Tree_DP.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
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  of this software and associated documentation files (the "Software"), to deal
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*/
 
#ifndef TREE_DP_H
#define TREE_DP_H
 
# include <ah-graph-concepts.H>
 
#include <algorithm>
#include <cstddef>
#include <functional>
#include <limits>
#include <utility>
 
#include <ah-errors.H>
#include <tpl_array.H>
#include <tpl_dynListStack.H>
#include <tpl_dynMapOhash.H>
#include <tpl_dynMapTree.H>
#include <tpl_graph.H>
 
namespace Aleph {
namespace tree_dp_detail {
template <AlephGraph GT, ArcFilter<GT> SA>
class Tree_Topology
{
public:
  using Node = typename GT::Node; 
  using Arc = typename GT::Arc;   
  static constexpr size_t NONE = std::numeric_limits<size_t>::max();
 
private:
  const GT *graph_ = nullptr; 
  SA sa_;                     
  Node *root_ = nullptr;      
  size_t n_ = 0;              
  Array<Node *> id_to_node_;             
  MapOLhash<Node *, size_t> node_to_id_; 
  Array<Array<size_t>> children_;        
  Array<size_t> parent_;                 
  Array<size_t> order_;                  
  void index_nodes()
  {
    n_ = graph_->get_num_nodes();
    if (n_ == 0)
      {
        ah_domain_error_if(root_ != nullptr)
          << "Tree_Topology: non-null root provided for empty graph";
        return;
      }
 
    id_to_node_ = Array<Node *>::create(n_);
    {
      MapOLhash<Node *, size_t> tmp(n_);
      node_to_id_.swap(tmp);
    }
 
    size_t next_id = 0;
    for (Node_Iterator<GT> it(*graph_); it.has_curr(); it.next_ne())
      {
        Node *p = it.get_curr();
        id_to_node_(next_id) = p;
        node_to_id_.insert(p, next_id);
        ++next_id;
      }
 
    if (root_ == nullptr)
      root_ = id_to_node_(0);
    else
      ah_domain_error_if(node_to_id_.search(root_) == nullptr)
        << "Tree_Topology: root node is not part of the graph";
  }
 
  void build_adjacency()
  {
    if (n_ == 0)
      return;
 
    children_.reserve(n_);
    for (size_t i = 0; i < n_; ++i)
      children_.append(Array<size_t>());
 
    using Pair_Key = std::pair<size_t, size_t>;
    DynMapTree<Pair_Key, char> unique_edges;
    size_t edge_count = 0;
 
    for (Arc_Iterator<GT, SA> it(*graph_, sa_); it.has_curr(); it.next_ne())
      {
        Arc *a = it.get_curr_ne();
        Node *src = graph_->get_src_node(a);
        Node *tgt = graph_->get_tgt_node(a);
 
        const auto *si = node_to_id_.search(src);
        const auto *ti = node_to_id_.search(tgt);
        ah_runtime_error_unless(si != nullptr and ti != nullptr)
          << "Tree_Topology: arc endpoint not indexed";
 
        const size_t u = si->second;
        const size_t v = ti->second;
        ah_domain_error_if(u == v) << "Tree_Topology: self-loop detected";
 
        Pair_Key key = u < v ? std::make_pair(u, v) : std::make_pair(v, u);
        if (unique_edges.search(key) != nullptr)
          continue;  // skip duplicate
        unique_edges.insert(key, 1);
        ++edge_count;
      }
 
    ah_domain_error_if(n_ > 1 and edge_count != n_ - 1)
      << "Tree_Topology: not a tree (expected " << (n_ - 1) << " edges, got " << edge_count << ")";
 
    for (typename DynMapTree<Pair_Key, char>::Iterator it(unique_edges); it.has_curr(); it.next_ne())
      {
        const auto &[fst, snd] = it.get_curr();
        const size_t u = fst.first;
        const size_t v = fst.second;
        children_(u).append(v);
        children_(v).append(u);
      }
  }
 
  void build_order()
  {
    if (n_ == 0)
      return;
 
    parent_ = Array<size_t>::create(n_);
    for (size_t i = 0; i < n_; ++i)
      parent_(i) = NONE;
 
    order_.reserve(n_);
 
    Array<char> visited = Array<char>::create(n_);
    for (size_t i = 0; i < n_; ++i)
      visited(i) = 0;
 
    const size_t root_id = node_to_id_.find(root_);
 
    struct Frame
    {
      size_t node;
      size_t next_child;
    };
    DynListStack<Frame> stack;
 
    visited(root_id) = 1;
    stack.push({root_id, 0});
 
    while (not stack.is_empty())
      {
        auto &fr = stack.top();
        if (fr.next_child == children_(fr.node).size())
          {
            order_.append(fr.node);
            (void) stack.pop();
            continue;
          }
 
        const size_t nxt = children_(fr.node)(fr.next_child++);
        if (visited(nxt))
          continue;
 
        visited(nxt) = 1;
        parent_(nxt) = fr.node;
        stack.push({nxt, 0});
      }
 
    ah_domain_error_if(order_.size() != n_) << "Tree_Topology: graph is not connected";
 
    // Filter children_ to only contain children after rooting
    for (size_t i = 0; i < n_; ++i)
      {
        Array<size_t> children;
        const size_t p = parent_(i);
        for (size_t j = 0; j < children_(i).size(); ++j)
          if (children_(i)[j] != p)
            children.append(children_(i)[j]);
        children_(i).swap(children);
      }
  }
 
public:
  Tree_Topology(const GT &g, Node *root, SA sa = SA()) : graph_(&g), sa_(std::move(sa)), root_(root)
  {
    index_nodes();
    build_adjacency();
    build_order();
  }
 
  [[nodiscard]] size_t size() const noexcept
  {
    return n_;
  }
 
  [[nodiscard]] Node *root() const noexcept
  {
    return root_;
  }
 
  [[nodiscard]] size_t id_of(Node *node) const
  {
    const auto *item = node_to_id_.search(node);
    ah_domain_error_if(item == nullptr) << "Tree_Topology::id_of: node not in graph";
    return item->second;
  }
 
  [[nodiscard]] Node *node_of(size_t id) const
  {
    ah_out_of_range_error_if(id >= n_) << "Tree_Topology::node_of: id out of range";
    return id_to_node_(id);
  }
 
  [[nodiscard]] const Array<size_t> &children(size_t id) const
  {
    return children_(id);
  }
 
  [[nodiscard]] size_t parent(size_t id) const noexcept
  {
    return parent_(id);
  }
 
  [[nodiscard]] const Array<size_t> &post_order() const noexcept
  {
    return order_;
  }
 
  [[nodiscard]] const Array<Node *> &nodes() const noexcept
  {
    return id_to_node_;
  }
};
}  // namespace tree_dp_detail
 
template <AlephGraph GT, typename T, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
class Gen_Tree_DP
{
public:
  using Node = typename GT::Node; 
  using Init_Fn = std::function<T(Node *)>;
 
  using Combine_Fn = std::function<T(Node *, const T &, Node *, const T &)>;
 
private:
  tree_dp_detail::Tree_Topology<GT, SA> topo_; 
  Array<T> dp_;                                
public:
  Gen_Tree_DP(const GT &g, Node *root, Init_Fn init, Combine_Fn combine, SA sa = SA())
    : topo_(g, root, std::move(sa))
  {
    const size_t n = topo_.size();
    if (n == 0)
      return;
 
    dp_ = Array<T>::create(n);
 
    // Initialize all nodes
    for (size_t i = 0; i < n; ++i)
      dp_(i) = init(topo_.node_of(i));
 
    // Process in post-order (leaves first)
    const auto &order = topo_.post_order();
    for (size_t k = 0; k < n; ++k)
      {
        const size_t v = order[k];
        const size_t par = topo_.parent(v);
        if (par == tree_dp_detail::Tree_Topology<GT, SA>::NONE)
          continue;  // root, no parent to update
        dp_(par) = combine(topo_.node_of(par), dp_(par), topo_.node_of(v), dp_(v));
      }
  }
 
  [[nodiscard]] const T &value(Node *node) const
  {
    return dp_(topo_.id_of(node));
  }
 
  [[nodiscard]] const Array<T> &values() const noexcept
  {
    return dp_;
  }
 
  [[nodiscard]] size_t size() const noexcept
  {
    return topo_.size();
  }
 
  [[nodiscard]] Node *node_of(size_t id) const
  {
    return topo_.node_of(id);
  }
 
  [[nodiscard]] size_t id_of(Node *node) const
  {
    return topo_.id_of(node);
  }
};
 
template <class GT, typename T, class SA = Dft_Show_Arc<GT>>
using Tree_DP = Gen_Tree_DP<GT, T, SA>;
 
template <AlephGraph GT, typename T, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
class Gen_Reroot_DP
{
public:
  using Node = typename GT::Node; 
  using Init_Fn = std::function<T(Node *)>;
 
  using Merge_Fn = std::function<T(const T &, const T &)>;
 
  using Apply_Edge_Fn = std::function<T(Node *, Node *, const T &)>;
 
private:
  tree_dp_detail::Tree_Topology<GT, SA> topo_; 
  T identity_;                                 
  Array<T> init_vals_;                         
  Array<T> dp_down_;                           
  Array<T> dp_up_;                             
  Array<T> answer_;                            
public:
  Gen_Reroot_DP(const GT &g,
                Node *root,
                const T &identity,
                Init_Fn init,
                Merge_Fn merge,
                Apply_Edge_Fn apply_edge,
                SA sa = SA())
    : topo_(g, root, std::move(sa)), identity_(identity)
  {
    const size_t n = topo_.size();
    if (n == 0)
      return;
 
    init_vals_ = Array<T>::create(n);
    dp_down_ = Array<T>::create(n);
    dp_up_ = Array<T>::create(n);
    answer_ = Array<T>::create(n);
 
    for (size_t i = 0; i < n; ++i)
      {
        init_vals_(i) = init(topo_.node_of(i));
        dp_down_(i) = init_vals_[i];
        dp_up_(i) = identity_;
      }
 
    // Phase 1: bottom-up
    const auto &order = topo_.post_order();
    for (size_t k = 0; k < n; ++k)
      {
        const size_t v = order[k];
        const size_t par = topo_.parent(v);
        if (par == tree_dp_detail::Tree_Topology<GT, SA>::NONE)
          continue;
        const T contrib = apply_edge(topo_.node_of(par), topo_.node_of(v), dp_down_(v));
        dp_down_(par) = merge(dp_down_(par), contrib);
      }
 
    // Phase 2: top-down with prefix/suffix
    // Process nodes in reverse post-order (root first)
    for (size_t k = n; k-- > 0;)
      {
        const size_t v = order[k];
        Node *vn = topo_.node_of(v);
 
        // Collect children of v
        const auto &children = topo_.children(v);
        const size_t nc = children.size();
        if (nc == 0)
          continue;
 
        Array<T> contribs = Array<T>::create(nc);
        for (size_t j = 0; j < nc; ++j)
          {
            const size_t c = children[j];
            contribs(j) = apply_edge(vn, topo_.node_of(c), dp_down_(c));
          }
 
        // Build prefix and suffix arrays of merged contributions
        Array<T> prefix = Array<T>::create(nc + 1);
        Array<T> suffix = Array<T>::create(nc + 1);
        prefix(0) = identity_;
        suffix(nc) = identity_;
 
        for (size_t j = 0; j < nc; ++j)
          prefix(j + 1) = merge(prefix(j), contribs(j));
 
        for (size_t j = nc; j-- > 0;)
          suffix(j) = merge(suffix(j + 1), contribs(j));
 
        const T base = merge(init_vals_[v], dp_up_(v));
 
        // For each child, compute dp_up
        for (size_t j = 0; j < nc; ++j)
          {
            const size_t c = children[j];
            Node *cn = topo_.node_of(c);
            // Value of v without child c's subtree:
            // merge(init(v), dp_up(v), prefix(j), suffix(j+1))
            T without_c = merge(base, prefix(j));
            without_c = merge(without_c, suffix(j + 1));
            dp_up_(c) = apply_edge(cn, vn, without_c);
          }
      }
 
    // Phase 3: compute answers
    for (size_t i = 0; i < n; ++i)
      answer_(i) = merge(dp_down_(i), dp_up_(i));
  }
 
  [[nodiscard]] const T &value(Node *node) const
  {
    return answer_(topo_.id_of(node));
  }
 
  [[nodiscard]] const Array<T> &values() const noexcept
  {
    return answer_;
  }
 
  [[nodiscard]] size_t size() const noexcept
  {
    return topo_.size();
  }
 
  [[nodiscard]] Node *node_of(size_t id) const
  {
    return topo_.node_of(id);
  }
 
  [[nodiscard]] size_t id_of(Node *node) const
  {
    return topo_.id_of(node);
  }
};
 
template <class GT, typename T, class SA = Dft_Show_Arc<GT>>
using Reroot_DP = Gen_Reroot_DP<GT, T, SA>;
 
// ── Convenience functions ─────────────────────────────────────────
 
template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
[[nodiscard]] Array<size_t> tree_subtree_sizes(const GT &g, typename GT::Node *root, SA sa = SA())
{
  Gen_Tree_DP<GT, size_t, SA> dp(g,
                                 root,
                                 [](auto *) -> size_t
  {
    return 1;
  },
                                 [](auto *, const size_t &acc, auto *, const size_t &child) -> size_t
  {
    return acc + child;
  },
                                 std::move(sa));
 
  // Copy values out
  const auto &vals = dp.values();
  Array<size_t> result = Array<size_t>::create(vals.size());
  for (size_t i = 0; i < vals.size(); ++i)
    result(i) = vals[i];
  return result;
}
 
template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
[[nodiscard]] Array<size_t> tree_max_distance(const GT &g, typename GT::Node *root, SA sa = SA())
{
  Gen_Reroot_DP<GT, size_t, SA> dp(g,
                                   root,
                                   static_cast<size_t>(0),
                                   [](auto *) -> size_t
  {
    return 0;
  },
                                   [](const size_t &a, const size_t &b) -> size_t
  {
    return std::max(a, b);
  },
                                   [](auto *, auto *, const size_t &v) -> size_t
  {
    return v + 1;
  },
                                   std::move(sa));
 
  const auto &vals = dp.values();
  Array<size_t> result = Array<size_t>::create(vals.size());
  for (size_t i = 0; i < vals.size(); ++i)
    result(i) = vals[i];
  return result;
}
 
template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
[[nodiscard]] Array<size_t> tree_sum_of_distances(const GT &g, typename GT::Node *root, SA sa = SA())
{
  using P = std::pair<size_t, size_t>;  // (count, sum_dist)
 
  Gen_Reroot_DP<GT, P, SA> dp(g,
                              root,
                              P{0, 0},
                              [](auto *) -> P
  {
    return {1, 0};
  },
                              [](const P &a, const P &b) -> P
  {
    return {a.first + b.first, a.second + b.second};
  },
                              [](auto *, auto *, const P &v) -> P
  {
    return {v.first, v.second + v.first};
  },
                              std::move(sa));
 
  const auto &vals = dp.values();
  Array<size_t> result = Array<size_t>::create(vals.size());
  for (size_t i = 0; i < vals.size(); ++i)
    result(i) = vals[i].second;
  return result;
}
}  // namespace Aleph
 
#endif  // TREE_DP_H