今天看Linux內核代碼時，看到了radix tree，從書上大概地了解了radix tree的一些基本知識，包括它的結構和操作。由於Linux內核代碼不容易看懂，因此，打算自己家先實現一下radix tree，然後再看內核中的代碼，由於懶得去查radix tree的標准表示方式，所以，這裡radix tree的結構與Linux內核使用的類似。
首先，簡單說一下radix tree的結構。
radix tree的葉節點是存放在樹中的數據，內節點包含子節點的指針，每個內節點的孩子個數固定，Linux內核一般設置為64，也就是內節點包含64個指針，內節點還包括本節點的有效孩子個數以及所在的層次，這裡為了簡單，並沒有包含Linux內核內節點那麼多數據。
《深入理解Linux內核》上關於radix tree的圖示：
看了圖應該很好理解了，直接貼代碼吧，由於時間有限，沒有對代碼進行嚴格的測試，只測試了插入和查找操作，因此，代碼有可能會有問題：<喎?http://www.Bkjia.com/kf/ware/vc/" target="_blank" class="keylink">vcD4KPHA+PC9wPgo8cHJlIGNsYXNzPQ=="brush:java;">#include
#include
#include
#include
using namespace std;
typedef unsigned int u_int;
//常量定義
const u_int RADIX_TREE_SLOTS = 64; //一個內節點包含的最多的孩子個數
const u_int RADIX_MAX_LEVEL = 5; //最大的層數
const u_int radix_level[RADIX_MAX_LEVEL + 1] = { 0x00000000,
0x0000003F,
0x00000FC0,
0x0003F000,
0x00FC0000,
0x3F000000 }; //層次掩碼，用於提取某一層上的索引值
//函數的返回值狀態
enum radix_status {
INSERT_SUCC,
INSERT_FAIL,
DELETE_SUCC,
DELETE_FAIL
};
//radix tree的內節點
struct __radix_tree_node {
u_int height; //內節點的高度，從下往上算起
u_int count; //有效子節點的個數
void *slot[RADIX_TREE_SLOTS];
};
//radix tree的根節點
struct __radix_tree_root {
u_int height; //整個樹的高度，不包括樹根
__radix_tree_node *rnode;
};
//radix tree的頁節點，存儲在樹中的數據，這裡暫時將數據成員設置為string
struct radix_tree_data {
string str;
};
class radix_tree {
public:
radix_tree();
void radix_tree_stretch(); //將樹向下擴展一層
void radix_tree_stretch_n(u_int); //將樹擴展到n層
radix_status radix_tree_insert(u_int, radix_tree_data&); //插入一個索引值為index的數據
radix_status radix_tree_delete(u_int, radix_tree_data *&); //刪除索引值為index的數據
radix_tree_data* radix_tree_lookup(u_int); //查詢索引值為index的數據
void radix_tree_print(); //打印整棵樹
~radix_tree();
private:
u_int get_want_level(u_int index) //從給定的索引值獲取樹所期望的層次
{
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) //從給定的索引值和層次，得到該層的索引值
{
return (index & radix_level[level]) >> ((level - 1) * 6);
}
__radix_tree_node* radix_tree_alloc_node() //分配一個樹的內節點
{
__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); //根據索引值得到該索引值所在的節點
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;
};
//構造函數，用於初始化radix tree
radix_tree::radix_tree()
{
r_tree.height = 0;
r_tree.rnode = NULL;
}
//銷毀某個內節點，並遞歸銷毀它的子節點
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;
}
//析構函數，用於銷毀radix tree
radix_tree::~radix_tree()
{
__radix_tree_destroy_node(r_tree.rnode);
}
//向下擴展一層：分配一個內節點，然後將這個新節點的第一個slot的指針指向根節點指向的節點
//最後更新新節點中的信息和整個樹的高度
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;
}
//向下擴展到level層
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;
}
}
//插入索引值的輔助函數，采用此函數時，說明該樹此時的高度能夠插入index值的數據
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;
}
//提供給用戶的插入函數：如果當前的樹高不足以存儲index時，需要對樹進行擴展
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);
}
//獲取index所在的內節點
__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;
}
//提供給用戶的查詢函數
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;
}
//提供給用戶的刪除函數：只是將index所在的slot置為NULL，返回存儲的數據，
//當內節點並沒有孩子時，並不刪除內節點
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;
}
//采用遞歸的方式打印內節點
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]));
}
}
//打印整個樹
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文件內容：
//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;
}
