请帮我用C++写一个B-tree程序，内容包括：B-tree的结构、B-tree的创建、插入若干个关键字、查找指定关键字、找出树中最大的K个值

好的，B-tree是一种多叉树，节点可以有多个子节点，用于高效地存储和查找大量数据。下面是一个简单的B-tree程序的实现：

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int M = 4;  // B-tree的阶数

struct BNode {
    vector<int> keys;  // 存储关键字
    vector<BNode*> children;  // 存储子节点指针
    bool is_leaf;  // 是否是叶子节点

    BNode() {
        keys.resize(M - 1);
        children.resize(M, nullptr);
        is_leaf = true;
    }
};

class BTree {
public:
    BTree() {
        root = new BNode();
    }

    ~BTree() {
        clear(root);
    }

    void insert(int key) {
        if (root->keys.size() == M - 1) {  // 根节点已满
            BNode *new_root = new BNode();
            new_root->is_leaf = false;
            new_root->children[0] = root;
            split_child(new_root, 0, root);
            root = new_root;
        }
        insert_nonfull(root, key);
    }

    bool search(int key) {
        return search_node(root, key) != nullptr;
    }

    vector<int> find_k_largest(int k) {
        vector<int> result;
        find_k_largest(root, k, result);
        return result;
    }

private:
    BNode *root;

    void split_child(BNode *node, int i, BNode *child) {
        BNode *new_node = new BNode();
        new_node->is_leaf = child->is_leaf;

        // 将子节点的后一半移动到新节点
        for (int j = 0; j < M / 2 - 1; j++) {
            new_node->keys[j] = child->keys[M / 2 + j];
        }
        if (!child->is_leaf) {
            for (int j = 0; j < M / 2; j++) {
                new_node->children[j] = child->children[M / 2 + j];
            }
        }

        // 更新原节点和父节点
        child->keys.resize(M / 2 - 1);
        if (!child->is_leaf) {
            child->children.resize(M / 2);
        }
        node->children.resize(node->keys.size() + 2);

        for (int j = node->keys.size() + 1; j > i + 1; j--) {
            node->children[j] = node->children[j - 1];
        }
        node->children[i + 1] = new_node;

        for (int j = node->keys.size(); j > i; j--) {
            node->keys[j] = node->keys[j - 1];
        }
        node->keys[i] = child->keys[M / 2 - 1];
    }

    void insert_nonfull(BNode *node, int key) {
        int i = node->keys.size() - 1;

        if (node->is_leaf) {
            while (i >= 0 && key < node->keys[i]) {
                node->keys[i + 1] = node->keys[i];
                i--;
            }
            node->keys[i + 1] = key;
        } else {
            while (i >= 0 && key < node->keys[i]) {
                i--;
            }
            i++;

            if (node->children[i]->keys.size() == M - 1) {
                split_child(node, i, node->children[i]);
                if (key > node->keys[i]) {
                    i++;
                }
            }
            insert_nonfull(node->children[i], key);
        }
    }

    BNode *search_node(BNode *node, int key) {
        int i = 0;
        while (i < node->keys.size() && key > node->keys[i]) {
            i++;
        }
        if (i < node->keys.size() && key == node->keys[i]) {
            return node;
        } else if (node->is_leaf) {
            return nullptr;
        } else {
            return search_node(node->children[i], key);
        }
    }

    void find_k_largest(BNode *node, int k, vector<int> &result) {
        if (node == nullptr) {
            return;
        }
        if (node->is_leaf) {
            for (int i = node->keys.size() - 1; i >= 0 && result.size() < k; i--) {
                result.push_back(node->keys[i]);
            }
        } else {
            for (int i = node->keys.size() - 1; i >= 0; i--) {
                find_k_largest(node->children[i + 1], k, result);
                if (result.size() == k) {
                    return;
                }
                result.push_back(node->keys[i]);
            }
            find_k_largest(node->children[0], k, result);
        }
    }

    void clear(BNode *node) {
        if (node == nullptr) {
            return;
        }
        for (int i = 0; i < node->children.size(); i++) {
            clear(node->children[i]);
        }
        delete node;
    }
};

int main() {
    BTree tree;
    tree.insert(5);
    tree.insert(3);
    tree.insert(7);
    tree.insert(6);
    tree.insert(4);
    tree.insert(10);
    tree.insert(1);

    cout << tree.search(5) << endl;
    cout << tree.search(2) << endl;

    vector<int> result = tree.find_k_largest(3);
    for (int i = 0; i < result.size(); i++) {
        cout << result[i] << " ";
    }
    cout << endl;

    return 0;
}

以上代码中，BNode表示B-tree的节点，包括存储关键字的keys、存储子节点指针的children和标识是否是叶子节点的is_leaf。BTree表示B-tree数据结构，包括插入关键字、查找关键字、找出树中最大的K个值等操作。关键的实现是插入操作和查找操作，都是通过递归实现的。另外，找出树中最大的K个值的操作也是通过递归实现，先找到最右边的叶子节点，然后依次向上遍历，找到前K大的关键字。