tpl_tdRbTreeRk.H

Go to the documentation of this file.

 
/*
                          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_TDRBTREERK_H
# define TPL_TDRBTREERK_H
 
# include <functional>
# include <tpl_binNode.H>
# include <tpl_binNodeUtils.H>
# include <tpl_binNodeXt.H>
# include <tpl_binTreeOps.H>
# include <rbNodeRk.H>
 
namespace Aleph
{
 
template <template <class> class NodeType, typename Key, 
          class Compare = std::less<Key>>
class GenTdRbTreeRk 
{
public:
  using Node = NodeType<Key>;
  using key_type = Key;
  using compare_type = Compare;
 
private:
  Node headNode;      
  Node headParent;    
  Node *head;         
  Node *fHead;        
  Node *&root;        
  Compare cmp;        
 
  bool less(const Key& a, const Key& b) const noexcept
  {
    return cmp(a, b);
  }
 
  bool equals(const Key& a, const Key& b) const noexcept
  {
    return not cmp(a, b) and not cmp(b, a);
  }
 
  static Node* rotate_to_right_rk(Node *p, Node *pp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(pp != Node::NullPtr);
    
    Node *q = LLINK(p);
    LLINK(p) = RLINK(q);
    RLINK(q) = p;
    
    // Update counters
    COUNT(p) = COUNT(LLINK(p)) + COUNT(RLINK(p)) + 1;
    COUNT(q) = COUNT(LLINK(q)) + COUNT(RLINK(q)) + 1;
    
    if (LLINK(pp) == p)
      LLINK(pp) = q;
    else
      RLINK(pp) = q;
    
    return q;
  }
 
  static Node* rotate_to_left_rk(Node *p, Node *pp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(pp != Node::NullPtr);
    
    Node *q = RLINK(p);
    RLINK(p) = LLINK(q);
    LLINK(q) = p;
    
    // Update counters
    COUNT(p) = COUNT(LLINK(p)) + COUNT(RLINK(p)) + 1;
    COUNT(q) = COUNT(LLINK(q)) + COUNT(RLINK(q)) + 1;
    
    if (LLINK(pp) == p)
      LLINK(pp) = q;
    else
      RLINK(pp) = q;
    
    return q;
  }
 
  void restoreRedCondition(Node *p, Node *&fp, Node *ffp, Node *fffp) noexcept
  {
    assert(LLINK(fp) == p or RLINK(fp) == p);
    assert(COLOR(fp) == RED);
    assert(COLOR(p) == RED);
 
    if (fp == root)
      {
        COLOR(fp) = BLACK;
        return;
      }
 
    assert(LLINK(ffp) == fp or RLINK(ffp) == fp);
    assert(COLOR(ffp) == BLACK);
    assert(LLINK(fffp) == ffp or RLINK(fffp) == ffp);
 
    COLOR(ffp) = RED;
 
    if (LLINK(fp) == p and LLINK(ffp) == fp)
      {
        COLOR(fp) = BLACK;
        rotate_to_right_rk(ffp, fffp);
      }
    else if (RLINK(fp) == p and RLINK(ffp) == fp)
      {
        COLOR(fp) = BLACK;
        rotate_to_left_rk(ffp, fffp);
      }
    else 
      {
        COLOR(p) = BLACK;
        if (RLINK(fp) == p)
          {
            rotate_to_left_rk(fp, ffp);
            rotate_to_right_rk(ffp, fffp);
          }
        else
          {
            rotate_to_right_rk(fp, ffp);
            rotate_to_left_rk(ffp, fffp);
          }
        fp = fffp;
      }
  }
  
  static void flipColors(Node* p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == BLACK);
    assert(COLOR(LLINK(p)) == RED and 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);
 
    // Stack to track visited nodes for count updates
    Node* stack[128];
    size_t stack_len = 0;
 
    Node *p    = root;
    Node *fp   = head;
    Node *ffp  = fHead;
    Node *fffp = Node::NullPtr;
    Node *nextNode;
 
    stack[stack_len++] = p;
 
    while (true)
      {
        if (equals(KEY(q), KEY(p)))
          return nullptr;  // Duplicate key
 
        if (COLOR(p) == BLACK and COLOR(LLINK(p)) == RED 
            and COLOR(RLINK(p)) == RED)
          {
            flipColors(p);
            if (COLOR(fp) == RED)
              {
                assert(fffp != Node::NullPtr);
                restoreRedCondition(p, fp, ffp, fffp);
              }
          }
 
        if (less(KEY(q), KEY(p)))
          { 
            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;
        stack[stack_len++] = p;
      }
 
    // Perform insertion
    if (less(KEY(q), KEY(p)))
      LLINK(p) = q;
    else 
      RLINK(p) = q;
 
    if (COLOR(p) == RED)
      restoreRedCondition(q, p, fp, ffp);
 
    // Update counts bottom-up - O(log n)
    // Each node's count = left_count + right_count + 1
    // Children are already correct (leaf has count=1, rotated nodes recalculated)
    updateCountsFromStack(stack, stack_len);
 
    return q;
  }
 
  Node* searchFlipColorsAndInsertDup(Node *q) noexcept
  {
    assert(q != Node::NullPtr);
    assert(root != Node::NullPtr);
    assert(COLOR(q) == RED);
 
    Node* stack[128];
    size_t stack_len = 0;
 
    Node *p    = root;
    Node *fp   = head;
    Node *ffp  = fHead;
    Node *fffp = Node::NullPtr;
    Node *nextNode;
 
    stack[stack_len++] = p;
 
    while (true)
      {
        if (COLOR(p) == BLACK and COLOR(LLINK(p)) == RED 
            and COLOR(RLINK(p)) == RED)
          {
            flipColors(p);
            if (COLOR(fp) == RED)
              {
                assert(fffp != Node::NullPtr);
                restoreRedCondition(p, fp, ffp, fffp);
              }
          }
 
        if (less(KEY(q), KEY(p)))
          { 
            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;
        stack[stack_len++] = p;
      }
 
    if (less(KEY(q), KEY(p)))
      LLINK(p) = q;
    else 
      RLINK(p) = q;
 
    if (COLOR(p) == RED)
      restoreRedCondition(q, p, fp, ffp);
 
    // Update counts bottom-up - O(log n)
    updateCountsFromStack(stack, stack_len);
 
    return q;
  }
 
  static size_t updateCountRec(Node *p) noexcept
  {
    if (p == Node::NullPtr)
      return 0;
    
    size_t left_count = updateCountRec(LLINK(p));
    size_t right_count = updateCountRec(RLINK(p));
    COUNT(p) = left_count + right_count + 1;
    return COUNT(p);
  }
  
  static void updateCountsFromStack(Node** stack, size_t len) noexcept
  {
    // Process bottom-up: children are already correct
    while (len > 0)
      {
        Node* p = stack[--len];
        COUNT(p) = COUNT(LLINK(p)) + COUNT(RLINK(p)) + 1;
      }
  }
  
 
  static Node* gotoLeftAndColorRed(Node *fp, Node *&ffp) noexcept
  {
    assert(fp != Node::NullPtr);
    assert(ffp != Node::NullPtr);
    assert(LLINK(fp) != Node::NullPtr);
 
    Node *p = LLINK(fp);
 
    if (COLOR(p) == RED)  
      return p; 
 
    Node *sp = RLINK(fp);
 
    if (COLOR(fp) == BLACK)
      {
        assert(COLOR(sp) == RED);
        rotate_to_left_rk(fp, ffp);
        COLOR(fp) = RED;
        COLOR(sp) = BLACK;
        ffp = sp;
        sp = RLINK(fp);
      }
 
    if (COLOR(LLINK(p)) == BLACK and COLOR(RLINK(p)) == BLACK)
      {
        assert(COLOR(fp) == RED);
 
        COLOR(p) = RED;
        COLOR(fp) = BLACK;
 
        Node *np  = RLINK(sp);
        Node *snp = LLINK(sp);
 
        if (COLOR(snp) == BLACK and COLOR(np) == BLACK) 
          {
            COLOR(sp) = RED;
            return p;
          }
 
        if (COLOR(np) == RED)
          {
            ffp = rotate_to_left_rk(fp, ffp);
            COLOR(sp) = RED;
            COLOR(np) = BLACK;
            return p;
          }
          
        assert(COLOR(snp) == RED);
 
        rotate_to_right_rk(sp, fp);
        ffp = rotate_to_left_rk(fp, ffp);
      }
    return p;
  }
 
  static Node* gotoRightAndColorRed(Node *fp, Node *&ffp) noexcept
  {
    assert(fp != Node::NullPtr);
    assert(ffp != Node::NullPtr);
    assert(RLINK(fp) != Node::NullPtr);
 
    Node *p = RLINK(fp);
 
    if (COLOR(p) == RED)  
      return p; 
 
    Node *sp = LLINK(fp);
 
    if (COLOR(fp) == BLACK)
      {
        assert(COLOR(sp) == RED);
        rotate_to_right_rk(fp, ffp);
        COLOR(fp) = RED;
        COLOR(sp) = BLACK;
        ffp = sp;
        sp = LLINK(fp);
      }
 
    if (COLOR(LLINK(p)) == BLACK and COLOR(RLINK(p)) == BLACK)
      {
        assert(COLOR(fp) == RED);
 
        COLOR(p) = RED;
        COLOR(fp) = BLACK;
 
        Node *np  = LLINK(sp);
        Node *snp = RLINK(sp);
 
        if (COLOR(snp) == BLACK and COLOR(np) == BLACK)
          {
            COLOR(sp) = RED;
            return p;
          }
 
        if (COLOR(np) == RED)
          {
            ffp = rotate_to_right_rk(fp, ffp);
            COLOR(sp) = RED;
            COLOR(np) = BLACK;
            return p;
          }
          
        assert(COLOR(snp) == RED);
 
        rotate_to_left_rk(sp, fp);
        ffp = rotate_to_right_rk(fp, ffp);
      }
    return p;
  }
 
  static void findSuccAndSwap(Node *p, Node *&fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(RLINK(p) != Node::NullPtr);
    
    size_t original_count = COUNT(p);
 
    Node *fSucc  = p;
    Node *succ   = gotoRightAndColorRed(p, fp); 
    Node *ffSucc = fp;
    
    while (LLINK(succ) != Node::NullPtr)
      {
        ffSucc = fSucc;
        fSucc  = succ;
        succ   = gotoLeftAndColorRed(fSucc, ffSucc);
      }
 
    if (LLINK(fp) == p)
      LLINK(fp) = succ;
    else
      RLINK(fp) = succ;
    
    LLINK(succ) = LLINK(p);
    LLINK(p)    = Node::NullPtr; 
 
    if (RLINK(p) == succ) 
      {
        RLINK(p)    = RLINK(succ); 
        RLINK(succ) = p;
        fSucc       = fp;
        fp          = succ;
      }
    else
      {
        Node *tmp    = fp;
        Node *succr  = RLINK(succ); 
          
        RLINK(succ)  = RLINK(p);
        LLINK(fSucc) = p;
        RLINK(p)     = succr;
        fp           = fSucc;
        fSucc        = tmp; 
      }
 
    Color tmp   = COLOR(succ);
    COLOR(succ) = COLOR(p); 
    COLOR(p)    = tmp;
    
    // Preserve count at successor's new position
    COUNT(succ) = original_count;
  }
 
  static void findPredAndSwap(Node *p, Node *&fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(LLINK(p) != Node::NullPtr);
    
    size_t original_count = COUNT(p);
 
    Node *fPred  = p;
    Node *pred   = gotoLeftAndColorRed(p, fp);
    Node *ffPred = fp;
    
    while (RLINK(pred) != Node::NullPtr)
      {
        ffPred = fPred;
        fPred  = pred;
        pred   = gotoRightAndColorRed(fPred, ffPred);
      }
 
    if (LLINK(fp) == p)
      LLINK(fp) = pred;
    else
      RLINK(fp) = pred;
    
    RLINK(pred) = RLINK(p);
    RLINK(p)    = Node::NullPtr; 
 
    if (LLINK(p) == pred) 
      {
        LLINK(p)    = LLINK(pred); 
        LLINK(pred) = p;
        fPred       = fp;
        fp          = pred;
      }
    else
      {
        Node *tmp    = fp;
        Node *predl  = LLINK(pred); 
          
        LLINK(pred)  = LLINK(p);
        RLINK(fPred) = p;
        LLINK(p)     = predl;
        fp           = fPred;
        fPred        = tmp; 
      }
 
    Color tmp   = COLOR(pred);
    COLOR(pred) = COLOR(p); 
    COLOR(p)    = tmp;
    
    COUNT(pred) = original_count;
  }
 
  void colorRootAsRed() noexcept
  {
    if (COLOR(root) == RED)
      return;
 
    if (COLOR(LLINK(root)) == BLACK and COLOR(RLINK(root)) == BLACK)
      COLOR(root) = RED;      
  }
 
  Node* searchAndColorRed(const Key& key, Node *&fp,
                          Node** stack, size_t& stack_len) noexcept
  {
    Node *p   = root;
    fp        = head;
    Node *ffp = fHead;
    
    stack_len = 0;
 
    colorRootAsRed();
    stack[stack_len++] = p;
 
    while (true)
      {
        if (equals(key, KEY(p)))
          return p;
 
        ffp = fp;
        fp  = p;
 
        if (less(key, KEY(p)))
          {
            if (LLINK(p) == Node::NullPtr)
              return p;  // Key not found, return current
            p = gotoLeftAndColorRed(fp, ffp);
          }
        else
          {
            if (RLINK(p) == Node::NullPtr)
              return p;  // Key not found, return current
            p = gotoRightAndColorRed(fp, ffp);
          }
        
        stack[stack_len++] = p;
      }
  }
 
  static void removeAndRendLeafRed(Node *p, Node *fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(fp != Node::NullPtr);
 
    while (LLINK(p) != Node::NullPtr or RLINK(p) != Node::NullPtr)
      {
        if (RLINK(p) != Node::NullPtr)
          findSuccAndSwap(p, fp);
        else if (LLINK(p) != Node::NullPtr)
          findPredAndSwap(p, fp);
      }
 
    if (LLINK(fp) == p)
      LLINK(fp) = Node::NullPtr;
    else
      RLINK(fp) = Node::NullPtr;
  }
 
  void init() noexcept
  {
    RLINK(fHead) = head;
    COLOR(Node::NullPtr) = BLACK;
    COUNT(Node::NullPtr) = 0;
    COLOR(head) = BLACK;
    COUNT(head) = 0;
  }
 
public:
  GenTdRbTreeRk() noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()), cmp()
  {
    init();
  }
 
  explicit GenTdRbTreeRk(const Compare & __cmp) noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()), cmp(__cmp)
  {
    init();
  }
 
  GenTdRbTreeRk(GenTdRbTreeRk && other) noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()),
      cmp(std::move(other.cmp))
  {
    init();
    root = other.root;
    other.root = Node::NullPtr;
  }
 
  GenTdRbTreeRk & operator=(GenTdRbTreeRk && other) noexcept
  {
    if (this != &other)
      {
        root = other.root;
        cmp = std::move(other.cmp);
        other.root = Node::NullPtr;
      }
    return *this;
  }
 
  GenTdRbTreeRk(const GenTdRbTreeRk &) = delete;
  GenTdRbTreeRk & operator=(const GenTdRbTreeRk &) = delete;
 
  void reset() noexcept
  {
    root = Node::NullPtr;
  }
 
  void swap(GenTdRbTreeRk & other) noexcept
  {
    std::swap(root, other.root);
    std::swap(cmp, other.cmp);
  }
 
  virtual ~GenTdRbTreeRk() = default;
 
  size_t size() const noexcept { return COUNT(root); }
 
  bool is_empty() const noexcept { return root == Node::NullPtr; }
 
  Compare & get_compare() noexcept { return cmp; }
  const Compare & get_compare() const noexcept { return cmp; }
 
  Node* insert(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == RED);
    COUNT(p) = 1;
 
    if (root == Node::NullPtr)
      {
        root = p;
        return p;
      }
 
    return searchFlipColorsAndInsert(p);
  }
 
  Node* insert_dup(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == RED);
    COUNT(p) = 1;
 
    if (root == Node::NullPtr)
      {
        root = p;
        return p;
      }
 
    return searchFlipColorsAndInsertDup(p);
  }
 
  Node* search_or_insert(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == RED);
    COUNT(p) = 1;
 
    if (root == Node::NullPtr)
      {
        root = p;
        return p;
      }
 
    Node *found = search(KEY(p));
    if (found != nullptr)
      return found;
 
    return searchFlipColorsAndInsert(p);
  }
 
  Node* search(const Key& key) const noexcept
  {
    Node* p = root;
    while (p != Node::NullPtr)
      {
        if (equals(key, KEY(p)))
          return p;
        p = less(key, KEY(p)) ? LLINK(p) : RLINK(p);
      }
    return nullptr;
  }
 
  Node* remove(const Key& key) noexcept
  {
    if (root == Node::NullPtr)
      return nullptr;
    
    Node* stack[128];
    size_t stack_len = 0;
      
    Node *fp;
    Node *p = searchAndColorRed(key, fp, stack, stack_len);
 
    if (not equals(KEY(p), key))
      return nullptr;
 
    removeAndRendLeafRed(p, fp);
    
    // Recalculate counts for visited nodes - usually O(log n)
    // For complex cases with many swaps, fall back to full recalc
    if (root != Node::NullPtr)
      {
        // The stack contains nodes visited during search
        // After swaps, some may have moved, so do full recalc for safety
        updateCountRec(root);
      }
 
    return p;
  }
 
  Node*& getRoot() noexcept { return root; }
  Node* getRoot() const noexcept { return root; }
 
  // ===================== RANK OPERATIONS =====================
 
  Node* select(size_t i) const
  {
    return Aleph::select(root, i);
  }
 
  std::pair<long, Node*> position(const Key & key) const noexcept
  {
    std::pair<long, Node*> ret_val;
    ret_val.first = BinTreeXt_Operation<Node, Compare>(cmp).
      inorder_position(root, key, ret_val.second);
    return ret_val;
  }
 
  std::pair<long, Node*> find_position(const Key & key) const noexcept
  {
    std::pair<long, Node*> r(-2, nullptr);
    r.first = BinTreeXt_Operation<Node, Compare>(cmp).
      find_position(root, key, r.second);
    return r;
  }
 
  Node* remove_pos(size_t i)
  {
    Node* p = select(i);
    if (p == nullptr)
      return nullptr;
    return remove(KEY(p));
  }
 
  void split_pos(size_t pos, GenTdRbTreeRk & t1, GenTdRbTreeRk & t2) noexcept
  {
    if (root == Node::NullPtr)
      return;
 
    if (pos == 0)
      {
        t2.root = root;
        root = Node::NullPtr;
        return;
      }
 
    if (pos >= size())
      {
        t1.root = root;
        root = Node::NullPtr;
        return;
      }
 
    // Simple O(n) implementation
    size_t count = 0;
    split_pos_inorder(root, pos, t1, t2, count);
    root = Node::NullPtr;
  }
 
private:
  void split_pos_inorder(Node *p, size_t pos, 
                         GenTdRbTreeRk & t1, GenTdRbTreeRk & t2,
                         size_t & count) noexcept
  {
    if (p == Node::NullPtr)
      return;
 
    Node *left = LLINK(p);
    Node *right = RLINK(p);
 
    split_pos_inorder(left, pos, t1, t2, count);
 
    p->reset();
    if (count < pos)
      t1.insert(p);
    else
      t2.insert(p);
    ++count;
 
    split_pos_inorder(right, pos, t1, t2, count);
  }
 
public:
  bool verify() const noexcept
  {
    return is_red_black_bst_rk(root, cmp) and check_rank_tree(root);
  }
 
  struct Iterator : public BinNodeInfixIterator<Node>
  {
    Iterator(GenTdRbTreeRk & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
    Iterator(const GenTdRbTreeRk & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
  };
};
 
template <typename Key, class Compare = std::less<Key>>
class TdRbTreeRk : public GenTdRbTreeRk<RbNodeRk, Key, Compare>
{
  using Base = GenTdRbTreeRk<RbNodeRk, Key, Compare>;
public:
  using Base::Base;
};
 
template <typename Key, class Compare = std::less<Key>>
class TdRbTreeRkVtl : public GenTdRbTreeRk<RbNodeRkVtl, Key, Compare>
{
  using Base = GenTdRbTreeRk<RbNodeRkVtl, Key, Compare>;
public:
  using Base::Base;
};
 
} // namespace Aleph
 
# endif /* TPL_TDRBTREERK_H */