红黑树的rotation是什么

红黑树的rotation是指通过旋转节点来保持红黑树的平衡。旋转操作有两种：左旋和右旋。左旋是指将一个节点的右子节点旋转到该节点的位置，同时该节点成为其右子节点的左子节点。右旋是指将一个节点的左子节点旋转到该节点的位置，同时该节点成为其左子节点的右子节点。旋转操作可以保持红黑树的性质不变，同时也可以使得红黑树的结构更加平衡。

相关问题

红黑树和树的区别，啥时候变成红黑树

红黑树是一种自平衡的二叉查找树，它在保持二叉搜索树特性的同时，通过额外的颜色标记（红色和黑色），保证了在最坏情况下的操作性能。红黑树的主要区别于普通二叉树在于其结构约束：

1. 每个节点要么是红色，要么是黑色。
2. 根节点是黑色。
3. 所有叶子节点（空节点）都是黑色。
4. 如果一个节点是红色，那么它的两个子节点必须是黑色。
5. 从任一节点到其所有后代叶节点的简单路径上，均包含相同数目的黑色节点。

当插入或删除操作导致红黑树的性质不再满足时，就需要进行调整，这个过程称为“重新着色”（re-coloring）或“旋转”（rotation）。比如，在插入新节点后可能导致某个路径上有过多的红色节点，这时需要通过变色和旋转操作将其恢复到红黑树的状态，以维持其性能保证。

生成一个红黑树代码C++

### 回答1：

这是一段简单的红黑树代码C：#include<stdio.h>

struct node
{
int key;
struct node *left, *right;
int color;
};

// A Red-Black tree node structure
struct node *newNode(int key)
{
struct node *temp = (struct node *)malloc(sizeof(struct node));

temp->key = key;
temp->left = temp->right = NULL;
temp->color = 1; // 1 for red, 0 for black

return temp;
}

// A utility function to right rotate subtree rooted with y
// See the diagram given above.
struct node *rightRotate(struct node *y)
{
struct node *x = y->left;
struct node *T2 = x->right;

// Perform rotation
x->right = y;
y->left = T2;

// Return new root
return x;
}

// A utility function to left rotate subtree rooted with x
// See the diagram given above.
struct node *leftRotate(struct node *x)
{
struct node *y = x->right;
struct node *T2 = y->left;

// Perform rotation
y->left = x;
x->right = T2;

// Return new root
return y;
}

// This function fixes the Red-Black tree
void fixViolation(struct node *temp)
{
struct node *parent_temp = NULL;
struct node *grand_parent_temp = NULL;

while ((temp != root) && (temp->color != 0) &&
(temp->parent->color == 1))
{

parent_temp = temp->parent;
grand_parent_temp = temp->parent->parent;

/* Case : A
Parent of temp is left child of Grand-parent of temp */
if (parent_temp == grand_parent_temp->left)
{

struct node *uncle_temp = grand_parent_temp->right;

/* Case : 1
The uncle of temp is also red
Only Recoloring required */
if (uncle_temp != NULL && uncle_temp->color == 1)
{
grand_parent_temp->color = 1;
parent_temp->color = 0;
uncle_temp->color = 0;
temp = grand_parent_temp;
}

else
{
/* Case : 2
temp is right child of its parent
Left-rotation required */
if (temp == parent_temp->right)
{
temp = parent_temp;
leftRotate(temp);
}

/* Case : 3
temp is left child of its parent
Right-rotation required */
rightRotate(grand_parent_temp);
swap(parent_temp->color,
grand_parent_temp->color);
temp = parent_temp;
}
}

/* Case : B
Parent of temp is right child of Grand-parent of temp */
else
{
struct node *uncle_temp = grand_parent_temp->left;

/* Case : 1
The uncle of temp is also red
Only Recoloring required */
if ((uncle_temp != NULL) && (uncle_temp->color == 1))
{
grand_parent_temp->color = 1;
parent_temp->color = 0;
uncle_temp->color = 0;
temp = grand_parent_temp;
}
else
{
/* Case : 2
temp is left child of its parent
Right-rotation required */
if (temp == parent_temp->left)
{
temp = parent_temp;
rightRotate(temp);
}

/* Case : 3
temp is right child of its parent
Left-rotation required */
leftRotate(grand_parent_temp);
swap(parent_temp->color,
grand_parent_temp->color);
temp = parent_temp;
}
}
}

root->color = 0;
}

### 回答2：
红黑树（Red-Black Tree）是一种自平衡的二叉搜索树，它的每个节点都具有一个颜色属性，可以是红色或黑色。红黑树具有以下几个性质：

1. 每个节点要么是红色，要么是黑色。
2. 根节点是黑色。
3. 叶子节点（NIL节点，空节点）是黑色。
4. 如果一个节点是红色，则它的两个子节点都是黑色（不能出现连续的红色节点）。
5. 对于每个节点，从该节点到其子孙节点的所有路径上包含相同数目的黑色节点。

以下是一个简单实现红黑树的C代码：

#include <stdio.h>
#include <stdlib.h>

enum Color {RED, BLACK};

// 红黑树节点结构定义
typedef struct node {
    int data;
    enum Color color;
    struct node *left, *right, *parent;
} Node;

// 红黑树结构定义
typedef struct rbtree {
    Node *root;
    Node *nil;
} RBTree;

// 左旋操作
void leftRotate(RBTree *tree, Node *x) {
    Node *y = x->right;
    
    x->right = y->left;
    if (y->left != tree->nil) {
        y->left->parent = x;
    }
    
    y->parent = x->parent;
    if (x->parent == tree->nil) {
        tree->root = y;
    } else if (x == x->parent->left) {
        x->parent->left = y;
    } else {
        x->parent->right = y;
    }
    
    y->left = x;
    x->parent = y;
}

// 右旋操作
void rightRotate(RBTree *tree, Node *y) {
    Node *x = y->left;
    
    y->left = x->right;
    if (x->right != tree->nil) {
        x->right->parent = y;
    }
    
    x->parent = y->parent;
    if (y->parent == tree->nil) {
        tree->root = x;
    } else if (y == y->parent->left) {
        y->parent->left = x;
    } else {
        y->parent->right = x;
    }
    
    x->right = y;
    y->parent = x;
}

// 插入操作的修复
void insertFixup(RBTree *tree, Node *z) {
    while (z->parent->color == RED) {
        if (z->parent == z->parent->parent->left) {
            Node *y = z->parent->parent->right;
            if (y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->right) {
                    z = z->parent;
                    leftRotate(tree, z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                rightRotate(tree, z->parent->parent);
            }
        } else {
            Node *y = z->parent->parent->left;
            if (y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->left) {
                    z = z->parent;
                    rightRotate(tree, z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                leftRotate(tree, z->parent->parent);
            }
        }
    }
    
    tree->root->color = BLACK;
}

// 插入操作
void insert(RBTree *tree, int data) {
    Node *z = (Node *) malloc(sizeof(Node));
    z->data = data;
    z->color = RED;
    z->left = tree->nil;
    z->right = tree->nil;
    
    Node *y = tree->nil;
    Node *x = tree->root;
    
    while (x != tree->nil) {
        y = x;
        if (z->data < x->data) {
            x = x->left;
        } else {
            x = x->right;
        }
    }
    
    z->parent = y;
    if (y == tree->nil) {
        tree->root = z;
    } else if (z->data < y->data) {
        y->left = z;
    } else {
        y->right = z;
    }
    
    insertFixup(tree, z);
}

// 中序遍历
void inorderTraversal(RBTree *tree, Node *root) {
    if (root != tree->nil) {
        inorderTraversal(tree, root->left);
        printf("%d ", root->data);
        inorderTraversal(tree, root->right);
    }
}

int main() {
    RBTree tree;
    Node nilNode;
    
    tree.nil = &nilNode;
    tree.nil->color = BLACK;
    
    tree.root = tree.nil;
    
    // 插入节点
    insert(&tree, 5);
    insert(&tree, 2);
    insert(&tree, 7);
    insert(&tree, 1);
    insert(&tree, 3);
    insert(&tree, 6);
    insert(&tree, 8);
    
    // 中序遍历输出
    inorderTraversal(&tree, tree.root);
    printf("\n");
    
    return 0;
}

以上代码实现了红黑树的插入操作，并通过中序遍历的方式输出了插入后的红黑树节点数据。可以根据需要修改插入数据和遍历方式来进行测试。

### 回答3：
红黑树是一种自平衡的二叉搜索树，其在插入和删除操作后通过一系列旋转和重新着色操作来保持平衡。

下面是一个简单的红黑树的 C 代码实现：

#include <stdio.h>
#include <stdlib.h>

// 定义红黑树的节点结构
typedef struct Node {
    int data;           // 节点存储的数据
    enum { RED, BLACK } color;  // 节点的颜色
    struct Node *parent;  // 指向父节点的指针
    struct Node *left;    // 指向左子节点的指针
    struct Node *right;   // 指向右子节点的指针
} Node;

// 全局变量，表示红黑树的根节点
Node *root = NULL;

// 左旋操作
void leftRotate(Node *x) {
    Node *y = x->right;
    x->right = y->left;
    if (y->left != NULL) {
        y->left->parent = x;
    }
    y->parent = x->parent;
    if (x->parent == NULL) {
        root = y;
    } else if (x == x->parent->left) {
        x->parent->left = y;
    } else {
        x->parent->right = y;
    }
    y->left = x;
    x->parent = y;
}

// 右旋操作
void rightRotate(Node *x) {
    Node *y = x->left;
    x->left = y->right;
    if (y->right != NULL) {
        y->right->parent = x;
    }
    y->parent = x->parent;
    if (x->parent == NULL) {
        root = y;
    } else if (x == x->parent->left) {
        x->parent->left = y;
    } else {
        x->parent->right = y;
    }
    y->right = x;
    x->parent = y;
}

// 插入操作
void insert(int data) {
    Node *node = (Node *)malloc(sizeof(Node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->color = RED;

    Node *y = NULL;
    Node *x = root;
    while (x != NULL) {
        y = x;
        if (data < x->data) {
            x = x->left;
        } else {
            x = x->right;
        }
    }
    node->parent = y;
    if (y == NULL) {
        root = node;
    } else if (data < y->data) {
        y->left = node;
    } else {
        y->right = node;
    }

    insertFixup(node);
}

// 插入修正操作
void insertFixup(Node *z) {
    while (z->parent != NULL && z->parent->color == RED) {
        if (z->parent == z->parent->parent->left) {
            Node *y = z->parent->parent->right;
            if (y != NULL && y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->right) {
                    z = z->parent;
                    leftRotate(z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                rightRotate(z->parent->parent);
            }
        } else {
            Node *y = z->parent->parent->left;
            if (y != NULL && y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->left) {
                    z = z->parent;
                    rightRotate(z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                leftRotate(z->parent->parent);
            }
        }
    }
    root->color = BLACK;
}

// 中序遍历输出红黑树
void inorderTraversal(Node *node) {
    if (node != NULL) {
        inorderTraversal(node->left);
        printf("%d\n", node->data);
        inorderTraversal(node->right);
    }
}

int main() {
    insert(5);
    insert(3);
    insert(8);
    insert(1);
    insert(4);
    insert(6);
    insert(9);

    printf("红黑树中序遍历结果：\n");
    inorderTraversal(root);

    return 0;
}

该代码实现了红黑树的基本操作，包括左旋、右旋、插入和插入修正等。每个节点包含数据、颜色和指向父节点、左子节点和右子节点的指针。插入操作使用了插入修正来保持红黑树的平衡性。

通过在 `main` 函数中插入一些数据，即可得到生成的红黑树，并通过中序遍历输出树中节点的数据，以验证树结构是否正确。