[C++] [算法] [Linux] radix tree

今天看Linux内核代码时，看到了radix tree，从书上大概地了解了radix tree的一些基本知识，包括它的结构和操作。由于Linux内核代码不容易看懂，因此，打算自己家先实现一下radix tree，然后再看内核中的代码，由于懒得去查radix tree的标准表示方式，所以，这里radix tree的结构与Linux内核使用的类似。

首先，简单说一下radix tree的结构。

radix tree的叶节点是存放在树中的数据，内节点包含子节点的指针，每个内节点的孩子个数固定，Linux内核一般设置为64，也就是内节点包含64个指针，内节点还包括本节点的有效孩子个数以及所在的层次，这里为了简单，并没有包含Linux内核内节点那么多数据。

《深入理解Linux内核》上关于radix tree的图示：

看了图应该很好理解了，直接贴代码吧，由于时间有限，没有对代码进行严格的测试，只测试了插入和查找操作，因此，代码有可能会有问题：< http://www.2cto.com/kf/ware/vc/" target="_blank" class="keylink">vcD4KPHA+PC9wPgo8cHJlIGNsYXNzPQ=="brush:java;">#include #include #include #include using namespace std; typedef unsigned int u_int; //常量定义 const u_int RADIX_TREE_SLOTS = 64; //一个内节点包含的最多的孩子个数 const u_int RADIX_MAX_LEVEL = 5; //最大的层数 const u_int radix_level[RADIX_MAX_LEVEL + 1] = { 0x00000000, 0x0000003F, 0x00000FC0, 0x0003F000, 0x00FC0000, 0x3F000000 }; //层次掩码，用于提取某一层上的索引值 //函数的返回值状态 enum radix_status { INSERT_SUCC, INSERT_FAIL, DELETE_SUCC, DELETE_FAIL }; //radix tree的内节点 struct __radix_tree_node { u_int height; //内节点的高度，从下往上算起 u_int count; //有效子节点的个数 void *slot[RADIX_TREE_SLOTS]; }; //radix tree的根节点 struct __radix_tree_root { u_int height; //整个树的高度，不包括树根 __radix_tree_node *rnode; }; //radix tree的页节点，存储在树中的数据，这里暂时将数据成员设置为string struct radix_tree_data { string str; }; class radix_tree { public: radix_tree(); void radix_tree_stretch(); //将树向下扩展一层 void radix_tree_stretch_n(u_int); //将树扩展到n层 radix_status radix_tree_insert(u_int, radix_tree_data&); //插入一个索引值为index的数据 radix_status radix_tree_delete(u_int, radix_tree_data *&); //删除索引值为index的数据 radix_tree_data* radix_tree_lookup(u_int); //查询索引值为index的数据 void radix_tree_print(); //打印整棵树 ~radix_tree(); private: u_int get_want_level(u_int index) //从给定的索引值获取树所期望的层次 { u_int level = RADIX_MAX_LEVEL; while(level >= 0) { if(index & radix_level[level]) { return level; } --level; } return level; } u_int get_level_index(u_int index, u_int level) //从给定的索引值和层次，得到该层的索引值 { return (index & radix_level[level]) >> ((level - 1) * 6); } __radix_tree_node* radix_tree_alloc_node() //分配一个树的内节点 { __radix_tree_node *pr_node = new __radix_tree_node; pr_node->height = 0; pr_node->count = 0; //for(u_int i = 0; i < RADIX_TREE_SLOTS; ++i) //pr_node->slot[i] = NULL; memset(pr_node->slot, 0, sizeof(pr_node->slot)); return pr_node; } __radix_tree_node* radix_tree_get_node(u_int); //根据索引值得到该索引值所在的节点 void __radix_tree_destroy_node(__radix_tree_node *&pr_node); void radix_tree_print_node(__radix_tree_node *pr_node); radix_status __radix_tree_insert(u_int, u_int, radix_tree_data&); __radix_tree_root r_tree; }; //构造函数，用于初始化radix tree radix_tree::radix_tree() { r_tree.height = 0; r_tree.rnode = NULL; } //销毁某个内节点，并递归销毁它的子节点 void radix_tree::__radix_tree_destroy_node(__radix_tree_node *&pr_node) { if(pr_node == NULL) return; if(pr_node->height == 1) { delete pr_node; pr_node = NULL; return; } for(u_int i = 0; i < RADIX_TREE_SLOTS; ++i) { __radix_tree_destroy_node((__radix_tree_node*&)(pr_node->slot[i])); } delete pr_node; pr_node = NULL; } //析构函数，用于销毁radix tree radix_tree::~radix_tree() { __radix_tree_destroy_node(r_tree.rnode); } //向下扩展一层：分配一个内节点，然后将这个新节点的第一个slot的指针指向根节点指向的节点 //最后更新新节点中的信息和整个树的高度 void radix_tree::radix_tree_stretch() { __radix_tree_node *pr_node = radix_tree_alloc_node(); pr_node->height = r_tree.height + 1; pr_node->count = 1; pr_node->slot[0] = r_tree.rnode; r_tree.rnode = pr_node; ++r_tree.height; return; } //向下扩展到level层 void radix_tree::radix_tree_stretch_n(u_int level) { u_int height = r_tree.height; if(height >= level) { return; } while(height < level) { radix_tree_stretch(); ++height; } } //插入索引值的辅助函数，采用此函数时，说明该树此时的高度能够插入index值的数据 radix_status radix_tree::__radix_tree_insert(u_int index, u_int max_level, radix_tree_data& data) { u_int cur_index = 0; __radix_tree_node *pr_node = r_tree.rnode, *pr_node_tmp = NULL; while(max_level > 1) { cur_index = get_level_index(index, max_level); pr_node_tmp = (__radix_tree_node*)(pr_node->slot[cur_index]); if(pr_node_tmp == NULL) { pr_node->slot[cur_index] = radix_tree_alloc_node(); ((__radix_tree_node*)(pr_node->slot[cur_index]))->height = pr_node->height - 1; pr_node_tmp = (__radix_tree_node*)(pr_node->slot[cur_index]); } pr_node = pr_node_tmp; --max_level; } cur_index = get_level_index(index, 1); if(pr_node->slot[cur_index]) { return INSERT_FAIL; } pr_node->count++; pr_node->slot[cur_index] = (void*)&data; return INSERT_SUCC; } //提供给用户的插入函数：如果当前的树高不足以存储index时，需要对树进行扩展 radix_status radix_tree::radix_tree_insert(u_int index, radix_tree_data& data) { u_int want_level = get_want_level(index); cout << index << " want level: " << want_level << endl; if(want_level <= r_tree.height) { return __radix_tree_insert(index, want_level, data); } radix_tree_stretch_n(want_level); cout << "stretch to " << want_level << " level" << endl; return __radix_tree_insert(index, want_level, data); } //获取index所在的内节点 __radix_tree_node* radix_tree::radix_tree_get_node(u_int index) { u_int cur_level = r_tree.height; u_int want_level = get_want_level(index); u_int cur_index = 0; __radix_tree_node *pr_node = r_tree.rnode, *pr_node_tmp = NULL; if(want_level <= r_tree.height) { while(cur_level > 1) { cur_index = get_level_index(index, cur_level); pr_node_tmp = (__radix_tree_node*)(pr_node->slot[cur_index]); if(pr_node_tmp == NULL) { return NULL; } pr_node = pr_node_tmp; --cur_level; } return pr_node; } return NULL; } //提供给用户的查询函数 radix_tree_data* radix_tree::radix_tree_lookup(u_int index) { __radix_tree_node *pr_node = radix_tree_get_node(index); if(pr_node == NULL) { return NULL; } u_int cur_index = get_level_index(index, 1); radix_tree_data *data = (radix_tree_data*)(pr_node->slot[cur_index]); if(data == NULL) { return NULL; } return data; } //提供给用户的删除函数：只是将index所在的slot置为NULL，返回存储的数据， //当内节点并没有孩子时，并不删除内节点 radix_status radix_tree::radix_tree_delete(u_int index, radix_tree_data *& rdata) { __radix_tree_node *pr_node = radix_tree_get_node(index); if(pr_node == NULL) { return DELETE_FAIL; } u_int cur_index = get_level_index(index, 1); radix_tree_data *data = (radix_tree_data*)(pr_node->slot[cur_index]); if(data == NULL) { rdata = NULL; return DELETE_FAIL; } rdata = data; pr_node->slot[cur_index] = NULL; pr_node->count--; return DELETE_SUCC; } //采用递归的方式打印内节点 void radix_tree::radix_tree_print_node(__radix_tree_node *pr_node) { if(pr_node == NULL) return; if(pr_node->height == 1) { for(u_int i = 0; i < RADIX_TREE_SLOTS; ++i) { if(pr_node->slot[i]) { cout << ((radix_tree_data*)(pr_node->slot[i]))->str << endl; } } return; } for(u_int i = 0; i < RADIX_TREE_SLOTS; ++i) { radix_tree_print_node((__radix_tree_node*)(pr_node->slot[i])); } } //打印整个树 void radix_tree::radix_tree_print() { radix_tree_print_node(r_tree.rnode); } int main() { radix_tree rdtree; u_int index = 0; string str; ifstream cin("test.txt"); //test.txt文件内容： //5 abc //6 def //131 mnp radix_tree_data data1; cin >> index >> str; data1.str = str; rdtree.radix_tree_insert(index, data1); radix_tree_data data2; cin >> index >> str; data2.str = str; rdtree.radix_tree_insert(index, data2); radix_tree_data data3; cin >> index >> str; data3.str = str; rdtree.radix_tree_insert(index, data3); rdtree.radix_tree_print(); cout << "lookup start..." << endl; radix_tree_data *pd = NULL; pd = rdtree.radix_tree_lookup(5); if(pd) cout << pd->str << endl; pd = rdtree.radix_tree_lookup(6); if(pd) cout << pd->str << endl; pd = rdtree.radix_tree_lookup(131); if(pd) cout << pd->str << endl; return 0; }