红黑树各种操作思路见 从B-树角度理解红黑树背后的原理 ，本文是红黑树的C++实现。但并没有全面的测试，如果大家发现了bug，欢迎指出。
本文的红黑树是从前面的BST继承而来，也是用到了AVL中用到的3+4重构和旋转操作。编译时要用到前面的BST.h Bintree.h 以及vector、stack、queue这些数据结构。
所有源代码地址：yalewoo/cpp-data-structure · GitHub
RBTree.h
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#ifndef RBTREE_H #define RBTREE_H #include "BST.h" #define IsBlack(x) ( (x) == 0 || (x)->color == BLACK ) #define IsRed(x) ( !IsBlack(x) ) template <typename T> class RBT : public BST<T>{ public: RBT(); virtual BinNodePosi(T) insert(const T &); virtual bool remove(const T &); protected: using BST<T>::_root; using BST<T>::_size; using BST<T>::_hot; using BST<T>::search; using BST<T>::siblingOf; using BST<T>::connect34; using BST<T>::removeAt; void solveDoubleRed(BinNodePosi(T) x); void solveDoubleBlack(BinNodePosi(T) r); void rotateLL(BinNodePosi(T) t1, BinNodePosi(T) t2); void rotateRR(BinNodePosi(T) t2, BinNodePosi(T) t1); virtual int updateHeight(BinNodePosi(T) x); }; //更新某结点的黑高度 template <typename T> int RBT<T>::updateHeight(BinNodePosi(T) x) { if (!x) return -1; x->height = max(stature(x->lchild), stature(x->rchild)); if (x->color == BLACK) ++x->height; return x->height; } template <typename T> RBT<T>::RBT() { _hot = 0; _size = 0; } template <typename T> BinNodePosi(T) RBT<T>::insert(const T & e) { BinNodePosi(T) p = search(e); if (p != NULL && p->data == e) //already exist { return p; } BinNodePosi(T) x = BST<T>::insert(e); p = x->parent; //新插入结点是根节点时 if (p == 0) { x->color = BLACK; x->height = 1; return x; } x->color = RED; //若p结点是黑色 红黑树的性质没有破坏 if (p->color == BLACK) { return x; } //若p是红色 出现双红缺陷 solveDoubleRed(x); //++_size; return x; } template <typename T> void RBT<T>::solveDoubleRed(BinNodePosi(T) x) { BinNodePosi(T) p = x->parent; BinNodePosi(T) g = p->parent; BinNodePosi(T) u = siblingOf(p); if (IsBlack(u)) //情况2.1 p红u黑 { BinNodePosi(T) par = g->parent; enum {ROOT, LEFT, RIGHT} ptoc; if (g->parent) { if (g == g->parent->lchild) ptoc = LEFT; else ptoc = RIGHT; } else ptoc = ROOT; BinNodePosi(T) t1; BinNodePosi(T) t2; BinNodePosi(T) t3; BinNodePosi(T) st1; BinNodePosi(T) st2; BinNodePosi(T) st3; BinNodePosi(T) st4; if (g->lchild && x == g->lchild->lchild) { t1 = x; t2 = p; t3 = g; st1 = x->lchild; st2 = x->rchild; st3 = p->rchild; st4 = g->rchild; } else if (g->lchild && x == g->lchild->rchild) { t1 = p; t2 = x; t3 = g; st1 = p->lchild; st2 = x->lchild; st3 = x->rchild; st4 = g->rchild; } else if (g->rchild && x == g->rchild->lchild) { t1 = g; t2 = x; t3 = p; st1 = g->lchild; st2 = x->lchild; st3 = x->rchild; st4 = p->rchild; } else { t1 = g; t2 = p; t3 = x; st1 = g->lchild; st2 = p->lchild; st3 = x->lchild; st4 = x->rchild; } t2->parent = par; switch (ptoc) { case ROOT : _root = t2; break; case LEFT : par->lchild = t2; break; case RIGHT : par->rchild = t2; break; } connect34(t1, t2, t3, st1, st2, st3, st4); t2->color = BLACK; t1->color = RED; t3->color = RED; t2->height++; t3->height--; } else //情况2.2 p红u红 { p->color = BLACK; u->color = BLACK; g->color = RED; p->height++; g->height--; if (g->parent == 0) g->color = BLACK; else if (IsRed(g->parent)) solveDoubleRed(g); } } template <typename T> bool RBT<T>::remove(const T & e) { //如果已存在则返回false BinNodePosi(T) x = search(e); if (!x) return false; //左右孩子都存在时，与中序后继交换元素 保证删除时有一个孩子为空 if (x->lchild && x->rchild) { BinNodePosi(T) p = x->succ(); T tmp = x->data; x->data = p->data; p->data = tmp; x = p; } BinNodePosi(T) r = removeAt(x); //如果删除后变为空树 直接返回 if ((_size) == 0) return true; //如果删除的是根节点重新将根节点染黑 并更新高度 if (_hot == 0) { _root->color = BLACK; updateHeight(_root); return true; } //x和r有一个为红 if (IsRed(x) || IsRed(r)) { if (IsRed(r)) r->color = BLACK; return true; } else { solveDoubleBlack(r); } delete x; return true; } template <typename T> void RBT<T>::solveDoubleBlack(BinNodePosi(T) r) { BinNodePosi(T) p = r ? r->parent : _hot; if (p == 0) return; BinNodePosi(T) s = ( r == p->lchild ? p->rchild : p->lchild ); if (IsBlack(s)) { if ( IsRed(s->lchild) || IsRed(s->rchild) ) //情况1 s为黑 t为红 { BinNodePosi(T) t; if (IsRed(s->rchild)) t = s->rchild; if (IsRed(s->lchild)) t = s->lchild; BinNodePosi(T) g = p; BinNodePosi(T) p1 = s; BinNodePosi(T) x = t; BinNodePosi(T) par = g->parent; enum {ROOT, LEFT, RIGHT} ptoc; if (g->parent) { if (g == g->parent->lchild) ptoc = LEFT; else ptoc = RIGHT; } else ptoc = ROOT; BinNodePosi(T) t1; BinNodePosi(T) t2; BinNodePosi(T) t3; BinNodePosi(T) st1; BinNodePosi(T) st2; BinNodePosi(T) st3; BinNodePosi(T) st4; if (g->lchild && x == g->lchild->lchild) { t1 = x; t2 = p1; t3 = g; st1 = x->lchild; st2 = x->rchild; st3 = p1->rchild; st4 = g->rchild; } else if (g->lchild && x == g->lchild->rchild) { t1 = p1; t2 = x; t3 = g; st1 = p1->lchild; st2 = x->lchild; st3 = x->rchild; st4 = g->rchild; } else if (g->rchild && x == g->rchild->lchild) { t1 = g; t2 = x; t3 = p1; st1 = g->lchild; st2 = x->lchild; st3 = x->rchild; st4 = p1->rchild; } else { t1 = g; t2 = p1; t3 = x; st1 = g->lchild; st2 = p1->lchild; st3 = x->lchild; st4 = x->rchild; } t2->parent = par; switch (ptoc) { case ROOT : _root = t2; break; case LEFT : par->lchild = t2; break; case RIGHT : par->rchild = t2; break; } connect34(t1, t2, t3, st1, st2, st3, st4); t2->color = g->color; t1->color = BLACK; t3->color = BLACK; } else //情况2 s为黑 s的两个孩子为黑 { s->color = RED; --s->height; if (IsRed(p)) //情况2.1 s为黑 s的两个孩子均为黑 p为红 { p->color = BLACK; } else //s为黑 s的两个孩子均为黑 p为黑 { p->height--; solveDoubleBlack(p); } } } else //情况3 s为红 { if (s == p->lchild) { rotateLL(s, p); } else { rotateRR(s, p); } s->color = BLACK; p->color = RED; solveDoubleBlack(r); } } template <typename T> void RBT<T>::rotateLL(BinNodePosi(T) t1, BinNodePosi(T) t2) { //t2 --> st2 t2->lchild = t1->rchild; //st2 --> t1 if (t1->rchild) t1->rchild->parent = t2; //t1 --> t2 t1->rchild = t2; //父节点 --> t1（树根情况） if (t2->parent == NULL) { t1->parent = NULL; this->_root = t1; t2->parent = t1; return; } //t1 --> 父节点 t1->parent = t2->parent; //父节点 --> t1（非树根） if (t2->parent->lchild == t2) t2->parent->lchild = t1; else t2->parent->rchild = t1; //t2 --> t1 t2->parent = t1; } template <typename T> void RBT<T>::rotateRR(BinNodePosi(T) t2, BinNodePosi(T) t1) { //t1 --> st2 t1->rchild = t2->lchild; //st2 --> t1 if (t2->lchild) t2->lchild->parent = t1; //t2 --> t1 t2->lchild = t1; //父节点 --> t2（树根） if (t1->parent == NULL) { this->_root = t2; t2->parent = NULL; t1->parent = t2; return; } //t2 --> 父节点 t2->parent = t1->parent; //父节点 --> t2（非树根） if (t1->parent->lchild == t1) t1->parent->lchild = t2; else t1->parent->rchild = t2; //t1 --> t2 t1->parent = t2; } #endif |
RBTree.cpp
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#include <iostream> #include "RBTree.h" int main() { RBT<int> rb; rb.insert(12); rb.display(); rb.insert(1); rb.display(); rb.insert(9); rb.display(); rb.insert(2); rb.display(); rb.insert(0); rb.display(); rb.insert(11); rb.display(); rb.insert(7); rb.display(); rb.insert(5); rb.display(); rb.insert(4); rb.display(); rb.display(); rb.remove(12); rb.display(); rb.remove(1); rb.display(); rb.remove(9); rb.display(); rb.remove(2); rb.display(); rb.remove(0); rb.display(); rb.remove(11); rb.display(); rb.remove(7); rb.display(); rb.remove(5); rb.display(); rb.remove(4); rb.display(); rb.display(); return 0; } |
使用QT显示红黑树
和二叉树的显示代码基本一致，不同的只是把画板中的BST改成RBT，画的时候根据结点颜色来修改画刷颜色。
运行效果
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