Dominators.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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# ifndef DOMINATORS_H
# define DOMINATORS_H
 
# include <ah-graph-concepts.H>
 
# include <utility>
# include <tpl_graph.H>
# include <tpl_graph_utils.H>
# include <tpl_array.H>
# include <htlist.H>
# include <tpl_dynListStack.H>
# include <ah-errors.H>
# include <tpl_dynSetTree.H>
 
namespace Aleph
{
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  class Lengauer_Tarjan_Dominators
  {
    SA sa;
 
    using Node = typename GT::Node;
    using Arc = typename GT::Arc;
 
    GT *gptr = nullptr;
    Node *root_ptr = nullptr;
    bool is_computed = false;
    long num_reachable = 0;
 
    // Internal arrays indexed by DFS number
    Array<Node *> vertex; // DFS number -> node pointer
    Array<long> par; // DFS parent (as DFS number)
    Array<long> semi; // semi-dominator (as DFS number)
    Array<long> idom_arr; // immediate dominator (as DFS number)
    Array<long> anc; // Union-Find ancestor
    Array<long> label_arr; // Union-Find label (best semi on path)
    Array<DynList<long>> pred; // predecessors[i] = DFS numbers of predecessors of node i
 
    void compress(long v)
    {
      if (anc[v] == -1 or anc[anc[v]] == -1)
        return;
 
      // First pass: find the path to the root
      Array<long> path;
      long root = v;
      while (anc[root] != -1 and anc[anc[root]] != -1)
        {
          path.append(root);
          root = anc[root];
        }
 
      // Second pass: compress path and update labels
      // Iterate from root-child down to v
      while (not path.is_empty())
        {
          const long u = path.remove_last();
          if (semi[label_arr[anc[u]]] < semi[label_arr[u]])
            label_arr[u] = label_arr[anc[u]];
          anc[u] = anc[anc[u]];
        }
    }
 
    void dfs(Node *root_ptr)
    {
      struct Frame
      {
        Node *u;
        Out_Iterator<GT, SA> it;
      };
 
      DynListStack<Frame> stack;
 
      // Initialize root
      const long root_num = num_reachable++;
      NODE_COUNTER(root_ptr) = root_num;
      vertex[root_num] = root_ptr;
      par[root_num] = -1;
      semi[root_num] = root_num;
      label_arr[root_num] = root_num;
      anc[root_num] = -1;
 
      stack.push(Frame{root_ptr, Out_Iterator<GT, SA>(root_ptr, sa)});
 
      while (not stack.is_empty())
        {
          if (Frame & top = stack.top(); top.it.has_curr())
            {
              Node *v = gptr->get_tgt_node(top.it.get_curr());
              top.it.next_ne();
 
              if (NODE_COUNTER(v) == -1)
                {
                  const long v_num = num_reachable++;
                  NODE_COUNTER(v) = v_num;
                  vertex[v_num] = v;
                  par[v_num] = NODE_COUNTER(top.u);
                  semi[v_num] = v_num;
                  label_arr[v_num] = v_num;
                  anc[v_num] = -1;
 
                  stack.push(Frame{v, Out_Iterator<GT, SA>(v, sa)});
                }
            }
          else
            static_cast<void>(stack.pop());
        }
    }
 
    [[nodiscard]] long eval(const long v)
    {
      if (anc[v] == -1)
        return v;
      compress(v);
      return label_arr[v];
    }
 
    void do_compute(GT & g, Node *root)
    {
      gptr = &g;
      root_ptr = root;
      is_computed = false;
      num_reachable = 0;
 
      const size_t N = g.get_num_nodes();
      if (N == 0)
        {
          is_computed = true;
          return;
        }
 
      // Allocate internal arrays
      vertex = Array<Node *>(N, nullptr);
      par = Array<long>(N, -1L);
      semi = Array<long>(N, -1L);
      idom_arr = Array<long>(N, -1L);
      anc = Array<long>(N, -1L);
      label_arr = Array<long>(N, -1L);
      pred = Array<DynList<long>>(N, DynList<long>());
 
      // Mark all nodes as unvisited
      gptr->for_each_node([](Node *p) { NODE_COUNTER(p) = -1; });
 
      // Phase 1: DFS from root
      dfs(root); // dfs updates num_reachable
 
      if (num_reachable <= 1)
        {
          if (num_reachable == 1)
            idom_arr[0] = -1; // root has no dominator
          is_computed = true;
          return;
        }
 
      // Build predecessor lists by iterating over all arcs.
      // In_Iterator does not work on List_Digraph because arcs are
      // only stored in the source node's adjacency list.
      pred = Array<DynList<long>>(static_cast<size_t>(num_reachable), DynList<long>());
      for (typename GT::Arc_Iterator ait(g); ait.has_curr(); ait.next_ne())
        {
          auto arc = ait.get_curr();
          if (not sa(arc))
            continue;
          long s = NODE_COUNTER(gptr->get_src_node(arc));
          long t = NODE_COUNTER(gptr->get_tgt_node(arc));
          if (s >= 0 and s < num_reachable and t >= 0 and t < num_reachable)
            pred[t].append(s);
        }
 
      // Allocate buckets (one per reachable node)
      Array<DynList<long>> bucket(static_cast<size_t>(num_reachable), DynList<long>());
 
      // Phase 2: Semi-dominators (process in reverse DFS order)
      for (long w = num_reachable - 1; w >= 1; --w)
        {
          // For each predecessor of w
          for (auto pit = pred[w].get_it(); pit.has_curr(); pit.next_ne())
            {
              const long v_num = pit.get_curr();
              const long u = eval(v_num);
              if (semi[u] < semi[w])
                semi[w] = semi[u];
            }
 
          bucket[semi[w]].append(w);
          anc[w] = par[w]; // LINK(parent[w], w)
 
          // Process bucket of parent[w]
          while (not bucket[par[w]].is_empty())
            {
              const long v = bucket[par[w]].remove_first();
              long u = eval(v);
              idom_arr[v] = (semi[u] == semi[v]) ? par[w] : u;
            }
        }
 
      // Phase 3: Resolve deferred idom assignments
      for (long w = 1; w < num_reachable; ++w)
        {
          if (idom_arr[w] != semi[w])
            idom_arr[w] = idom_arr[idom_arr[w]];
        }
 
      idom_arr[0] = -1; // root has no dominator
      is_computed = true;
    }
 
    void ensure_computed(GT & g, Node *root)
    {
      ah_domain_error_if(root == nullptr)
        << "Lengauer_Tarjan_Dominators: root cannot be null";
 
      if (is_computed and gptr == &g and root_ptr == root)
        return;
 
      do_compute(g, root);
    }
 
  public:
    Lengauer_Tarjan_Dominators(SA __sa = SA()) noexcept
      : sa(std::move(__sa))
    { /* empty */
    }
 
    Lengauer_Tarjan_Dominators(const Lengauer_Tarjan_Dominators &) = delete;
 
    Lengauer_Tarjan_Dominators &operator=(const Lengauer_Tarjan_Dominators &) = delete;
 
    Lengauer_Tarjan_Dominators(Lengauer_Tarjan_Dominators &&) = default;
 
    Lengauer_Tarjan_Dominators &operator=(Lengauer_Tarjan_Dominators &&) = default;
 
    [[nodiscard]] DynList<std::pair<Node *, Node *>>
    compute_idom(GT & g, Node *root)
    {
      ensure_computed(g, root);
 
      DynList<std::pair<Node *, Node *>> result;
      for (long i = 0; i < num_reachable; ++i)
        {
          Node *idom_node = (idom_arr[i] >= 0) ? vertex[idom_arr[i]] : nullptr;
          result.append(std::make_pair(vertex[i], idom_node));
        }
      return result;
    }
 
    void build_tree(GT & g, Node *root, GT & tree)
    {
      ensure_computed(g, root);
 
      clear_graph(tree);
 
      if (num_reachable == 0)
        return;
 
      // Create tree nodes and establish mapping
      Array<Node *> tree_nodes(num_reachable, nullptr);
      for (long i = 0; i < num_reachable; ++i)
        {
          auto tn = tree.insert_node(vertex[i]->get_info());
          GT::map_nodes(vertex[i], tn);
          tree_nodes[i] = tn;
        }
 
      // Create arcs: idom(v) -> v
      for (long i = 1; i < num_reachable; ++i)
        if (idom_arr[i] >= 0)
          tree.insert_arc(tree_nodes[idom_arr[i]], tree_nodes[i]);
    }
 
    [[nodiscard]] Node * get_idom(GT & g, Node *root, Node *node)
    {
      ah_domain_error_if(node == nullptr)
        << "Lengauer_Tarjan_Dominators::get_idom: node cannot be null";
      ensure_computed(g, root);
 
      long v = NODE_COUNTER(node);
      if (v < 0 or v >= num_reachable or vertex[v] != node)
        return nullptr; // unreachable node
 
      return (idom_arr[v] >= 0) ? vertex[idom_arr[v]] : nullptr;
    }
 
    [[nodiscard]] bool dominates(GT & g, Node *root, Node *d, Node *v)
    {
      ensure_computed(g, root);
 
      if (d == v)
        return true; // reflexive
 
      long d_num = NODE_COUNTER(d);
      long v_num = NODE_COUNTER(v);
 
      if (d_num < 0 or d_num >= num_reachable or vertex[d_num] != d)
        return false;
      if (v_num < 0 or v_num >= num_reachable or vertex[v_num] != v)
        return false;
 
      // Walk up the idom chain from v
      long curr = idom_arr[v_num];
      while (curr != -1)
        {
          if (curr == d_num)
            return true;
          curr = idom_arr[curr];
        }
      return false;
    }
 
    [[nodiscard]] DynMapTree<Node *, DynSetTree<Node *>>
    dominance_frontiers(GT & g, Node *root)
    {
      ensure_computed(g, root);
 
      DynMapTree<Node *, DynSetTree<Node *>> df;
 
      // Initialize empty frontiers for all reachable nodes
      for (long i = 0; i < num_reachable; ++i)
        df.insert(vertex[i], DynSetTree<Node *>());
 
      if (num_reachable <= 1)
        return df;
 
      // For each node with 2+ predecessors, walk up from each pred
      for (long b = 0; b < num_reachable; ++b)
        {
          if (pred[b].size() < 2)
            continue;
 
          Node *bnode = vertex[b];
 
          // Walk up from each predecessor to idom(b)
          for (auto it = pred[b].get_it(); it.has_curr(); it.next_ne())
            {
              long runner = it.get_curr();
              while (runner != idom_arr[b] and runner != -1)
                {
                  df.find(vertex[runner]).insert(bnode);
                  runner = idom_arr[runner];
                }
            }
        }
 
      return df;
    }
 
    void operator()(GT & g, Node *root, GT & tree)
    {
      build_tree(g, root, tree);
    }
 
 
    [[nodiscard]] SA &get_filter() noexcept { return sa; }
 
    [[nodiscard]] const SA &get_filter() const noexcept { return sa; }
 
    [[nodiscard]] bool has_computation() const noexcept { return is_computed; }
 
    [[nodiscard]] GT * get_graph() const noexcept { return gptr; }
 
    [[nodiscard]] Node * get_root() const noexcept { return root_ptr; }
 
    [[nodiscard]] long get_num_reachable() const noexcept
    {
      return num_reachable;
    }
 
  };
 
 
  // =========================================================================
  // Free functions
  // =========================================================================
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  [[nodiscard]] DynList<std::pair<typename GT::Node *, typename GT::Node *>>
  compute_dominators(GT & g, typename GT::Node *root, SA sa = SA())
  {
    return Lengauer_Tarjan_Dominators<GT, SA>(sa).compute_idom(g, root);
  }
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  void build_dominator_tree(GT & g, typename GT::Node *root,
                            GT & tree, SA sa = SA())
  {
    Lengauer_Tarjan_Dominators<GT, SA>(sa).build_tree(g, root, tree);
  }
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  [[nodiscard]] DynMapTree<typename GT::Node *, DynSetTree<typename GT::Node *>>
  compute_dominance_frontiers(GT & g, typename GT::Node *root,
                              SA sa = SA())
  {
    return Lengauer_Tarjan_Dominators<GT, SA>(sa).dominance_frontiers(g, root);
  }
 
  // =========================================================================
  // Post-dominator computation (Lengauer-Tarjan on the reversed graph)
  // =========================================================================
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  class Lengauer_Tarjan_Post_Dominators
  {
    SA sa;
 
    using Node = typename GT::Node;
    using Arc = typename GT::Arc;
 
    GT rev;
    Lengauer_Tarjan_Dominators<GT, SA> dom;
 
    GT *gptr = nullptr;
    Node *exit_ptr = nullptr;
    bool is_computed = false;
 
    // Saved node mappings (orig ↔ rev) to avoid NODE_COOKIE conflicts
    DynMapTree<Node *, Node *> orig_to_rev;
    DynMapTree<Node *, Node *> rev_to_orig;
 
    [[nodiscard]] Node * to_rev(Node *orig) const
    {
      auto *p = orig_to_rev.search(orig);
      return p ? p->second : nullptr;
    }
 
    [[nodiscard]] Node * to_orig(Node *rev_n) const
    {
      auto *p = rev_to_orig.search(rev_n);
      return p ? p->second : nullptr;
    }
 
    void ensure_computed(const GT & g, Node *exit_node)
    {
      ah_domain_error_if(exit_node == nullptr)
        << "Lengauer_Tarjan_Post_Dominators: exit node cannot be null";
 
      gptr = &const_cast<GT &>(g);
      exit_ptr = exit_node;
      is_computed = false;
 
      // Step 1: Invert the digraph (sets NODE_COOKIE for mapping)
      rev = invert_digraph(g);
 
      // Step 2: Save orig↔rev mappings before dom overwrites anything
      orig_to_rev = DynMapTree<Node *, Node *>();
      rev_to_orig = DynMapTree<Node *, Node *>();
      for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
        {
          auto orig = it.get_curr();
          auto rev_n = mapped_node<GT>(orig);
          orig_to_rev.insert(orig, rev_n);
          rev_to_orig.insert(rev_n, orig);
        }
 
      // Step 3: Run forward dominators on reversed graph from exit
      //         (discard return value; we only need the cached state)
      auto rev_exit = to_rev(exit_node);
      (void) dom.compute_idom(rev, rev_exit);
 
      is_computed = true;
    }
 
  public:
    Lengauer_Tarjan_Post_Dominators(SA __sa = SA()) noexcept
      : sa(std::move(__sa)), dom(sa)
    { /* empty */
    }
 
    Lengauer_Tarjan_Post_Dominators(const Lengauer_Tarjan_Post_Dominators &) = delete;
 
    Lengauer_Tarjan_Post_Dominators &
    operator=(const Lengauer_Tarjan_Post_Dominators &) = delete;
 
    Lengauer_Tarjan_Post_Dominators(Lengauer_Tarjan_Post_Dominators &&) = default;
 
    Lengauer_Tarjan_Post_Dominators &
    operator=(Lengauer_Tarjan_Post_Dominators &&) = default;
 
    [[nodiscard]] DynList<std::pair<Node *, Node *>>
    compute_ipdom(const GT & g, Node *exit_node)
    {
      ensure_computed(g, exit_node);
 
      auto rev_exit = to_rev(exit_node);
      auto rev_idoms = dom.compute_idom(rev, rev_exit);
 
      DynList<std::pair<Node *, Node *>> result;
      for (auto it = rev_idoms.get_it(); it.has_curr(); it.next_ne())
        {
          auto [rev_n, rev_id] = it.get_curr();
          auto orig_n = to_orig(rev_n);
          auto orig_id = rev_id ? to_orig(rev_id) : nullptr;
          result.append(std::make_pair(orig_n, orig_id));
        }
      return result;
    }
 
    void build_tree(const GT & g, Node *exit_node, GT & tree)
    {
      ensure_computed(g, exit_node);
 
      clear_graph(tree);
 
      auto rev_exit = to_rev(exit_node);
      auto rev_idoms = dom.compute_idom(rev, rev_exit);
 
      if (rev_idoms.is_empty())
        return;
 
      // Create tree nodes with mapping to original graph.
      // NODE_COOKIE(orig) may still point to a reversed-graph node
      // left by invert_digraph; clear it so that map_nodes creates
      // a clean orig↔tree bidirectional mapping.
      DynMapTree<Node *, Node *> orig_to_tree;
      for (auto it = rev_idoms.get_it(); it.has_curr(); it.next_ne())
        {
          auto [rev_n, rev_id] = it.get_curr();
          auto orig = to_orig(rev_n);
          auto tn = tree.insert_node(orig->get_info());
          NODE_COOKIE(orig) = nullptr;
          GT::map_nodes(orig, tn);
          orig_to_tree.insert(orig, tn);
        }
 
      // Create arcs: ipdom(v) -> v
      for (auto it = rev_idoms.get_it(); it.has_curr(); it.next_ne())
        {
          auto [rev_n, rev_id] = it.get_curr();
          if (rev_id == nullptr)
            continue; // exit node has no ipdom
          auto orig = to_orig(rev_n);
          auto orig_id = to_orig(rev_id);
          tree.insert_arc(orig_to_tree.find(orig_id),
                          orig_to_tree.find(orig));
        }
    }
 
    [[nodiscard]] Node * get_ipdom(const GT & g, Node *exit_node, Node *node)
    {
      ah_domain_error_if(node == nullptr)
        << "Lengauer_Tarjan_Post_Dominators::get_ipdom: node cannot be null";
      ensure_computed(g, exit_node);
 
      auto rev_n = to_rev(node);
      if (rev_n == nullptr)
        return nullptr; // node not in graph
 
      auto rev_exit = to_rev(exit_node);
      auto rev_idom = dom.get_idom(rev, rev_exit, rev_n);
      return rev_idom ? to_orig(rev_idom) : nullptr;
    }
 
    [[nodiscard]] bool
    post_dominates(const GT & g, Node *exit_node, Node *d, Node *v)
    {
      ensure_computed(g, exit_node);
 
      if (d == v)
        return true; // reflexive
 
      auto rev_d = to_rev(d);
      auto rev_v = to_rev(v);
      if (rev_d == nullptr or rev_v == nullptr)
        return false;
 
      auto rev_exit = to_rev(exit_node);
      return dom.dominates(rev, rev_exit, rev_d, rev_v);
    }
 
    [[nodiscard]] DynMapTree<Node *, DynSetTree<Node *>>
    post_dominance_frontiers(const GT & g, Node *exit_node)
    {
      ensure_computed(g, exit_node);
 
      auto rev_exit = to_rev(exit_node);
      auto rev_df = dom.dominance_frontiers(rev, rev_exit);
 
      DynMapTree<Node *, DynSetTree<Node *>> result;
      for (auto it = rev_df.get_it(); it.has_curr(); it.next_ne())
        {
          auto & [rev_n, rev_frontier] = it.get_curr();
          auto orig = to_orig(rev_n);
          DynSetTree<Node *> orig_frontier;
          for (typename DynSetTree<Node *>::Iterator fi(rev_frontier); fi.has_curr(); fi.next_ne())
            orig_frontier.insert(to_orig(fi.get_curr()));
          result.insert(orig, std::move(orig_frontier));
        }
      return result;
    }
 
    void operator()(const GT & g, Node *exit_node, GT & tree)
    {
      build_tree(g, exit_node, tree);
    }
 
 
    [[nodiscard]] SA &get_filter() noexcept { return sa; }
 
    [[nodiscard]] const SA &get_filter() const noexcept { return sa; }
 
    [[nodiscard]] bool has_computation() const noexcept { return is_computed; }
 
    [[nodiscard]] GT * get_graph() const noexcept { return gptr; }
 
    [[nodiscard]] Node * get_exit() const noexcept { return exit_ptr; }
 
  };
 
 
  // =========================================================================
  // Post-dominator free functions
  // =========================================================================
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  [[nodiscard]] DynList<std::pair<typename GT::Node *, typename GT::Node *>>
  compute_post_dominators(const GT & g, typename GT::Node *exit_node,
                          SA sa = SA())
  {
    return Lengauer_Tarjan_Post_Dominators<GT, SA>(sa)
        .compute_ipdom(g, exit_node);
  }
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  void build_post_dominator_tree(const GT & g, typename GT::Node *exit_node,
                                 GT & tree, SA sa = SA())
  {
    Lengauer_Tarjan_Post_Dominators<GT, SA>(sa)
        .build_tree(g, exit_node, tree);
  }
 
  template <AlephGraph GT, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
  [[nodiscard]] DynMapTree<typename GT::Node *, DynSetTree<typename GT::Node *>>
  compute_post_dominance_frontiers(const GT & g,
                                   typename GT::Node *exit_node,
                                   SA sa = SA())
  {
    return Lengauer_Tarjan_Post_Dominators<GT, SA>(sa)
        .post_dominance_frontiers(g, exit_node);
  }
} // end namespace Aleph
 
# endif // DOMINATORS_H