C语言实现毕达哥拉斯树 你需要知道的一切！

**毕达哥拉斯树（B-Tree）概述**

毕达哥拉斯树是一种自平衡的多叉查找树，主要用于数据库索引、文件系统等场景。它以其高效的查找性能和稳定的存储结构而闻名。毕达哥拉斯树的设计思想是，将数据分散在多个节点中，以便快速找到所需的信息。

**C语言实现毕达哥拉斯树**

下面是C语言实现毕达哥拉斯树的一些关键代码和注释：

### **btree.h**

c#ifndef BTREE_H#define BTREE_Htypedef struct BTreeNode {
 int key;
 int numChild;
 struct BTreeNode** child;
} BTreeNode;

typedef struct BTree {
 int root;
 int t; // 最小度数} BTree;

void initBTree(BTree* tree, int t);
int insertNode(BTree* tree, int key);
int searchNode(BTree* tree, int key);

#endif // BTREE_H

c#include <stdio.h>
#include "btree.h"

// 初始化毕达哥拉斯树void initBTree(BTree* tree, int t) {
 tree->root = -1;
 tree->t = t;
}

// 插入新节点int insertNode(BTree* tree, int key) {
 // 如果根节点不存在，创建一个新的根节点 if (tree->root == -1) {
 BTreeNode* newNode = malloc(sizeof(BTreeNode));
 newNode->key = key;
 newNode->numChild =0;
 newNode->child = NULL;

 tree->root = newNode;
 return0; // 插入成功 }

 // 找到合适的叶子节点插入新值 BTreeNode* leafNode = findLeafNode(tree, key);
 if (leafNode != NULL) {
 insertValueIntoLeafNode(leafNode, key);
 return0; // 插入成功 }

 // 如果找不到合适的叶子节点，创建一个新的内部节点 BTreeNode* newNode = malloc(sizeof(BTreeNode));
 newNode->key = key;
 newNode->numChild =1;
 newNode->child = malloc(sizeof(BTreeNode*));

 // 将新值插入到叶子节点中 insertValueIntoLeafNode(newNode->child[0], key);

 // 将新内部节点添加到树中 addInternalNode(tree, newNode);
 return0; // 插入成功}

// 查找合适的叶子节点BTreeNode* findLeafNode(BTree* tree, int key) {
 BTreeNode* currentNode = getRootNode(tree);

 while (currentNode != NULL && currentNode->numChild >0) {
 if (key < currentNode->key) {
 // 如果新值小于当前内部节点的值，向左移动 currentNode = currentNode->child[0];
 } else if (key > currentNode->key) {
 // 如果新值大于当前内部节点的值，向右移动 currentNode = currentNode->child[currentNode->numChild -1];
 } else {
 // 如果新值等于当前内部节点的值，找到叶子节点 return currentNode;
 }
 }

 // 如果找不到合适的叶子节点，返回NULL return NULL;
}

// 将新值插入到叶子节点中void insertValueIntoLeafNode(BTreeNode* leafNode, int key) {
 // 在叶子节点中添加新值 leafNode->key = key;

 // 如果叶子节点的孩子数超过了最小度数，分裂叶子节点 if (leafNode->numChild > tree->t -1) {
 splitLeafNode(leafNode);
 }
}

// 将新内部节点添加到树中void addInternalNode(BTree* tree, BTreeNode* newNode) {
 // 如果根节点不存在，设置新内部节点为根节点 if (tree->root == -1) {
 tree->root = newNode;
 return;
 }

 // 找到合适的叶子节点添加新内部节点 BTreeNode* leafNode = findLeafNode(tree, newNode->key);
 if (leafNode != NULL) {
 addInternalNodeToLeafNode(leafNode, newNode);
 return;
 }
}

// 将新内部节点添加到叶子节点中void addInternalNodeToLeafNode(BTreeNode* leafNode, BTreeNode* newNode) {
 // 在叶子节点的孩子列表中添加新内部节点 leafNode->child = realloc(leafNode->child, (leafNode->numChild +1) * sizeof(BTreeNode*));
 leafNode->child[leafNode->numChild] = newNode;
 leafNode->numChild++;
}

// 分裂叶子节点void splitLeafNode(BTreeNode* leafNode) {
 // 创建一个新的内部节点 BTreeNode* newInternalNode = malloc(sizeof(BTreeNode));

 // 将新值添加到新内部节点中 newInternalNode->key = leafNode->child[0]->key;
 newInternalNode->numChild =1;
 newInternalNode->child = malloc(sizeof(BTreeNode*));
 newInternalNode->child[0] = leafNode->child[0];

 // 将剩余的孩子添加到新内部节点中 for (int i =1; i < leafNode->numChild; i++) {
 newInternalNode->child[i -1] = leafNode->child[i];
 }
 newInternalNode->numChild = leafNode->numChild -1;

 // 将新内部节点添加到树中 addInternalNode(NULL, newInternalNode);

 // 将剩余的孩子添加到叶子节点中 for (int i =0; i < leafNode->numChild; i++) {
 if (i ==0) {
 leafNode->child[i] = newInternalNode;
 } else {
 leafNode->child[i -1] = leafNode->child[i];
 }
 }
 leafNode->numChild--;
}

// 查找根节点BTreeNode* getRootNode(BTree* tree) {
 return (tree->root != -1) ? tree->root : NULL;
}

c#include <stdio.h>
#include "btree.h"

int main() {
 BTree tree;
 initBTree(&tree,3);

 int keys[] = {10,20,5,15,25};
 for (int i =0; i < sizeof(keys) / sizeof(int); i++) {
 insertNode(&tree, keys[i]);
 }

 printf("Root Node Key: %d
", tree.root->key);

 return0;
}