使用C语言实现一个红黑树

红黑树是一种平衡二叉搜索树，它的操作包括插入、删除和查找。下面是一个使用C语言实现红黑树的示例代码：

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

typedef enum { RED, BLACK } Color;

typedef struct Node {
    int key;
    Color color;
    struct Node *left, *right, *parent;
} Node;

Node *createNode(int key) {
    Node *node = (Node *)malloc(sizeof(Node));
    node->key = key;
    node->color = RED;
    node->left = node->right = node->parent = NULL;
    return node;
}

void leftRotate(Node **root, 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;
}

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

void insertFixup(Node **root, 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(root, z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                rightRotate(root, 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(root, z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                leftRotate(root, z->parent->parent);
            }
        }
    }
    (*root)->color = BLACK;
}

void insert(Node **root, int key) {
    Node *z = createNode(key);
    Node *y = NULL;
    Node *x = *root;
    while (x != NULL) {
        y = x;
        if (z->key < x->key)
            x = x->left;
        else
            x = x->right;
    }
    z->parent = y;
    if (y == NULL)
        *root = z;
    else if (z->key < y->key)
        y->left = z;
    else
        y->right = z;
    insertFixup(root, z);
}

void inorderTraversal(Node *node) {
    if (node == NULL)
        return;
    inorderTraversal(node->left);
    printf("%d ", node->key);
    inorderTraversal(node->right);
}

int main() {
    Node *root = NULL;
    int keys[] = {10, 20, 30, 15, 18, 25, 40};
    int n = sizeof(keys) / sizeof(keys[0]);
    for (int i = 0; i < n; i++)
        insert(&root, keys[i]);
    inorderTraversal(root);
    return 0;
}

这个示例代码实现了红黑树的插入操作和中序遍历操作。在插入新节点时，需要按照二叉搜索树的规则找到它应该插入的位置，然后根据红黑树的规则进行修复。修复过程中需要进行左旋和右旋操作，以保证树的平衡性。在最后输出中序遍历结果时，可以看到红黑树的特征：所有红色节点都有黑色父节点，树的高度比普通二叉搜索树低，从而提高了插入、删除和查找的效率。