary& op) const override {
      auto r = std::make_shared<Choice>(label_, *this, op);
      return Unique(r);
    }
 
    NodePtr apply(const UnaryAssignment& op,
                  const Assignment<L>& assignment) const override {
      auto r = std::make_shared<Choice>(label_, *this, op, assignment);
      return Unique(r);
    }
 
    // Apply binary operator "h = f op g" on Choice node
    // Note op is not assumed commutative so we need to keep track of order
    // Simply calls apply on argument to call correct virtual method:
    // fC.apply_f_op_g(gL) -> gL.apply_g_op_fC(fC) -> (Leaf)
    // fC.apply_f_op_g(gC) -> gC.apply_g_op_fC(fC) -> (below)
    NodePtr apply_f_op_g(const Node& g, const Binary& op) const override {
      return g.apply_g_op_fC(*this, op);
    }
 
    // If second argument of binary op is Leaf node, recurse on branches
    NodePtr apply_g_op_fL(const Leaf& fL, const Binary& op) const override {
      auto h = std::make_shared<Choice>(label(), nrChoices());
      for (auto&& branch : branches_)
        h->push_back(fL.apply_f_op_g(*branch, op));
      return Unique(h);
    }
 
    // If second argument of binary op is Choice, call constructor
    NodePtr apply_g_op_fC(const Choice& fC, const Binary& op) const override {
      auto h = std::make_shared<Choice>(fC, *this, op);
      return Unique(h);
    }
 
    // If second argument of binary op is Leaf
    template<typename OP>
    NodePtr apply_fC_op_gL(const Leaf& gL, OP op) const {
      auto h = std::make_shared<Choice>(label(), nrChoices());
      for (auto&& branch : branches_)
        h->push_back(branch->apply_f_op_g(gL, op));
      return Unique(h);
    }
 
    NodePtr choose(const L& label, size_t index) const override {
      if (label_ == label) return branches_[index];  // choose branch
 
      // second case, not label of interest, just recurse
      auto r = std::make_shared<Choice>(label_, branches_.size());
      for (auto&& branch : branches_) {
        r->push_back(branch->choose(label, index));
      }
 
      return Unique(r);
    }
 
   private:
    using Base = DecisionTree<L, Y>::Node;
 
#ifdef GTSAM_ENABLE_BOOST_SERIALIZATION
 
    friend class boost::serialization::access;
    template <class ARCHIVE>
    void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
      ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
      ar& BOOST_SERIALIZATION_NVP(label_);
      ar& BOOST_SERIALIZATION_NVP(branches_);
      ar& BOOST_SERIALIZATION_NVP(allSame_);
    }
#endif
  };  // Choice
 
  /****************************************************************************/
  // DecisionTree
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree() {}
 
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const NodePtr& root) :
    root_(root) {}
 
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const Y& y)  {
    root_ = NodePtr(new Leaf(y));
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const L& label, const Y& y1, const Y& y2) {
    auto a = std::make_shared<Choice>(label, 2);
    NodePtr l1(new Leaf(y1)), l2(new Leaf(y2));
    a->push_back(l1);
    a->push_back(l2);
    root_ = Choice::Unique(a);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const LabelC& labelC, const Y& y1,
                                   const Y& y2) {
    if (labelC.second != 2) throw std::invalid_argument(
        "DecisionTree: binary constructor called with non-binary label");
    auto a = std::make_shared<Choice>(labelC.first, 2);
    NodePtr l1(new Leaf(y1)), l2(new Leaf(y2));
    a->push_back(l1);
    a->push_back(l2);
    root_ = Choice::Unique(a);
  }
 
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const std::vector<LabelC>& labelCs,
      const std::vector<Y>& ys) {
    // call recursive Create
    root_ = create(labelCs.begin(), labelCs.end(), ys.begin(), ys.end());
  }
 
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const std::vector<LabelC>& labelCs,
      const std::string& table) {
    // Convert std::string to values of type Y
    std::vector<Y> ys;
    std::istringstream iss(table);
    copy(std::istream_iterator<Y>(iss), std::istream_iterator<Y>(),
         back_inserter(ys));
 
    // now call recursive Create
    root_ = create(labelCs.begin(), labelCs.end(), ys.begin(), ys.end());
  }
 
  /****************************************************************************/
  template<typename L, typename Y>
  template<typename Iterator> DecisionTree<L, Y>::DecisionTree(
      Iterator begin, Iterator end, const L& label) {
    root_ = compose(begin, end, label);
  }
 
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y>::DecisionTree(const L& label,
      const DecisionTree& f0, const DecisionTree& f1)  {
    const std::vector<DecisionTree> functions{f0, f1};
    root_ = compose(functions.begin(), functions.end(), label);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  template <typename X, typename Func>
  DecisionTree<L, Y>::DecisionTree(const DecisionTree<L, X>& other,
                                   Func Y_of_X) {
    // Define functor for identity mapping of node label.
    auto L_of_L = [](const L& label) { return label; };
    root_ = convertFrom<L, X>(other.root_, L_of_L, Y_of_X);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  template <typename M, typename X, typename Func>
  DecisionTree<L, Y>::DecisionTree(const DecisionTree<M, X>& other,
                                   const std::map<M, L>& map, Func Y_of_X) {
    auto L_of_M = [&map](const M& label) -> L { return map.at(label); };
    root_ = convertFrom<M, X>(other.root_, L_of_M, Y_of_X);
  }
 
  /****************************************************************************/
  // Called by two constructors above.
  // Takes a label and a corresponding range of decision trees, and creates a
  // new decision tree. However, the order of the labels needs to be respected,
  // so we cannot just create a root Choice node on the label: if the label is
  // not the highest label, we need a complicated/ expensive recursive call.
  template <typename L, typename Y>
  template <typename Iterator>
  typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::compose(
      Iterator begin, Iterator end, const L& label) const {
    // find highest label among branches
    std::optional<L> highestLabel;
    size_t nrChoices = 0;
    for (Iterator it = begin; it != end; it++) {
      if (it->root_->isLeaf())
        continue;
      std::shared_ptr<const Choice> c =
          std::dynamic_pointer_cast<const Choice>(it->root_);
      if (!highestLabel || c->label() > *highestLabel) {
        highestLabel = c->label();
        nrChoices = c->nrChoices();
      }
    }
 
    // if label is already in correct order, just put together a choice on label
    if (!nrChoices || !highestLabel || label > *highestLabel) {
      auto choiceOnLabel = std::make_shared<Choice>(label, end - begin);
      for (Iterator it = begin; it != end; it++)
        choiceOnLabel->push_back(it->root_);
      // If no reordering, no need to call Choice::Unique
      return choiceOnLabel;
    } else {
      // Set up a new choice on the highest label
      auto choiceOnHighestLabel =
          std::make_shared<Choice>(*highestLabel, nrChoices);
      // now, for all possible values of highestLabel
      for (size_t index = 0; index < nrChoices; index++) {
        // make a new set of functions for composing by iterating over the given
        // functions, and selecting the appropriate branch.
        std::vector<DecisionTree> functions;
        for (Iterator it = begin; it != end; it++) {
          // by restricting the input functions to value i for labelBelow
          DecisionTree chosen = it->choose(*highestLabel, index);
          functions.push_back(chosen);
        }
        // We then recurse, for all values of the highest label
        NodePtr fi = compose(functions.begin(), functions.end(), label);
        choiceOnHighestLabel->push_back(fi);
      }
      return choiceOnHighestLabel;
    }
  }
 
  /****************************************************************************/
  // "build" is a bit of a complicated thing, but very useful.
  // It takes a range of labels and a corresponding range of values,
  // and builds a decision tree, as follows:
  // - if there is only one label, creates a choice node with values in leaves
  // - otherwise, it evenly splits up the range of values and creates a tree for
  //   each sub-range, and assigns that tree to first label's choices
  // Example:
  // build([B A],[1 2 3 4]) would call
  //   build([A],[1 2])
  //   build([A],[3 4])
  // and produce
  // B=0
  //  A=0: 1
  //  A=1: 2
  // B=1
  //  A=0: 3
  //  A=1: 4
  // Note, through the magic of "compose", create([A B],[1 3 2 4]) will produce
  // exactly the same tree as above: the highest label is always the root.
  // However, it will be *way* faster if labels are given highest to lowest.
  template<typename L, typename Y>
  template<typename It, typename ValueIt>
  typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::build(
      It begin, It end, ValueIt beginY, ValueIt endY) const {
    // get crucial counts
    size_t nrChoices = begin->second;
    size_t size = endY - beginY;
 
    // Find the next key to work on
    It labelC = begin + 1;
    if (labelC == end) {
      // Base case: only one key left
      // Create a simple choice node with values as leaves.
      if (size != nrChoices) {
        std::cout << "Trying to create DD on " << begin->first << std::endl;
        std::cout << "DecisionTree::create: expected " << nrChoices
                  << " values but got " << size << " instead" << std::endl;
        throw std::invalid_argument("DecisionTree::create invalid argument");
      }
      auto choice = std::make_shared<Choice>(begin->first, endY - beginY);
      for (ValueIt y = beginY; y != endY; y++) {
        choice->push_back(NodePtr(new Leaf(*y)));
      }
      return choice;
    }
 
    // Recursive case: perform "Shannon expansion"
    // Creates one tree (i.e.,function) for each choice of current key
    // by calling create recursively, and then puts them all together.
    std::vector<DecisionTree> functions;
    size_t split = size / nrChoices;
    for (size_t i = 0; i < nrChoices; i++, beginY += split) {
      NodePtr f = build<It, ValueIt>(labelC, end, beginY, beginY + split);
      functions.emplace_back(f);
    }
    return compose(functions.begin(), functions.end(), begin->first);
  }
 
  /****************************************************************************/
  // Top-level factory method, which takes a range of labels and a corresponding
  // range of values, and creates a decision tree.
  template<typename L, typename Y>
  template<typename It, typename ValueIt>
  typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::create(
      It begin, It end, ValueIt beginY, ValueIt endY) const {
    auto node = build(begin, end, beginY, endY);
    if (auto choice = std::dynamic_pointer_cast<const Choice>(node)) {
      return Choice::Unique(choice);
    } else {
      return node;
    }
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  template <typename M, typename X>
  typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::convertFrom(
      const typename DecisionTree<M, X>::NodePtr& f,
      std::function<L(const M&)> L_of_M,
      std::function<Y(const X&)> Y_of_X) const {
    using LY = DecisionTree<L, Y>;
 
    // Ugliness below because apparently we can't have templated virtual
    // functions.
    // If leaf, apply unary conversion "op" and create a unique leaf.
    using MXLeaf = typename DecisionTree<M, X>::Leaf;
    if (auto leaf = std::dynamic_pointer_cast<const MXLeaf>(f)) {
      return NodePtr(new Leaf(Y_of_X(leaf->constant())));
    }
 
    // Check if Choice
    using MXChoice = typename DecisionTree<M, X>::Choice;
    auto choice = std::dynamic_pointer_cast<const MXChoice>(f);
    if (!choice) throw std::invalid_argument(
        "DecisionTree::convertFrom: Invalid NodePtr");
 
    // get new label
    const M oldLabel = choice->label();
    const L newLabel = L_of_M(oldLabel);
 
    // put together via Shannon expansion otherwise not sorted.
    std::vector<LY> functions;
    for (auto&& branch : choice->branches()) {
      functions.emplace_back(convertFrom<M, X>(branch, L_of_M, Y_of_X));
    }
    return Choice::Unique(LY::compose(functions.begin(), functions.end(), newLabel));
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  struct Visit {
    using F = std::function<void(const Y&)>;
    explicit Visit(F f) : f(f) {}  
    F f;                           
 
    void operator()(const typename DecisionTree<L, Y>::NodePtr& node) const {
      using Leaf = typename DecisionTree<L, Y>::Leaf;
      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
        return f(leaf->constant());
 
      using Choice = typename DecisionTree<L, Y>::Choice;
      auto choice = std::dynamic_pointer_cast<const Choice>(node);
      if (!choice)
        throw std::invalid_argument("DecisionTree::Visit: Invalid NodePtr");
      for (auto&& branch : choice->branches()) (*this)(branch);  // recurse!
    }
  };
 
  template <typename L, typename Y>
  template <typename Func>
  void DecisionTree<L, Y>::visit(Func f) const {
    Visit<L, Y> visit(f);
    visit(root_);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  struct VisitLeaf {
    using F = std::function<void(const typename DecisionTree<L, Y>::Leaf&)>;
    explicit VisitLeaf(F f) : f(f) {}  
    F f;                           
 
    void operator()(const typename DecisionTree<L, Y>::NodePtr& node) const {
      using Leaf = typename DecisionTree<L, Y>::Leaf;
      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
        return f(*leaf);
 
      using Choice = typename DecisionTree<L, Y>::Choice;
      auto choice = std::dynamic_pointer_cast<const Choice>(node);
      if (!choice)
        throw std::invalid_argument("DecisionTree::VisitLeaf: Invalid NodePtr");
      for (auto&& branch : choice->branches()) (*this)(branch);  // recurse!
    }
  };
 
  template <typename L, typename Y>
  template <typename Func>
  void DecisionTree<L, Y>::visitLeaf(Func f) const {
    VisitLeaf<L, Y> visit(f);
    visit(root_);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  struct VisitWith {
    using F = std::function<void(const Assignment<L>&, const Y&)>;
    explicit VisitWith(F f) : f(f) {}  
    Assignment<L> assignment;  
    F f;                       
 
    void operator()(const typename DecisionTree<L, Y>::NodePtr& node) {
      using Leaf = typename DecisionTree<L, Y>::Leaf;
      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
        return f(assignment, leaf->constant());
 
      using Choice = typename DecisionTree<L, Y>::Choice;
      auto choice = std::dynamic_pointer_cast<const Choice>(node);
      if (!choice)
        throw std::invalid_argument("DecisionTree::VisitWith: Invalid NodePtr");
      for (size_t i = 0; i < choice->nrChoices(); i++) {
        assignment[choice->label()] = i;  // Set assignment for label to i
 
        (*this)(choice->branches()[i]);  // recurse!
 
        // Remove the choice so we are backtracking
        auto choice_it = assignment.find(choice->label());
        assignment.erase(choice_it);
      }
    }
  };
 
  template <typename L, typename Y>
  template <typename Func>
  void DecisionTree<L, Y>::visitWith(Func f) const {
    VisitWith<L, Y> visit(f);
    visit(root_);
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  size_t DecisionTree<L, Y>::nrLeaves() const {
    size_t total = 0;
    visit([&total](const Y& node) { total += 1; });
    return total;
  }
 
  /****************************************************************************/
  // fold is just done with a visit
  template <typename L, typename Y>
  template <typename Func, typename X>
  X DecisionTree<L, Y>::fold(Func f, X x0) const {
    visit([&](const Y& y) { x0 = f(y, x0); });
    return x0;
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  std::set<L> DecisionTree<L, Y>::labels() const {
    std::set<L> unique;
    auto f = [&](const Assignment<L>& assignment, const Y&) {
      for (auto&& kv : assignment) {
        unique.insert(kv.first);
      }
    };
    visitWith(f);
    return unique;
  }
 
/****************************************************************************/
  template <typename L, typename Y>
  bool DecisionTree<L, Y>::equals(const DecisionTree& other,
                                  const CompareFunc& compare) const {
    return root_->equals(*other.root_, compare);
  }
 
  template <typename L, typename Y>
  void DecisionTree<L, Y>::print(const std::string& s,
                                 const LabelFormatter& labelFormatter,
                                 const ValueFormatter& valueFormatter) const {
    root_->print(s, labelFormatter, valueFormatter);
  }
 
  template<typename L, typename Y>
  bool DecisionTree<L, Y>::operator==(const DecisionTree& other) const {
    return root_->equals(*other.root_);
  }
 
  template<typename L, typename Y>
  const Y& DecisionTree<L, Y>::operator()(const Assignment<L>& x) const {
    return root_->operator ()(x);
  }
 
  template<typename L, typename Y>
  DecisionTree<L, Y> DecisionTree<L, Y>::apply(const Unary& op) const {
    // It is unclear what should happen if tree is empty:
    if (empty()) {
      throw std::runtime_error(
          "DecisionTree::apply(unary op) undefined for empty tree.");
    }
    return DecisionTree(root_->apply(op));
  }
 
  template <typename L, typename Y>
  DecisionTree<L, Y> DecisionTree<L, Y>::apply(
      const UnaryAssignment& op) const {
    // It is unclear what should happen if tree is empty:
    if (empty()) {
      throw std::runtime_error(
          "DecisionTree::apply(unary op) undefined for empty tree.");
    }
    Assignment<L> assignment;
    return DecisionTree(root_->apply(op, assignment));
  }
 
  /****************************************************************************/
  template<typename L, typename Y>
  DecisionTree<L, Y> DecisionTree<L, Y>::apply(const DecisionTree& g,
      const Binary& op) const {
    // It is unclear what should happen if either tree is empty:
    if (empty() || g.empty()) {
      throw std::runtime_error(
          "DecisionTree::apply(binary op) undefined for empty trees.");
    }
    // apply the operaton on the root of both diagrams
    NodePtr h = root_->apply_f_op_g(*g.root_, op);
    // create a new class with the resulting root "h"
    DecisionTree result(h);
    return result;
  }
 
  /****************************************************************************/
  // The way this works:
  // We have an ADT, picture it as a tree.
  // At a certain depth, we have a branch on "label".
  // The function "choose(label,index)" will return a tree of one less depth,
  // where there is no more branch on "label": only the subtree under that
  // branch point corresponding to the value "index" is left instead.
  // The function below get all these smaller trees and "ops" them together.
  // This implements marginalization in Darwiche09book, pg 330
  template<typename L, typename Y>
  DecisionTree<L, Y> DecisionTree<L, Y>::combine(const L& label,
      size_t cardinality, const Binary& op) const {
    DecisionTree result = choose(label, 0);
    for (size_t index = 1; index < cardinality; index++) {
      DecisionTree chosen = choose(label, index);
      result = result.apply(chosen, op);
    }
    return result;
  }
 
  /****************************************************************************/
  template <typename L, typename Y>
  void DecisionTree<L, Y>::dot(std::ostream& os,
                               const LabelFormatter& labelFormatter,
                               const ValueFormatter& valueFormatter,
                               bool showZero) const {
    os << "digraph G {\n";
    root_->dot(os, labelFormatter, valueFormatter, showZero);
    os << " [ordering=out]}" << std::endl;
  }
 
  template <typename L, typename Y>
  void DecisionTree<L, Y>::dot(const std::string& name,
                               const LabelFormatter& labelFormatter,
                               const ValueFormatter& valueFormatter,
                               bool showZero) const {
    std::ofstream os((name + ".dot").c_str());
    dot(os, labelFormatter, valueFormatter, showZero);
    int result =
        system(("dot -Tpdf " + name + ".dot -o " + name + ".pdf >& /dev/null")
                   .c_str());
    if (result == -1)
      throw std::runtime_error("DecisionTree::dot system call failed");
  }
 
  template <typename L, typename Y>
  std::string DecisionTree<L, Y>::dot(const LabelFormatter& labelFormatter,
                                      const ValueFormatter& valueFormatter,
                                      bool showZero) const {
    std::stringstream ss;
    dot(ss, labelFormatter, valueFormatter, showZero);
    return ss.str();
  }
 
/******************************************************************************/
 
  }  // namespace gtsam