欢迎您访问新疆栾骏商贸有限公司，公司主营电子五金轴承产品批发业务！
全国咨询热线： 400-8878-609
新闻资讯
技术学院红黑树通过着色规则和旋转保持平衡，插入后修复以确保根黑、无连续红、黑高一致，C++实现包含左旋右旋与insertFixup，最终中序遍历验证有序性。
红黑树是一种自平衡的二叉搜索树（BST），它通过为每个节点着色（红色或黑色）并遵循特定规则来保持树的近似平衡，从而保证查找、插入和删除操作的时间复杂度为 O(log n)。下面用 C++ 实现一个基础的红黑树，包含插入操作和必要的旋转调整逻辑。
在实现前先明确红黑树必须满足的五条性质：
每个节点需要存储值、颜色、左右子节点指针和父节点指针：
enum Color { RED, BLACK };
struct Node {
int data;
Color color;
Node left, right, *parent;
Node(int data) : data(data), color(RED), left(nullptr), right(nullptr), parent(nullptr) {}};
旋转是维持红黑树平衡的核心操作。左旋用于处理右倾情况，右旋用于处理左倾中的特定问题。
void leftRotate(Node* &root, Node* x) {
Node* y = x->right;
x->right = y->left;
if (y->left != nullptr)
y->left->parent = x;
y->parent = x->parent;
if (x->parent == nullptr)
root = y;
else if (x == x->parent->left)
x->parent->left = y;
else
x->parent->right = y;
y->left = x;
x->parent = y;}
void rightRotate(Node &root, Node y) {
Node* x = y->left;
y->left = x->right;
if (x->right != nullptr)
x->right->parent = y;
x->parent = y->parent;
if (y->parent == nullptr)
root = x;
else if (y == y->parent->left)
y->parent->left = x;
else
y->parent->right = x;
x->right = y;
y->parent = x;}
插入新节点后，可能破坏红黑性质，需进行修复。新节点默认为红色，然后根据父节点颜色和叔节点状态分情况处理。
void insertFixup(Node* &root, Node* z) { while (z != root && z->parent->color == RED) { if (z->parent == z->parent->parent->left) { Node* uncle = z->parent->parent->right; if (uncle != nullptr && uncle->color == RED) { // 情况1：叔节点为红 z->parent->color = BLACK; uncle->color = BLACK; z->parent->parent->color = RED; z = z->parent->parent; } else { // 情况2：叔节点为黑且当前节点为右孩子 if (z == z->parent->right) { z = z->parent; leftRotate(root, z); } // 情况3：叔节点为黑且当前节点为左孩子 z->parent->color = BLACK; z->parent->parent->color = RED; rightRotate(root, z->parent->parent); } } else { Node* uncle = z->parent->parent->left; if (uncle != nullptr && uncle->color == RED) { z->parent->color = BLACK; uncle->color = BLACK; z->parent->parent->color = RED; z = z->parent->parent; } else { if (z == z->parent->left) { z = z->parent; rightRotate(root, z); } z->parent->color = BLACK; z->parent->parent->color = RED; leftRotate(root, z->parent->parent); } } } root->color = BLACK; // 根节点始终为黑 }
void insert(Node &root, int data) { Node z = new Node(data); Node y = nullptr; Node x = root;
while (x != nullptr) { y = x; if (z->data < x->data) x = x->left; else x = x->right; } z->parent = y; if (y == nullptr) root = z; else if (z->data < y->data) y->left = z; else y->right = z; insertFixup(root, z);}
以下是一个简单的测试主函数：
#includeusing namespace std; // 上述所有代码放在这里
void inorder(Node* root) { if (root != nullptr) { inorder(root->left); cout << root->data << " "; inorder(root->right); } }
int main() { Node* root = nullptr; insert(root, 10); insert(root, 20); insert(root, 30); insert(root, 15); insert(root, 25);
cout zuojiankuohaophpcnzuojiankuohaophpcn "Inorder traversal: "; inorder(root); cout zuojiankuohaophpcnzuojiankuohaophpcn endl; return 0;}
基本上就这些。这个实现涵盖了红黑树插入和旋转的核心机制。虽然没有包含删除操作（更复杂），但已足够理解其平衡原理。实际工程中可考虑使用 std::set 或 std::map，它们底层正是基于红黑树实现的。
) {
while (z != root && z->parent->color == RED) {
if (z->parent == z->parent->parent->left) {
Node* uncle = z->parent->parent->right;
if (uncle != nullptr && uncle->color == RED) {
// 情况1：叔节点为红
z->parent->color = BLACK;
uncle->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent;
} else {
// 情况2：叔节点为黑且当前节点为右孩子
if (z == z->parent->right) {
z = z->parent;
leftRotate(root, z);
}
// 情况3：叔节点为黑且当前节点为左孩子
z->parent->color = BLACK;
z->parent->parent->color = RED;
rightRotate(root, z->parent->parent);
}
} else {
Node* uncle = z->parent->parent->left;
if (uncle != nullptr && uncle->color == RED) {
z->parent->color = BLACK;
uncle->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent;
} else {
if (z == z->parent->left) {
z = z->parent;
rightRotate(root, z);
}
z->parent->color = BLACK;
z->parent->parent->color = RED;
leftRotate(root, z->parent->parent);
}
}
}
root->color = BLACK; // 根节点始终为黑
}