Red-Black-Tree
This commit is contained in:
e2hang
370
BinaryTree/BalanceTree/Red-Black Tree/RBTree.h
Normal file
370
BinaryTree/BalanceTree/Red-Black Tree/RBTree.h
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@@ -0,0 +1,370 @@
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#pragma once
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#include <iostream>
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#include "TreeNode.h"
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template <class T>
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class RBTree {
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private:
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TreeNode<T>* root;
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TreeNode<T>* nul;
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int size;
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void initNul() {
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nul = new TreeNode<T>(0, nul, nul, nul);
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nul->color = Color::RED;
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}
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void inorder(TreeNode<T>* x);
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void dispose(TreeNode<T>* x) {
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if (x == nullptr || x == nul) return;
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dispose(x->left);
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dispose(x->right);
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delete x;
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//<2F>ص㲻<D8B5><E3B2BB>delete nul<75><6C><EFBFBD><EFBFBD>Ϊȫ<CEAA>ֵ<EFBFBD><D6B5>ڱ<EFBFBD><DAB1><EFBFBD>
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}
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public:
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RBTree() : size(0) { initNul(); root = nul; }
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RBTree(TreeNode<T>* r, int s) : root(r), size(s) { initNul(); }
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~RBTree() {
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dispose(root);
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root = nullptr;
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delete nul;
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//ɾ<><C9BE><EFBFBD>ڱ<EFBFBD><DAB1><EFBFBD><EFBFBD><EFBFBD>Ҫɾ<D2AA><C9BE>
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}
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TreeNode<T>* RotateLeft(TreeNode<T>* x);//RR
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TreeNode<T>* RotateRight(TreeNode<T>* x);//LL
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void insert(const T& e);
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void fixinsert(TreeNode<T>* x);
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void fixdelete(TreeNode<T>* x);
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void inorder() { inorder(root); }
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void erase(const T& e);
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TreeNode<T>* find(const T& e);
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};
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template<class T>
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inline TreeNode<T>* RBTree<T>::RotateLeft(TreeNode<T>* x) {
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TreeNode<T>* y = x->right; // <20>Һ<EFBFBD><D2BA><EFBFBD>
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TreeNode<T>* T2 = y->left; // y <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ݴ<EFBFBD>
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// <20><><EFBFBD><EFBFBD>
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y->left = x;
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x->right = T2;
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// <20><><EFBFBD><EFBFBD> parent ָ<><D6B8>
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if (T2) T2->parent = x; // <20><><EFBFBD><EFBFBD> T2 <20><><EFBFBD><EFBFBD>
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y->parent = x->parent; // y <20><><EFBFBD><EFBFBD> x <20>ĸ<EFBFBD><C4B8>ڵ<EFBFBD>
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if (x->parent == nul) { // x <20>Ǹ<EFBFBD><C7B8>ڵ<EFBFBD>
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root = y;
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}
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else if (x == x->parent->left) {
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x->parent->left = y;
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}
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else {
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x->parent->right = y;
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}
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x->parent = y;
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return y; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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}
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template<class T>
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TreeNode<T>* RBTree<T>::RotateRight(TreeNode<T>* x) {
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//<2F><>parent<6E><74><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>ݹ飬ֱ<E9A3AC><D6B1><EFBFBD><EFBFBD>parent
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TreeNode<T>* y = x->left;
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TreeNode<T>* T2 = y->right;
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// <20><>ת
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y->right = x;
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x->left = T2;
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// <20><><EFBFBD><EFBFBD> parent ָ<><D6B8>
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if (T2) T2->parent = x; // <20><><EFBFBD><EFBFBD> T2 <20><><EFBFBD><EFBFBD>
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y->parent = x->parent; // y <20><><EFBFBD><EFBFBD> x <20>ĸ<EFBFBD><C4B8>ڵ<EFBFBD>
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if (x->parent == nul) { // x <20>Ǹ<EFBFBD><C7B8>ڵ<EFBFBD>
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root = y;
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}
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else if (x == x->parent->left) {
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x->parent->left = y;
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}
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else {
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x->parent->right = y;
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}
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x->parent = y;
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return y; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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}
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template<class T>
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inline void RBTree<T>::inorder(TreeNode<T>* x)
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{
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if (x == nul) return;
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inorder(x->left);
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std::cout << x->element << " ";
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inorder(x->right);
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}
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template<class T>
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inline void RBTree<T>::insert(const T& e)
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{
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TreeNode<T>* p = new TreeNode<T>(e, nul, nul, nul);
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TreeNode<T>* current = root;
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TreeNode<T>* parent = nul;
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//BST<53><54><EFBFBD>룬<EFBFBD><EBA3AC>parent<6E>Ͳ<EFBFBD><CDB2><EFBFBD>Ҫ<EFBFBD>ݹ<EFBFBD><DDB9>ڵ<EFBFBD><DAB5><EFBFBD>
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while (current != nul) {
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parent = current;
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if (e < parent->element) current = parent->left;
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else current = parent->right;
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}
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p->parent = parent;
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if (parent == nul) root = p;
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if (parent == nul) root = p;
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else if (e < parent->element) parent->left = p;
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else parent->right = p;
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//FixInsert
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fixinsert(p);
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}
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template<class T>
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inline void RBTree<T>::fixinsert(TreeNode<T>* x)
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{
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while (x != root && x->parent->color == Color::RED) {
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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (x->parent->parent->left == x->parent) {
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//<2F><><EFBFBD>ڵ<EFBFBD>
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if (x->parent->parent->right->color == Color::RED) {
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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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x->parent->color = x->parent->parent->right->color = Color::BLACK;
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x->parent->parent->color = Color::RED;
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//fixinsert(x->parent->parent);<3B>ݹ鲻<DDB9>ã<EFBFBD><C3A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ظ<EFBFBD><D8B8>жϣ<D0B6><CFA3><EFBFBD><EFBFBD>״<EFBFBD><D7B4><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD>ɫ
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x = x->parent->parent;
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continue;
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}
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if (x == x->parent->left) {
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//LL//<2F>ȱ<EFBFBD>ɫ<EFBFBD>游<EFBFBD><E6B8B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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x->parent->parent->color = Color::RED;
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x->parent->color = Color::BLACK;
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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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RotateRight(x->parent->parent);
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}
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//LR
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if (x == x->parent->right) {
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//<2F><><EFBFBD><EFBFBD>LL
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x = x->parent;
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RotateLeft(x);
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//<2F><><EFBFBD><EFBFBD>Ҫ<EFBFBD><D2AA>LL<4C>ˣ<EFBFBD><CBA3><EFBFBD>һ<EFBFBD><D2BB>ѭ<EFBFBD><D1AD><EFBFBD>Զ<EFBFBD><D4B6><EFBFBD><EFBFBD><EFBFBD>LL
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}
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}
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//else<73>Գ<EFBFBD><D4B3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD>ҽڵ<D2BD>
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else {
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//1-<2D><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (x->parent->parent->left->color == Color::RED) {
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x->parent->parent->left->color = Color::BLACK;
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x->parent->color = Color::BLACK;
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x->parent->parent->color = Color::RED;
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x = x->parent->parent;
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}
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//2-<2D><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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else {
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//2-1-RL -> <20><><EFBFBD><EFBFBD>ΪRR<52><52><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (x == x->parent->left) {
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x = x->parent;
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RotateRight(x);
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}
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//3-RR<52><52><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>2-1
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x->parent->color = Color::BLACK;
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x->parent->parent->color = Color::RED;
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RotateLeft(x->parent->parent);
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}
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}
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}
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root->color = Color::BLACK;
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}
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// x <20><>ʾ<EFBFBD><CABE>ɾ<EFBFBD><C9BE><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ㣨<DAB5><E3A3A8><EFBFBD><EFBFBD><EFBFBD><EFBFBD> nul <20>ڱ<EFBFBD><DAB1><EFBFBD>
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// ֻ<>е<EFBFBD><D0B5><EFBFBD>ɾ<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><DAB5>Ǻ<EFBFBD>ɫʱ<C9AB><CAB1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD><D2AA><EFBFBD><EFBFBD> fixdelete
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template<class T>
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void RBTree<T>::fixdelete(TreeNode<T>* x) {
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while (x != root && x->color == Color::BLACK) {
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// <20><><EFBFBD><EFBFBD>1<EFBFBD><31>x <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (x == x->parent->left) {
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TreeNode<T>* w = x->parent->right; // x <20><><EFBFBD>ֵܽڵ<DCBD>
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// case 1: <20>ֵ<EFBFBD><D6B5>Ǻ<EFBFBD>ɫ
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// -> <20><><EFBFBD>ֵ<EFBFBD>Ⱦ<EFBFBD>ڣ<EFBFBD><DAA3><EFBFBD><EFBFBD><EFBFBD>Ⱦ<EFBFBD>죬Ȼ<ECA3AC><C8BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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// -> ת<><D7AA>Ϊ<EFBFBD>ֵ<EFBFBD><D6B5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (w->color == Color::RED) {
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w->color = Color::BLACK;
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x->parent->color = Color::RED;
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RotateLeft(x->parent);
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w = x->parent->right; // <20><><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD>
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}
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// case 2: <20>ֵ<EFBFBD><D6B5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֶ<EFBFBD>ӣ<EFBFBD>w->left, w->right<68><74><EFBFBD><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ
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// -> <20><><EFBFBD>ֵ<EFBFBD>Ⱦ<EFBFBD>죬<EFBFBD>൱<EFBFBD>ڰ<EFBFBD> "<22><><EFBFBD><EFBFBD><EFBFBD>ĺ<EFBFBD>ɫ" <20><><EFBFBD>ϴ<EFBFBD><CFB4><EFBFBD>
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// -> <20><EFBFBD><DEB8><EFBFBD><EFBFBD>̼<EFBFBD><CCBC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ͻ<EFBFBD><CFBD><EFBFBD>
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if (w->left->color == Color::BLACK && w->right->color == Color::BLACK) {
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w->color = Color::RED;
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x = x->parent; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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}
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else {
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// case 3: <20>ֵ<EFBFBD><D6B5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD>ֵܵ<D6B5><DCB5>Һ<EFBFBD><D2BA><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ
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// -> <20>Ȱ<EFBFBD><C8B0>ֵ<EFBFBD>Ⱦ<EFBFBD>죬<EFBFBD><ECA3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ⱦ<EFBFBD>ڣ<EFBFBD>Ȼ<EFBFBD><C8BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD>
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// -> ת<><D7AA>Ϊ case 4
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if (w->right->color == Color::BLACK) {
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w->left->color = Color::BLACK;
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w->color = Color::RED;
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RotateRight(w);
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w = x->parent->right; // <20><><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD>
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}
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// case 4: <20>ֵ<EFBFBD><D6B5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD>ֵܵ<D6B5><DCB5>Һ<EFBFBD><D2BA><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ
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// -> <20><><EFBFBD>ֵ<EFBFBD><D6B5>滻<EFBFBD><E6BBBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ⱦ<EFBFBD>ڣ<EFBFBD><DAA3>ֵܵ<D6B5><DCB5>Һ<EFBFBD><D2BA><EFBFBD>Ⱦ<EFBFBD><C8BE>
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// -> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ף<EFBFBD><D7A3><EFBFBD><DEB8><EFBFBD><EFBFBD>ɣ<EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD>˳<EFBFBD>ѭ<EFBFBD><D1AD>
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w->color = x->parent->color;
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x->parent->color = Color::BLACK;
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w->right->color = Color::BLACK;
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RotateLeft(x->parent);
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x = root; // <20><><EFBFBD><EFBFBD>ѭ<EFBFBD><D1AD>
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}
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}
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// <20><><EFBFBD><EFBFBD>2<EFBFBD><32>x <20><><EFBFBD>Һ<EFBFBD><D2BA>ӣ<EFBFBD><D3A3>Գ<EFBFBD><D4B3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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else {
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TreeNode<T>* w = x->parent->left;
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if (w->color == Color::RED) {
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w->color = Color::BLACK;
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x->parent->color = Color::RED;
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RotateRight(x->parent);
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w = x->parent->left;
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}
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if (w->right->color == Color::BLACK && w->left->color == Color::BLACK) {
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w->color = Color::RED;
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x = x->parent;
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}
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else {
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if (w->left->color == Color::BLACK) {
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w->right->color = Color::BLACK;
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w->color = Color::RED;
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RotateLeft(w);
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w = x->parent->left;
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}
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w->color = x->parent->color;
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x->parent->color = Color::BLACK;
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w->left->color = Color::BLACK;
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RotateRight(x->parent);
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x = root;
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}
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}
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}
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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>֤ x <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ǹ<EFBFBD><C7B8><EFBFBD><EFBFBD><EFBFBD> nul<75><6C>
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x->color = Color::BLACK;
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}
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template<class T>
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inline void RBTree<T>::erase(const T& e)
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{
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TreeNode<T>* z = find(e);
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//1-BSTɾ<54><C9BE><EFBFBD><EFBFBD><EFBFBD>ã<EFBFBD><C3A3>ұ<EFBFBD><D2B1>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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TreeNode<T>* y = z; // ʵ<><CAB5>Ҫɾ<D2AA><C9BE><EFBFBD>Ľڵ㣨<DAB5><E3A3A8><EFBFBD><EFBFBD><EFBFBD><EFBFBD> z<><7A>Ҳ<EFBFBD><D2B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD> z <20>ĺ<EFBFBD><C4BA>̣<EFBFBD>
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TreeNode<T>* x; // y <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ㣨<DAB5><E3A3A8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ㣬Ҳ<E3A3AC><D2B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD> nul<75><6C>
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Color yOriginalColor = y->color; // <20><>¼ y <20><>ԭʼ<D4AD><CABC>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><C7B7><EFBFBD>Ҫ fixdelete
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// case 1: z û<><C3BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> z
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if (z->left == nul) {
|
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x = z->right; // <20><><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>
|
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// <20><> z <20>Ӹ<EFBFBD><D3B8>Ͽ<D7B6>
|
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if (z->parent == nul) root = x;
|
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else if (z == z->parent->left) z->parent->left = x;
|
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else z->parent->right = x;
|
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x->parent = z->parent;
|
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}
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// case 2: z û<><C3BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> z
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else if (z->right == nul) {
|
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x = z->left;
|
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if (z->parent == nul) root = x;
|
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else if (z == z->parent->left) z->parent->left = x;
|
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else z->parent->right = x;
|
||||
x->parent = z->parent;
|
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}
|
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// case 3: z <20><><EFBFBD>Һ<EFBFBD><D2BA>Ӷ<EFBFBD><D3B6><EFBFBD> -> <20>ҵ<EFBFBD> z <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
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else {
|
||||
// <20><> z <20>ĺ<EFBFBD><C4BA>̣<EFBFBD><CCA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ㣩
|
||||
y = z->right;
|
||||
while (y->left != nul) y = y->left;
|
||||
yOriginalColor = y->color; // <20><>¼<EFBFBD><C2BC><EFBFBD>̵<EFBFBD><CCB5><EFBFBD>ɫ
|
||||
x = (y->right != nul ? y->right : nul); // <20><><EFBFBD>̵<EFBFBD><CCB5>Һ<EFBFBD><D2BA><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA><EFBFBD><EFBFBD>
|
||||
|
||||
// <20><><EFBFBD><EFBFBD> y <20><><EFBFBD><EFBFBD> z <20><>ֱ<EFBFBD><D6B1><EFBFBD>Һ<EFBFBD><D2BA><EFBFBD>
|
||||
if (y->parent != z) {
|
||||
// <20><> y->right <20><><EFBFBD><EFBFBD> y
|
||||
if (y->parent->left == y) y->parent->left = x;
|
||||
else y->parent->right = x;
|
||||
x->parent = y->parent;
|
||||
|
||||
// <20><> z->right <20>ҵ<EFBFBD> y <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||||
y->right = z->right;
|
||||
y->right->parent = y;
|
||||
}
|
||||
|
||||
// <20><> z->left <20>ҵ<EFBFBD> y <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||||
if (z->parent == nul) root = y;
|
||||
else if (z == z->parent->left) z->parent->left = y;
|
||||
else z->parent->right = y;
|
||||
y->parent = z->parent;
|
||||
|
||||
y->left = z->left;
|
||||
y->left->parent = y;
|
||||
y->color = z->color;
|
||||
}
|
||||
delete z;
|
||||
|
||||
//2-RBT<42><54><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||||
// <20><><EFBFBD><EFBFBD>ɾ<EFBFBD><C9BE><EFBFBD><EFBFBD>ʵ<EFBFBD>ʽڵ<CABD><DAB5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ƻ<EFBFBD><C6BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><> fixdelete
|
||||
if (yOriginalColor == Color::BLACK) {
|
||||
fixdelete(x);
|
||||
}
|
||||
|
||||
}
|
||||
template<class T>
|
||||
inline TreeNode<T>* RBTree<T>::find(const T& e)
|
||||
{
|
||||
TreeNode<T>* p = root;
|
||||
while (p != nul) {
|
||||
if (e < p->element) p = p->left;
|
||||
else if (e > p->element) p = p->right;
|
||||
else break;
|
||||
}
|
||||
if (!p) p = nul;
|
||||
return p;
|
||||
}
|
||||
/*
|
||||
<EFBFBD>Ƽ<EFBFBD>д<EFBFBD><EFBFBD>
|
||||
if (x->parent == x->parent->parent->left) { // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||||
TreeNode<T>* y = x->parent->parent->right; // <20><><EFBFBD><EFBFBD>
|
||||
if (y->color == Color::RED) { // Case 1: <20><><EFBFBD><EFBFBD>
|
||||
x->parent->color = Color::BLACK;
|
||||
y->color = Color::BLACK;
|
||||
x->parent->parent->color = Color::RED;
|
||||
x = x->parent->parent; // <20><><EFBFBD><EFBFBD><EFBFBD>游
|
||||
} else {
|
||||
if (x == x->parent->right) { // Case 2: LR
|
||||
x = x->parent;
|
||||
RotateLeft(x);
|
||||
}
|
||||
// Case 3: LL
|
||||
x->parent->color = Color::BLACK;
|
||||
x->parent->parent->color = Color::RED;
|
||||
RotateRight(x->parent->parent);
|
||||
}
|
||||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>˳<EFBFBD><EFBFBD>д<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Կ<EFBFBD>else<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD>ҽڵ㣩<EFBFBD><EFBFBD>˼·
|
||||
*/
|
||||
263
BinaryTree/BalanceTree/Red-Black Tree/README.MD
Normal file
263
BinaryTree/BalanceTree/Red-Black Tree/README.MD
Normal file
@@ -0,0 +1,263 @@
|
||||
[TOC]
|
||||
## 红黑树插入思路
|
||||
好的，我们把 **红黑树插入的完整逻辑**整理一下，分步骤、分情况讲，保证清晰易懂：
|
||||
|
||||
---
|
||||
|
||||
## 🔹 红黑树插入逻辑
|
||||
|
||||
### 1️⃣ 基本步骤
|
||||
|
||||
1. **普通 BST 插入**
|
||||
|
||||
* 按二叉搜索树的规则，把新节点 `x` 插入到合适位置。
|
||||
* 新节点初始化为 **红色**（因为插入红色节点更容易维持黑高）。
|
||||
|
||||
2. **判断是否需要修复**
|
||||
``` cpp
|
||||
插入新节点 z (红色)
|
||||
|
|
||||
+-- 父是黑色 → OK，直接插入
|
||||
|
|
||||
+-- 父是红色
|
||||
|
|
||||
+-- 叔叔是红色 → 父黑叔黑，祖红，上移到祖父，继续检查
|
||||
|
|
||||
+-- 叔叔是黑色
|
||||
|
|
||||
+-- z 在父的同向（左左或右右） → Case 3，旋转 + 颜色交换
|
||||
+-- z 在父的异向（左右或右左） → Case 2，先旋转父，再变为同向，继续 Case 3
|
||||
```
|
||||
* 如果父节点是黑色 → 红黑性质不破坏，不需要 fix。
|
||||
* 如果父节点是红色 → 违反“红色节点不能有红色子节点”，需要修复。
|
||||
* 考虑叔叔是不是红的
|
||||
* ->叔叔是红的就 一起变黑，祖父变红
|
||||
* ->叔叔不是红的，考虑旋转+变色
|
||||
|
||||
---
|
||||
|
||||
### 2️⃣ fixinsert 修复逻辑
|
||||
|
||||
设：
|
||||
|
||||
* `x` = 当前插入节点
|
||||
* `p` = 父节点
|
||||
* `u` = 叔叔节点（父节点的兄弟）
|
||||
* `g` = 祖父节点
|
||||
|
||||
#### **情况 1：叔叔节点是红色**
|
||||
|
||||
* **条件**：`p` 是红色，`u` 是红色
|
||||
* **处理**：
|
||||
|
||||
1. 父节点 `p` 染黑
|
||||
2. 叔叔节点 `u` 染黑
|
||||
3. 祖父节点 `g` 染红
|
||||
4. 将 `x` 上移到祖父节点 `g`，继续循环判断
|
||||
* **原因**：通过重新染色，把红红冲突上移，保持黑高不变
|
||||
|
||||
---
|
||||
|
||||
#### **情况 2：叔叔节点是黑色**
|
||||
|
||||
* **条件**：`p` 是红色，`u` 是黑色
|
||||
* **子情况**（根据 `x` 在父节点的左右位置）：
|
||||
|
||||
1. **左-左（LL）**
|
||||
|
||||
* `x` 是 `p` 的左孩子，`p` 是 `g` 的左孩子
|
||||
* **处理**：
|
||||
|
||||
1. 父节点染黑，祖父染红
|
||||
2. 右旋祖父
|
||||
|
||||
2. **左-右（LR）**
|
||||
|
||||
* `x` 是 `p` 的右孩子，`p` 是 `g` 的左孩子
|
||||
* **处理**：
|
||||
|
||||
1. 左旋父节点（将 LR 转化为 LL）
|
||||
2. 再执行 LL 情况的右旋 + 染色
|
||||
|
||||
3. **右-右（RR）**
|
||||
|
||||
* 对称 LL：右孩子的右孩子插入
|
||||
* 左旋祖父 + 调整颜色
|
||||
|
||||
4. **右-左（RL）**
|
||||
|
||||
* 对称 LR：右孩子的左孩子插入
|
||||
* 右旋父节点 → 变成 RR → 左旋祖父 + 调整颜色
|
||||
|
||||
---
|
||||
|
||||
### 3️⃣ 循环终止
|
||||
|
||||
* 当父节点是黑色，或者到达根节点，循环结束
|
||||
* 最后 **根节点必须染黑**
|
||||
|
||||
---
|
||||
|
||||
### 🔹 总结关键点
|
||||
|
||||
1. **新节点红色** → 保持黑高不变
|
||||
2. **红红冲突** → 根据叔叔颜色分两类处理：
|
||||
|
||||
* 红色叔叔 → 上移染色
|
||||
* 黑色叔叔 → 旋转 + 染色
|
||||
3. **旋转 + 染色** → 只改变局部结构，保持整体 BST 和红黑性质
|
||||
4. **根节点保持黑色** → 保证树的黑高一致
|
||||
|
||||
---
|
||||
|
||||
如果你需要，我可以帮你画一张 **红黑树插入示意图**，把 LL/LR/RR/RL 四种旋转场景和颜色变化可视化，看起来非常直观。
|
||||
|
||||
你想让我画吗？
|
||||
|
||||
|
||||
## 红黑树删除思路
|
||||
好，我给你梳理一下 **红黑树删除的整体思路**，只讲逻辑，不贴代码：
|
||||
|
||||
---
|
||||
|
||||
### 1️⃣ 找到要删除的节点
|
||||
|
||||
* 首先按照普通二叉搜索树（BST）查找待删除节点 `z`。
|
||||
* 如果节点不存在，就结束。
|
||||
|
||||
---
|
||||
|
||||
### 2️⃣ 分情况处理节点
|
||||
|
||||
红黑树删除跟 BST 删除类似，分三种情况：
|
||||
|
||||
1. **节点没有子节点（叶子）**
|
||||
|
||||
* 直接把它从父节点断开。
|
||||
* 如果节点是黑色，删除会破坏黑高，需要修复。
|
||||
|
||||
2. **节点只有一个孩子**
|
||||
|
||||
* 用唯一的孩子替代该节点挂到父节点上。
|
||||
* 如果删除的是黑色节点，也可能破坏红黑性质，需要修复。
|
||||
|
||||
3. **节点有两个孩子**
|
||||
|
||||
* 找该节点的 **中序后继**（右子树最左的节点）替代它。
|
||||
* 删除后继节点（后继最多有一个右孩子），这一步退化为情况 1 或 2。
|
||||
* 然后把被删除节点的左右孩子接到后继上，继承颜色。
|
||||
* 如果后继原本是黑色，也需要修复。
|
||||
|
||||
---
|
||||
|
||||
### 3️⃣ 修复红黑树性质
|
||||
|
||||
* 删除黑色节点或用黑色节点替代时，会破坏 **黑高** 或 **红黑性质**。
|
||||
* 修复核心思路：
|
||||
|
||||
1. **兄弟节点红色** → 旋转并调整颜色，使兄弟变黑。
|
||||
2. **兄弟黑色，兄弟的孩子都是黑色** → 兄弟染红，把“双重黑”向上传递。
|
||||
3. **兄弟黑色，有红色侄子** → 旋转 + 染色，直接消除双重黑。
|
||||
* 修复循环一直执行，直到双重黑消除或者到达根节点。
|
||||
|
||||
---
|
||||
|
||||
### 4️⃣ 特别注意
|
||||
|
||||
* 根节点始终要保持黑色。
|
||||
* 删除过程尽量使用 **哨兵节点 `nul`** 替代空指针，避免每次判断 `nullptr`。
|
||||
* 删除逻辑主要是 **BST 替换 + fixdelete 修复** 两步结合。
|
||||
|
||||
---
|
||||
|
||||
简单总结一句话就是：
|
||||
|
||||
**“先按 BST 删除节点，再根据被删节点颜色决定是否修复，用旋转和染色处理双重黑。”**
|
||||
|
||||
好，我们把 **红黑树删除后修复的核心步骤**细化讲解一下，把每种情况的逻辑和原因都拆开看。假设删除后出现的节点 `x` 带有 **“双重黑”（double black）**，这是修复的触发条件。
|
||||
|
||||
---
|
||||
|
||||
## 🔹 修复红黑树性质（Double Black 处理）
|
||||
|
||||
### 情景概念
|
||||
|
||||
* 删除或替代节点是黑色 → 破坏了红黑树的黑高。
|
||||
* 我们用 `x` 表示替代节点（可能是哨兵 `nul`）。
|
||||
* `w` 表示 `x` 的兄弟节点。
|
||||
|
||||
---
|
||||
|
||||
### **情况 1：兄弟节点红色**
|
||||
|
||||
**条件**：`w->color == RED`
|
||||
|
||||
**处理逻辑**：
|
||||
|
||||
1. 把兄弟染黑，父节点染红。
|
||||
2. 对父节点做旋转（左旋或右旋，视 x 在左还是右）。
|
||||
3. 转换成“兄弟是黑色”的情况，进入下一轮循环处理。
|
||||
|
||||
**原因**：
|
||||
|
||||
* 红色兄弟意味着父节点必然是黑色（红黑性质），旋转后可以让黑高平衡，同时把问题转化为更容易处理的兄弟黑色情况。
|
||||
|
||||
---
|
||||
|
||||
### **情况 2：兄弟是黑色且兄弟两个孩子都是黑色**
|
||||
|
||||
**条件**：`w->color == BLACK && w->left->color == BLACK && w->right->color == BLACK`
|
||||
|
||||
**处理逻辑**：
|
||||
|
||||
1. 把兄弟染红。
|
||||
2. 把 x 的双重黑向父节点传递：`x = x->parent`，循环继续。
|
||||
|
||||
**原因**：
|
||||
|
||||
* 黑高减少发生在 x 所在的路径上。
|
||||
* 兄弟的两个子节点都是黑色 → 黑高没法补偿，只能把多余的黑色“向上递归”。
|
||||
|
||||
---
|
||||
|
||||
### **情况 3：兄弟是黑色且有红色侄子**
|
||||
|
||||
**条件**：`w->color == BLACK` 且至少有一个子节点红色
|
||||
|
||||
**处理逻辑**：
|
||||
|
||||
1. 如果 x 是左孩子：
|
||||
|
||||
* case RL：先对兄弟右旋，让红色侄子转到右侧。
|
||||
* case RR：父亲左旋，同时调整父亲、兄弟和红色侄子的颜色。
|
||||
2. 对称地，如果 x 是右孩子：
|
||||
|
||||
* case LR：先左旋兄弟
|
||||
* case LL：父亲右旋 + 染色
|
||||
|
||||
**原因**：
|
||||
|
||||
* 红色侄子可以“补偿”被删除黑色节点造成的黑高缺失。
|
||||
* 通过旋转和染色，双重黑立即消除，红黑树性质恢复。
|
||||
|
||||
---
|
||||
|
||||
### 🔹 循环结束条件
|
||||
|
||||
* 双重黑消除（x 被重新染黑或者到达根节点）。
|
||||
* 根节点必须保持黑色 → 最后再显式设置 `root->color = BLACK`。
|
||||
|
||||
---
|
||||
|
||||
💡 **直观理解**：
|
||||
|
||||
1. **红兄弟** → 转化问题
|
||||
2. **黑兄弟+黑侄子** → 往上递
|
||||
3. **黑兄弟+红侄子** → 补偿黑高，立即解决
|
||||
|
||||
---
|
||||
|
||||
如果你想，我可以画一张 **删除修复流程图**，用节点颜色标注每一步的旋转和染色，直观展示三种情况。
|
||||
|
||||
你希望我画吗？
|
||||
|
||||
16
BinaryTree/BalanceTree/Red-Black Tree/TreeNode.h
Normal file
16
BinaryTree/BalanceTree/Red-Black Tree/TreeNode.h
Normal file
@@ -0,0 +1,16 @@
|
||||
#pragma once
|
||||
enum Color { RED, BLACK };
|
||||
|
||||
template <class T>
|
||||
class TreeNode {
|
||||
public:
|
||||
T element;
|
||||
TreeNode<T>* left;
|
||||
TreeNode<T>* right;
|
||||
TreeNode<T>* parent;
|
||||
Color color;
|
||||
|
||||
TreeNode() : left(nullptr), right(nullptr), parent(nullptr), color(Color::RED) {}
|
||||
TreeNode(const T& e) : element(e), left(nullptr), right(nullptr), parent(nullptr), color(Color::RED) {}
|
||||
TreeNode(const T& e, TreeNode<T>* l, TreeNode<T>* r, TreeNode<T>* p) : element(e), left(l), right(r), parent(p), color(Color::RED) {}
|
||||
};
|
||||
21
BinaryTree/BalanceTree/Red-Black Tree/main.cpp
Normal file
21
BinaryTree/BalanceTree/Red-Black Tree/main.cpp
Normal file
@@ -0,0 +1,21 @@
|
||||
#include "RBTree.h"
|
||||
using namespace std;
|
||||
int main() {
|
||||
RBTree<int> t;
|
||||
//һ<><D2BB><EFBFBD><EFBFBD>עNILָ<4C><D6B8><EFBFBD><EFBFBD>ʹ<EFBFBD>ã<EFBFBD><C3A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ҳ<EFBFBD><D2B3>Ľڵ㶼Ҫ<E3B6BC><D2AA>NIL
|
||||
t.insert(8);
|
||||
t.insert(5);
|
||||
t.insert(3);
|
||||
t.insert(2);
|
||||
t.insert(7);
|
||||
t.insert(1);
|
||||
t.inorder();
|
||||
cout << endl;
|
||||
t.erase(7);
|
||||
t.inorder();
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
1 2 3 5 7 8
|
||||
1 2 3 5 8
|
||||
*/
|
||||
Reference in New Issue
Block a user