tpl_tdRbTree.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_TDRBTREE_H
# define TPL_TDRBTREE_H
 
# include <functional>
# include <tpl_binNode.H>
# include <tpl_binNodeUtils.H>
# include <tpl_arrayStack.H>
# include <rbNode.H>
 
namespace Aleph
{
 
template <template <class> class NodeType, typename Key, 
          class Compare = std::less<Key>>
class GenTdRbTree 
{
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;        
  size_t num_nodes;   
 
  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* getSibling(Node *p, Node *fp) noexcept
  {
    assert(LLINK(fp) == p or RLINK(fp) == p);
    return LLINK(fp) == p ? RLINK(fp) : LLINK(fp);
  }
 
  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(ffp, fffp);
      }
    else if (RLINK(fp) == p and 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 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);
    assert(LLINK(q) == Node::NullPtr and RLINK(q) == Node::NullPtr);
 
    Node *p    = root;              // Current node
    Node *fp   = head;              // p's parent
    Node *ffp  = fHead;             // p's grandparent
    Node *fffp = Node::NullPtr;     // p's great-grandparent
    Node *nextNode;
 
    while (true)
      {
        if (equals(KEY(q), KEY(p)))
          return nullptr;  // Duplicated key, insertion not possible
 
        // Proactive color flip: if p is black with two red children, flip
        if (COLOR(p) == BLACK and COLOR(LLINK(p)) == RED 
            and COLOR(RLINK(p)) == RED)
          {
            flipColors(p);
            if (COLOR(fp) == RED)  // May violate red condition
              {
                assert(fffp != Node::NullPtr);
                restoreRedCondition(p, fp, ffp, fffp);
              }
          }
 
        // Descend to appropriate child
        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);
          }
 
        // Update ancestor chain
        fffp = ffp;
        ffp  = fp;
        fp   = p;
        p    = nextNode;
      }
 
    ++num_nodes;
 
    // Perform insertion
    if (less(KEY(q), KEY(p)))
      LLINK(p) = q;
    else 
      RLINK(p) = q;
 
    if (COLOR(p) == RED)  // May violate 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 and RLINK(q) == Node::NullPtr);
 
    Node *p    = root;
    Node *fp   = head;
    Node *ffp  = fHead;
    Node *fffp = Node::NullPtr;
    Node *nextNode;
 
    while (true)
      {
        // Proactive color flip
        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);
              }
          }
 
        // Descend (duplicates go right)
        if (less(KEY(q), KEY(p)))
          { 
            if (LLINK(p) == Node::NullPtr)
              break;
            nextNode = LLINK(p);
          }
        else  // >= goes right
          {
            if (RLINK(p) == Node::NullPtr)
              break;
            nextNode = RLINK(p);
          }
 
        fffp = ffp;
        ffp  = fp;
        fp   = p;
        p    = nextNode;
      }
 
    ++num_nodes;
 
    if (less(KEY(q), KEY(p)))
      LLINK(p) = q;
    else 
      RLINK(p) = q;
 
    if (COLOR(p) == RED)
      restoreRedCondition(q, p, fp, ffp);
 
    return q;
  }
 
  static Node* gotoLeftAndColorRed(Node *fp, Node *&ffp) noexcept
  {
    assert(fp != Node::NullPtr);
    assert(ffp != Node::NullPtr);
    assert(LLINK(ffp) == fp or RLINK(ffp) == fp);
    assert(LLINK(fp) != Node::NullPtr);
 
    Node *p = LLINK(fp);
 
    if (COLOR(p) == RED)  
      return p; 
 
    Node *sp = RLINK(fp);
 
    // fp black means we came from another black node
    if (COLOR(fp) == BLACK)
      {
        assert(COLOR(sp) == RED);
        rotate_to_left(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(LLINK(fp)) == BLACK);
        assert(COLOR(RLINK(fp)) == BLACK);
        assert(COLOR(fp) == RED);
 
        COLOR(p) = RED;
        COLOR(fp) = BLACK;
 
        Node *np  = RLINK(sp);   // Nephew of p
        Node *snp = LLINK(sp);   // Sibling-nephew of p
 
        if (COLOR(snp) == BLACK and COLOR(np) == BLACK) 
          {
            COLOR(sp) = RED;
            return p;
          }
 
        if (COLOR(np) == RED)
          {
            ffp = rotate_to_left(fp, ffp);
            COLOR(sp) = RED;
            COLOR(np) = BLACK;
            assert(ffp == sp);
            return p;
          }
          
        assert(COLOR(snp) == RED);
 
        rotate_to_right(sp, fp);
        ffp = rotate_to_left(fp, ffp);
        assert(ffp == snp);
      }
    return p;
  }
 
  static Node* gotoRightAndColorRed(Node *fp, Node *&ffp) noexcept
  {
    assert(fp != Node::NullPtr);
    assert(ffp != Node::NullPtr);
    assert(LLINK(ffp) == fp or RLINK(ffp) == fp);
    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(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(RLINK(fp)) == BLACK);
        assert(COLOR(LLINK(fp)) == BLACK);
        assert(COLOR(fp) == RED);
 
        COLOR(p) = RED;
        COLOR(fp) = BLACK;
 
        Node *np  = LLINK(sp);   // Nephew of p
        Node *snp = RLINK(sp);   // Sibling-nephew of p
 
        if (COLOR(snp) == BLACK and COLOR(np) == BLACK)
          {
            COLOR(sp) = RED;
            return p;
          }
 
        if (COLOR(np) == RED)
          {
            ffp = rotate_to_right(fp, ffp);
            COLOR(sp) = RED;
            COLOR(np) = BLACK;
            assert(ffp == sp);
            return p;
          }
          
        assert(COLOR(snp) == RED);
 
        rotate_to_left(sp, fp);
        ffp = rotate_to_right(fp, ffp);
        assert(ffp == snp);
      }
    return p;
  }
 
  static void findSuccAndSwap(Node *p, Node *&fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(RLINK(p) != Node::NullPtr);
    assert(fp != Node::NullPtr);
    assert(LLINK(fp) == p or RLINK(fp) == 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);
      }
 
    // Update parent of p to point to succ
    if (LLINK(fp) == p)
      LLINK(fp) = succ;
    else
      RLINK(fp) = succ;
    
    // Swap left branches
    LLINK(succ) = LLINK(p);
    LLINK(p)    = Node::NullPtr; 
 
    // Swap right branches (two cases)
    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; 
      }
 
    // Swap colors
    Color tmp   = COLOR(succ);
    COLOR(succ) = COLOR(p); 
    COLOR(p)    = tmp;
  }
 
  static void findPredAndSwap(Node *p, Node *&fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(LLINK(p) != Node::NullPtr);
    assert(fp != Node::NullPtr);
    assert(LLINK(fp) == p or RLINK(fp) == 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);
      }
 
    // Update parent of p to point to pred
    if (LLINK(fp) == p)
      LLINK(fp) = pred;
    else
      RLINK(fp) = pred;
    
    // Swap right branches
    RLINK(pred) = RLINK(p);
    RLINK(p)    = Node::NullPtr; 
 
    // Swap left branches (two cases)
    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; 
      }
 
    // Swap colors
    Color tmp   = COLOR(pred);
    COLOR(pred) = COLOR(p); 
    COLOR(p)    = tmp;
  }
 
  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) noexcept
  {
    Node *p   = root;
    fp        = head;
    Node *ffp = fHead;
 
    colorRootAsRed();
 
    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;
            p = gotoLeftAndColorRed(fp, ffp);
          }
        else
          {
            if (RLINK(p) == Node::NullPtr)
              return p;
            p = gotoRightAndColorRed(fp, ffp);
          }
      }
  }
 
  static void removeAndRendLeafRed(Node *p, Node *fp) noexcept
  {
    assert(p != Node::NullPtr);
    assert(fp != Node::NullPtr);
    assert(LLINK(fp) == p or RLINK(fp) == p);
 
    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;
    COLOR(head) = BLACK;
    num_nodes = 0;
  }
 
public:
  GenTdRbTree() noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()), cmp()
  {
    init();
  }
 
  explicit GenTdRbTree(const Compare & __cmp) noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()), cmp(__cmp)
  {
    init();
  }
 
  GenTdRbTree(GenTdRbTree && other) noexcept
    : head(&headNode), fHead(&headParent), root(headNode.getR()),
      cmp(std::move(other.cmp)), num_nodes(other.num_nodes)
  {
    RLINK(fHead) = head;
    COLOR(Node::NullPtr) = BLACK;
    COLOR(head) = BLACK;
    root = other.root;
    other.root = Node::NullPtr;
    other.num_nodes = 0;
  }
 
  GenTdRbTree & operator=(GenTdRbTree && other) noexcept
  {
    if (this != &other)
      {
        root = other.root;
        num_nodes = other.num_nodes;
        cmp = std::move(other.cmp);
        other.root = Node::NullPtr;
        other.num_nodes = 0;
      }
    return *this;
  }
 
  GenTdRbTree(const GenTdRbTree &) = delete;
  
  GenTdRbTree & operator=(const GenTdRbTree &) = delete;
 
  void reset() noexcept
  {
    root = Node::NullPtr;
    num_nodes = 0;
  }
 
  void swap(GenTdRbTree & other) noexcept
  {
    std::swap(root, other.root);
    std::swap(num_nodes, other.num_nodes);
    std::swap(cmp, other.cmp);
  }
 
  virtual ~GenTdRbTree() = default;
 
  size_t size() const noexcept { return num_nodes; }
 
  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);
    assert(LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr);
 
    if (root == Node::NullPtr)
      {
        root = p;
        ++num_nodes;
        return p;
      }
 
    return searchFlipColorsAndInsert(p);
  }
 
  Node* insert_dup(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == RED);
    assert(LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr);
 
    if (root == Node::NullPtr)
      {
        root = p;
        ++num_nodes;
        return p;
      }
 
    return searchFlipColorsAndInsertDup(p);
  }
 
  Node* search_or_insert(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(COLOR(p) == RED);
    assert(LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr);
 
    if (root == Node::NullPtr)
      {
        root = p;
        ++num_nodes;
        return p;
      }
 
    // Search first
    Node *found = search(KEY(p));
    if (found != nullptr)
      return found;  // Return existing node
 
    // Not found, insert
    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 *fp;
    Node *p = searchAndColorRed(key, fp);
 
    if (not equals(KEY(p), key))
      return nullptr;
 
    removeAndRendLeafRed(p, fp);
    --num_nodes;
 
    return p;
  }
 
  Node*& getRoot() noexcept { return root; }
  
  Node* getRoot() const noexcept { return root; }
 
private:
  static bool testBlackHeight(Node *p, int &max, int bh = 0) noexcept
  {
    if (p == Node::NullPtr)
      return true;
 
    if (COLOR(p) == BLACK)
      ++bh;
 
    if (LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr)
      {
        if (max == -1)
          max = bh;
        return bh == max;
      }
 
    return testBlackHeight(LLINK(p), max, bh)
        and testBlackHeight(RLINK(p), max, bh);
  }
 
  static bool testNode(Node* p) noexcept
  {
    if (p == Node::NullPtr)
      return true;
      
    // Red nodes must have black children
    if (COLOR(p) == RED and
        not (COLOR(LLINK(p)) == BLACK and COLOR(RLINK(p)) == BLACK))
      return false;
 
    int max = -1;
    int bh  = 0;
 
    return testBlackHeight(p, max, bh);
  }
 
  static bool verify(Node* p) noexcept
  {
    if (p == Node::NullPtr)
      return true;
    if (not testNode(p))
      return false;
    return verify(LLINK(p)) and verify(RLINK(p));
  }
 
public:
  bool verifyRedBlack() const noexcept
  {
    if (root == Node::NullPtr)
      return true;
    return verify(root);
  }
 
  bool verify() const noexcept { return verifyRedBlack(); }
 
  struct Iterator : public BinNodeInfixIterator<Node>
  {
    Iterator(GenTdRbTree & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
    Iterator(const GenTdRbTree & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
  };
};
 
template <typename Key, class Compare = std::less<Key>>
class TdRbTree : public GenTdRbTree<RbNode, Key, Compare>
{
  using Base = GenTdRbTree<RbNode, Key, Compare>;
public:
  using Base::Base;
};
 
template <typename Key, class Compare = std::less<Key>>
class TdRbTreeVtl : public GenTdRbTree<RbNodeVtl, Key, Compare>
{
  using Base = GenTdRbTree<RbNodeVtl, Key, Compare>;
public:
  using Base::Base;
};
 
} // namespace Aleph
 
# endif /* TPL_TDRBTREE_H */