tpl_hRbTree.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
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef TPL_HTDRBTREE_H
# define TPL_HTDRBTREE_H
 
# ifdef DEBUG
# include <cmath>
# endif
# include <tpl_binNode.H>
# include <tpl_binNodeUtils.H>
# include <tpl_arrayStack.H>
# include <rbNode.H>
 
namespace Aleph
{
 
  template <class Key, class Compare = Aleph::less<Key>>
  class HtdRbTree
  {
  public:
    using Color = unsigned char;
    
    using Node = RbNode<Key>;
 
  private:
 
  private:
    Node headNode;        
    Node headParent;      
    Node headGrandParent; 
 
    Node *head;           
    Node *fHead;          
    Node *ffHead;         
    Node *& root;         
 
    FixedStack<Node *> path{Node::MaxHeight}; 
 
    size_t node_count = 0; 
 
    Compare cmp;          
 
    static Node * getSibling(Node *p, Node *fp) noexcept
    {
      assert(LLINK(fp) == p || RLINK(fp) == p);
      return LLINK(fp) == p ? RLINK(fp) : LLINK(fp);
    }
 
    // ===================== INSERTION ROUTINES =====================
 
    void restoreRedCondition(Node *p,
                             Node *& fp,
                             Node *ffp,
                             Node *fffp)
    {
      /* Sanity checks */
      assert(LLINK(fp) == p || RLINK(fp) == p);
      assert(COLOR(fp) == RED);
      assert(COLOR(p) == RED);
 
      if (fp == root)
        {
          COLOR(fp) = BLACK;
          return;
        }
 
      assert(LLINK(ffp) == fp || RLINK(ffp) == fp);
      assert(COLOR(ffp) == BLACK);
      assert(LLINK(fffp) == ffp || RLINK(fffp) == ffp);
 
      COLOR(ffp) = RED;
 
      if (LLINK(fp) == p && LLINK(ffp) == fp)
        {
          COLOR(fp) = BLACK;
          rotate_to_right(ffp, fffp);
        }
      else if (RLINK(fp) == p && RLINK(ffp) == fp)
        {
          COLOR(fp) = BLACK;
          rotate_to_left(ffp, fffp);
        }
      else
        {
          COLOR(p) = BLACK;
          if (RLINK(fp) == p)
            {
              rotate_to_left(fp, ffp);
              rotate_to_right(ffp, fffp);
            }
          else
            {
              rotate_to_right(fp, ffp);
              rotate_to_left(ffp, fffp);
            }
          fp = fffp;
        }
    }
 
    static void flipColors(Node *p) noexcept
    {
      assert(p != Node::NullPtr);
      assert(COLOR(p) == BLACK);
      assert(COLOR(LLINK(p)) == RED && COLOR(RLINK(p)) == RED);
 
      COLOR(p) = RED;
      COLOR(LLINK(p)) = COLOR(RLINK(p)) = BLACK;
    }
 
    Node * searchFlipColorsAndInsert(Node *q) noexcept
    {
      assert(q != Node::NullPtr);
      assert(root != Node::NullPtr);
      assert(COLOR(q) == RED);
      assert(LLINK(q) == Node::NullPtr && RLINK(q) == Node::NullPtr);
 
      const Key & qk = KEY(q);
 
      Node *p = root; // Current node
      Node *fp = head; // p's parent
      Node *ffp = fHead; // p's grand parent
      Node *fffp = ffHead; // p's great grand parent
      Node *nextNode;
 
      while (true)
        {
          const Key & pk = KEY(p);
 
          if (are_equals<Key, Compare>(qk, pk, cmp)) [[unlikely]]
            return nullptr; /* Duplicated key, insertion is not possible */
 
          if (COLOR(p) == BLACK && COLOR(LLINK(p)) == RED
              && COLOR(RLINK(p)) == RED)
            {
              flipColors(p); // Rends p red
              if (COLOR(fp) == RED) // violation of red condition
                {
                  assert(fffp != Node::NullPtr);
                  restoreRedCondition(p, fp, ffp, fffp);
                }
            }
 
          if (cmp(qk, pk))
            {
              if (LLINK(p) == Node::NullPtr)
                break;
              nextNode = LLINK(p);
            }
          else
            {
              if (RLINK(p) == Node::NullPtr)
                break;
              nextNode = RLINK(p);
            }
 
          fffp = ffp;
          ffp = fp;
          fp = p;
          p = nextNode;
        }
 
      ++node_count;
 
      /* Insertion act */
      const Key & pk = KEY(p);
      if (cmp(qk, pk))
        LLINK(p) = q;
 
      else
        RLINK(p) = q;
 
      if (COLOR(p) == RED) // Violation of red condition
        restoreRedCondition(q, p, fp, ffp);
 
      return q;
    }
 
    Node * searchFlipColorsAndInsertDup(Node *q) noexcept
    {
      assert(q != Node::NullPtr);
      assert(root != Node::NullPtr);
      assert(COLOR(q) == RED);
      assert(LLINK(q) == Node::NullPtr && RLINK(q) == Node::NullPtr);
 
      const Key & qk = KEY(q);
 
      Node *p = root; // Current node
      Node *fp = head; // p's parent
      Node *ffp = fHead; // p's grand parent
      Node *fffp = ffHead; // p's great grand parent
      Node *nextNode;
 
      while (true)
        {
          const Key & pk = KEY(p);
 
          if (COLOR(p) == BLACK && COLOR(LLINK(p)) == RED
              && COLOR(RLINK(p)) == RED)
            {
              flipColors(p); // Rends p red
              if (COLOR(fp) == RED) // violation of red condition
                {
                  assert(fffp != Node::NullPtr);
                  restoreRedCondition(p, fp, ffp, fffp);
                }
            }
 
          if (cmp(qk, pk))
            {
              if (LLINK(p) == Node::NullPtr)
                break;
              nextNode = LLINK(p);
            }
          else
            {
              if (RLINK(p) == Node::NullPtr)
                break;
              nextNode = RLINK(p);
            }
 
          fffp = ffp;
          ffp = fp;
          fp = p;
          p = nextNode;
        }
 
      ++node_count;
 
      const Key & pk = KEY(p);
      if (cmp(qk, pk))
        LLINK(p) = q;
      else
        RLINK(p) = q;
 
      if (COLOR(p) == RED) // Violation of red condition
        restoreRedCondition(q, p, fp, ffp);
 
      return q;
    }
 
    // ===================== DELETION ROUTINES =====================
 
    Node * searchAndBuildPath(const Key & key) noexcept
    {
      assert(root != Node::NullPtr);
 
      Node *p = root;
      path.push(head);
 
      while (true)
        {
          path.push(p);
 
          const Key & pk = KEY(p);
 
          if (are_equals<Key, Compare>(key, pk, cmp))
            {
#           ifdef DEBUG
              assert(path.size() - 1.0 <= 2*log(node_count + 1)/log(2));
#           endif
              return p;
            }
 
          if (cmp(key, pk))
            {
              if (LLINK(p) == Node::NullPtr)
                {
#               ifdef DEBUG
                  assert(path.size() - 1.0 <= 2*log(node_count + 1)/log(2));
#               endif
                  return p;
                }
 
              p = LLINK(p);
              continue;
            }
 
          if (RLINK(p) == Node::NullPtr)
            {
#           ifdef DEBUG
              assert(path.size() - 1.0 <= 2*log(node_count + 1)/log(2));
#           endif
              return p;
            }
 
          p = RLINK(p);
        }
    }
 
    void findSuccAndSwap(Node *p, Node *& fp) noexcept
    {
      assert(p != Node::NullPtr);
      assert(RLINK(p) != Node::NullPtr);
      assert(fp != Node::NullPtr);
      assert(LLINK(fp) == p || RLINK(fp) == p);
 
      /*
        We save a reference to current stack content because p will be
        swapped and p's position in stack should be occupied by
        successor of p
      */
      Node *& refToSearchPath = path.top();
 
      assert(refToSearchPath == p);
 
      /* Find succesor while updating searchPath */
      Node *fSucc = p; // succesor's parent
      Node *succ = RLINK(p); // Searching starts from p's right child
 
      path.push(succ);
      while (LLINK(succ) != Node::NullPtr) // go down to leftmost
        {
          fSucc = succ;
          succ = LLINK(succ);
          path.push(succ);
        }
#   ifdef DEBUG
      assert(path.size() - 1.0 <= 2*log(node_count + 1)/log(2));
#   endif
 
      /*
         update old stack entry occupied by p These operations are
         equivalents to swap old top with current top
      */
      refToSearchPath = succ;
      path.top() = p;
 
      /* Setting of parent of p to its new child (succ) */
      if (LLINK(fp) == p)
        LLINK(fp) = succ;
      else
        RLINK(fp) = succ;
 
      /* Swaps left branches */
      LLINK(succ) = LLINK(p);
      LLINK(p) = Node::NullPtr;
 
      /* For right branches there are two cases */
      if (RLINK(p) == succ)
        { /* successor is just right's child of p */
          RLINK(p) = RLINK(succ);
          RLINK(succ) = p;
          fp = succ;
        }
      else
        { /*
             successor is the leftmost nodo descending from right child of p
          */
          Node *succr = RLINK(succ);
          RLINK(succ) = RLINK(p);
          LLINK(fSucc) = p;
          RLINK(p) = succr;
          fp = fSucc;
        }
 
      // Swap of colors
      Color tmp = COLOR(succ);
      COLOR(succ) = COLOR(p);
      COLOR(p) = tmp;
    }
 
 
    void balanceDownAndColor(Node *p, Node *& fp, Node *& sp) noexcept
    {
      assert(LLINK(fp) == p || RLINK(fp) == p);
      assert(LLINK(fp) == sp || RLINK(fp) == sp);
      assert(COLOR(fp) == BLACK);
      assert(COLOR(sp) == RED);
      assert(COLOR(p) == BLACK);
      assert(!path.is_empty());
 
      /* needed by rotation for links' update. We save a reference to search
       stack because stack's head will cahnge after rotation */
      Node *& ffp = path.top();
 
      assert(LLINK(ffp) == fp || RLINK(ffp) == fp);
 
      /* balancing down of p, update of out parameters and update of stack
         entry corresponding to fp */
      if (LLINK(fp) == p)
        {
          sp = LLINK(sp);
          ffp = rotate_to_left(fp, ffp);
        }
      else
        {
          sp = RLINK(sp);
          ffp = rotate_to_right(fp, ffp);
        }
 
      assert(LLINK(fp) == sp || RLINK(fp) == sp);
      assert(COLOR(ffp) == RED);
 
      /* coloring  for ensuring to apply sibling black cases */
      COLOR(ffp) = BLACK;
      COLOR(fp) = RED;
    }
 
    void rotateNephewAndColor(Node *fp, Node *sp, Node *np) noexcept
    {
      assert(LLINK(fp) == sp || RLINK(fp) == sp);
      assert(LLINK(sp) == np || RLINK(sp) == np);
      assert(COLOR(sp) == BLACK);
      assert(COLOR(np) == RED);
      assert(!path.is_empty());
 
      Node *ffp = path.top();
 
      assert(LLINK(ffp) == fp || RLINK(ffp) == fp);
 
      /* rotation for downing low fp */
      if (RLINK(sp) == np)
        rotate_to_left(fp, ffp);
      else
        rotate_to_right(fp, ffp);
 
      /* coloring for fixing up red black conditions */
      COLOR(sp) = COLOR(fp);
      COLOR(fp) = BLACK;
      COLOR(np) = BLACK;
    }
 
    void doubleRotateNephewAndColor(Node *fp, Node *sp, Node *snp) noexcept
    {
      assert(LLINK(fp) == sp || RLINK(fp) == sp);
      assert(LLINK(sp) == snp || RLINK(sp) == snp);
      assert(COLOR(sp) == BLACK);
      assert(COLOR(snp) == RED);
      assert(!path.is_empty());
 
      Node *ffp = path.top();
 
      assert(LLINK(ffp) == fp || RLINK(ffp) == fp);
 
      /* double rotation for raising up of snp. snp becomes the new root of
         sub tree fp  */
      if (LLINK(sp) == snp)
        {
          rotate_to_right(sp, fp);
          rotate_to_left(fp, ffp);
        }
      else
        {
          rotate_to_left(sp, fp);
          rotate_to_right(fp, ffp);
        }
 
      /* coloring for restoring all red black tree conditions */
      COLOR(snp) = COLOR(fp);
      COLOR(fp) = BLACK;
    }
 
    static void colorSiblingAsRed(Node *sp) noexcept
    {
      assert(COLOR(sp) == BLACK);
      COLOR(sp) = RED;
    }
 
    static void colorParentAndSibling(Node *fp, Node *sp) noexcept
    {
      assert(LLINK(fp) == sp || RLINK(fp) == sp);
      assert(COLOR(fp) == RED);
      assert(COLOR(sp) == BLACK);
 
      COLOR(fp) = BLACK;
      COLOR(sp) = RED;
    }
 
    void removeAndFixBlackCondition(Node *q) noexcept
    {
      assert(path.top() == q);
 
      /* look at second item after stack's head. We cannot pop it because
         successor finding would require stack pushing */
      Node *fq = path.top(1);
      Node *p; /* Saves the new child of fp after p has been deleted, this
                  node can be a violating black condition black node */
 
      assert(fq != Node::NullPtr);
      assert(LLINK(fq) == q || RLINK(fq) == q);
 
      /* Deletion step: by pass if there is a Node::NullPtr link or swap
         with successor */
      while (1)
        {
          if (LLINK(q) == Node::NullPtr) // by pass to the left side
            {
              if (LLINK(fq) == q)
                p = LLINK(fq) = RLINK(q);
              else
                p = RLINK(fq) = RLINK(q);
              break;
            }
 
          if (RLINK(q) == Node::NullPtr) // by pass to the right side
            {
              if (LLINK(fq) == q)
                p = LLINK(fq) = LLINK(q);
              else
                p = RLINK(fq) = LLINK(q);
              break;
            }
 
          findSuccAndSwap(q, fq);
        }
 
      /* if color of deleted node is red, then all red black conditions are
         met and adjust is not necessary */
      if (COLOR(q) == RED)
        {
          assert(COLOR(p) == BLACK);
          path.empty();
          return;
        }
 
      /* if color of p is black, then it misses a black node and four condition
         is violated. However, if p's child is red we can recoloring it black
         for restoring the missing black node */
      if (COLOR(p) == RED)
        {
          COLOR(p) = BLACK;
          path.empty();
          return;
        }
 
      /* Bad luck we must do recoloring and/or balancing for restoring the
         four condition */
      // p's sibling
      Node *np, *snp; // p's nephew and nephewg's sibling
      Node *fp = fq; // we process in function of p
 
      path.popn(2); // pops deleted node and fp
 
      /* we examine p and we restore red black properties */
      while (true)
        {
          if (p == root)
            break;
 
          Node *sp = getSibling(p, fp);
 
          /* if sibling is red, we rotate down for assuring that p' sibling
             to be black */
          if (COLOR(sp) == RED)
            balanceDownAndColor(p, fp, sp);
 
          assert(COLOR(sp) == BLACK);
 
          /* Compute nephews */
          if (LLINK(fp) == p)
            {
              np = RLINK(sp);
              snp = LLINK(sp);
            }
          else
            {
              np = LLINK(sp);
              snp = RLINK(sp);
            }
 
          if (COLOR(np) == RED)
            {
              rotateNephewAndColor(fp, sp, np);
              break;
            }
 
          if (COLOR(snp) == RED)
            {
              doubleRotateNephewAndColor(fp, sp, snp);
              break;
            }
 
          if (COLOR(fp) == RED)
            {
              colorParentAndSibling(fp, sp);
              break;
            }
 
          /* color and restart process with fp */
          colorSiblingAsRed(sp);
          p = fp;
          fp = path.pop(); // colorSiblingAsRed(sp) does not pop it
        }
      path.empty();
    }
 
  public:
    using key_type = Key;
 
    Compare & key_comp() noexcept { return cmp; }
    
    const Compare & key_comp() const noexcept { return cmp; }
 
    Compare & get_compare() noexcept { return cmp; }
    
    [[nodiscard]] constexpr const Compare & get_compare() const noexcept { return cmp; }
 
    HtdRbTree(Compare __cmp = Compare()) noexcept
      : head(&headNode),
        fHead(&headParent),
        ffHead(&headGrandParent),
        root(headNode.getR()),
        cmp(__cmp)
    {
      RLINK(fHead) = head;
      RLINK(ffHead) = fHead;
      COLOR(Node::NullPtr) = BLACK;
      COLOR(head) = BLACK;
      COLOR(fHead) = BLACK;
      COLOR(ffHead) = BLACK;
    }
 
    void swap(HtdRbTree & tree) noexcept
    {
      std::swap(root, tree.root);
      std::swap(node_count, tree.node_count);
      std::swap(cmp, tree.cmp);
    }
 
    HtdRbTree(HtdRbTree && tree) noexcept
      : head(&headNode),
        fHead(&headParent),
        ffHead(&headGrandParent),
        root(headNode.getR()),
        path(Node::MaxHeight),
        node_count(0),
        cmp()
    {
      RLINK(fHead) = head;
      RLINK(ffHead) = fHead;
      COLOR(Node::NullPtr) = BLACK;
      COLOR(head) = BLACK;
      COLOR(fHead) = BLACK;
      COLOR(ffHead) = BLACK;
      swap(tree);
    }
 
    HtdRbTree & operator=(HtdRbTree && tree) noexcept
    {
      swap(tree);
      return *this;
    }
    
    HtdRbTree(const HtdRbTree &) = delete;
    
    HtdRbTree & operator=(const HtdRbTree &) = delete;
 
    virtual ~HtdRbTree() = default;
 
    [[nodiscard]] constexpr bool is_empty() const noexcept { return root == Node::NullPtr; }
 
    [[nodiscard]] constexpr size_t size() const noexcept { return node_count; }
    
    void reset() noexcept
    {
      root = Node::NullPtr;
      node_count = 0;
    }
 
    Node * insert(Node *p) noexcept
    {
      assert(p != Node::NullPtr);
      assert(COLOR(p) == RED);
      assert(LLINK(p) == Node::NullPtr && RLINK(p) == Node::NullPtr);
 
      if (root == Node::NullPtr) [[unlikely]]
        {
          root = p;
          ++node_count;
          return p;
        }
 
      return searchFlipColorsAndInsert(p);
    }
 
    Node * search_or_insert(Node *p) noexcept
    {
      assert(p != Node::NullPtr);
      assert(COLOR(p) == RED);
      assert(LLINK(p) == Node::NullPtr && RLINK(p) == Node::NullPtr);
 
      if (root == Node::NullPtr) [[unlikely]]
        {
          root = p;
          ++node_count;
          return p;
        }
 
      const Key & pk = KEY(p);
      Node *found = search(pk);
      if (found != nullptr) [[unlikely]]
        return found;
 
      return insert(p);
    }
 
    Node * insert_dup(Node *p) noexcept
    {
      assert(p != Node::NullPtr);
      assert(COLOR(p) == RED);
      assert(LLINK(p) == Node::NullPtr && RLINK(p) == Node::NullPtr);
 
      if (root == Node::NullPtr) [[unlikely]]
        {
          root = p;
          ++node_count;
          return p;
        }
 
      return searchFlipColorsAndInsertDup(p);
    }
 
    Node * search(const Key & key) const noexcept
    {
      Node *retVal = searchInBinTree(root, key, cmp);
      return retVal == Node::NullPtr ? nullptr : retVal;
    }
 
    Node * remove(const Key & key) noexcept
    {
      if (root == Node::NullPtr) [[unlikely]]
        return nullptr;
 
      Node *p = searchAndBuildPath(key);
 
      if (no_equals<Key, Compare>(KEY(p), key, cmp))
        {
          path.empty();
          return nullptr;
        }
 
      removeAndFixBlackCondition(p);
 
      assert(node_count > 0);
      --node_count;
 
      p->reset();
 
      return p;
    }
 
 
    Node *& getRoot() noexcept { return root; }
    
    Node * getRoot() const noexcept { return root; }
 
  private:
    static void blackHeight(Node *p, int & max, int bh = 0) noexcept
    {
      if (COLOR(p) == BLACK)
        bh++; // Another seen black node
 
      /* if a leaf is reached, we must verify max with current bh (number of
       visited black nodes */
      if (LLINK(p) == Node::NullPtr && RLINK(p) == Node::NullPtr)
        {
          if (max == -1) // This is onbly for the first leaf reached
            max = bh;
          assert(bh == max);
          return;
        }
 
      if (LLINK(p) != Node::NullPtr) /* continue counting in the left side */
        blackHeight(LLINK(p), max, bh);
 
      if (RLINK(p) != Node::NullPtr) /* continue counting in the right side */
        blackHeight(RLINK(p), max, bh);
    }
 
    static void testNode(Node *p) noexcept
    {
      /* verify red condition */
      COND_assert(COLOR(p) == RED,
                  COLOR(LLINK(p)) == BLACK && COLOR(RLINK(p)) == BLACK);
 
      int max = -1;
      int bh = 0;
 
      blackHeight(p, max, bh);
    }
 
  public:
    void verifyRedBlack() const
    {
      preOrderRec(root, testNode);
    }
 
    bool verify() const noexcept
    {
      return is_red_black_bst(const_cast<Node *>(root),
                              const_cast<HtdRbTree *>(this)->cmp);
    }
 
    struct Iterator : public BinNodeInfixIterator<Node>
    {
      Iterator(HtdRbTree & t) noexcept
        : BinNodeInfixIterator<Node>(t.getRoot()) {}
 
      Iterator(const HtdRbTree & t) noexcept
        : BinNodeInfixIterator<Node>(const_cast<HtdRbTree &>(t).getRoot()) {}
    };
  };
 
  template <class Key, class Compare = Aleph::less<Key>>
  class HtdRbTreeVtl : public HtdRbTree<Key, Compare>
  {
  public:
    using Base = HtdRbTree<Key, Compare>;
    using Node = typename Base::Node;
    using Base::Base;  // Inherit constructors
  };
 
} // namespace Aleph
 
#endif /* TPL_HTDRBTREE_H */