Redis基础-跳表
一、跳表原理
1.1、什么是跳表
跳跃表是一种随机化的数据结构，在查找、插入和删除这些字典操作上，其效率可比拟于平衡二叉树（如红黑树），大多数操作只需要O(log n)平均时间，但它的代码以及原理更简单。跳跃表的定义如下：
“Skip lists are data structures that use probabilistic balancing rather than strictly enforced balancing. As a result, the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees.”
译文：跳跃表使用概率平衡，而不是强制平衡，因此，对于插入和删除结点比传统上的平衡树算法更为简洁高效。
1.2、理想跳表
在理想情况下:
- 最底层元素是一个单链表
- 从最底层往上,每一层的元素个数是之前一层的1/2
二、跳表redis实现
Base:redis version: 5.0.8
2.1、redis跳表原理和数据结构
2.2、Redis跳表代码
2.2.1、Redis跳表数据结构
#跳表节点
typedef struct zskiplistNode {
sds ele;
double score;
struct zskiplistNode *backward;
#跳表表示level的数据
struct zskiplistLevel {
struct zskiplistNode *forward;
unsigned long span;
} level[];
} zskiplistNode;
#跳表 list结构
typedef struct zskiplist {
struct zskiplistNode *header, *tail;
unsigned long length;
int level;
} zskiplist;
#zset 结构
typedef struct zset {
dict *dict;
zskiplist *zsl;
} zset;
2.2.2、跳表执行流程
#zset 添加/更新操作入口
int zsetAdd(robj *zobj, double score, sds ele, int *flags, double *newscore) {
/* Turn options into simple to check vars. */
int incr = (*flags & ZADD_INCR) != 0;
int nx = (*flags & ZADD_NX) != 0;
int xx = (*flags & ZADD_XX) != 0;
*flags = 0; /* We'll return our response flags. */
double curscore;
/* NaN as input is an error regardless of all the other parameters. */
if (isnan(score)) {
*flags = ZADD_NAN;
return 0;
}
/* Update the sorted set according to its encoding. */
if (zobj->encoding == OBJ_ENCODING_ZIPLIST) {
unsigned char *eptr;
if ((eptr = zzlFind(zobj->ptr,ele,&curscore)) != NULL) {
/* NX? Return, same element already exists. */
if (nx) {
*flags |= ZADD_NOP;
return 1;
}
/* Prepare the score for the increment if needed. */
if (incr) {
score += curscore;
if (isnan(score)) {
*flags |= ZADD_NAN;
return 0;
}
if (newscore) *newscore = score;
}
/* Remove and re-insert when score changed. */
if (score != curscore) {
zobj->ptr = zzlDelete(zobj->ptr,eptr);
zobj->ptr = zzlInsert(zobj->ptr,ele,score);
*flags |= ZADD_UPDATED;
}
return 1;
} else if (!xx) {
/* Optimize: check if the element is too large or the list
* becomes too long *before* executing zzlInsert. */
zobj->ptr = zzlInsert(zobj->ptr,ele,score);
if (zzlLength(zobj->ptr) > server.zset_max_ziplist_entries ||
sdslen(ele) > server.zset_max_ziplist_value)
zsetConvert(zobj,OBJ_ENCODING_SKIPLIST);
if (newscore) *newscore = score;
*flags |= ZADD_ADDED;
return 1;
} else {
*flags |= ZADD_NOP;
return 1;
}
} else if (zobj->encoding == OBJ_ENCODING_SKIPLIST) {
#当前zset编码是 skipList
zset *zs = zobj->ptr;
zskiplistNode *znode;
dictEntry *de;
#根据 ele从dict中获取元素,如果获取到直接更新该节点value,如果获取不到就插入
de = dictFind(zs->dict,ele);
if (de != NULL) {
/* NX? Return, same element already exists. */
if (nx) {
*flags |= ZADD_NOP;
return 1;
}
curscore = *(double*)dictGetVal(de);
/* Prepare the score for the increment if needed. */
if (incr) {
score += curscore;
if (isnan(score)) {
*flags |= ZADD_NAN;
return 0;
}
if (newscore) *newscore = score;
}
/* Remove and re-insert when score changes. */
if (score != curscore) {
//更新znode节点
znode = zslUpdateScore(zs->zsl,curscore,ele,score);
/* Note that we did not removed the original element from
* the hash table representing the sorted set, so we just
* update the score. */
dictGetVal(de) = &znode->score; /* Update score ptr. */
*flags |= ZADD_UPDATED;
}
return 1;
} else if (!xx) {
ele = sdsdup(ele);
//插入新的节点
znode = zslInsert(zs->zsl,score,ele);
serverAssert(dictAdd(zs->dict,ele,&znode->score) == DICT_OK);
*flags |= ZADD_ADDED;
if (newscore) *newscore = score;
return 1;
} else {
*flags |= ZADD_NOP;
return 1;
}
} else {
serverPanic("Unknown sorted set encoding");
}
return 0; /* Never reached. */
}
插入新的节点流程
zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) {
zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
unsigned int rank[ZSKIPLIST_MAXLEVEL];
int i, level;
serverAssert(!isnan(score));
#初始化遍历初始值
#rank 数组收集每层level从header到小于score的最后一个节点的span值
#update 数组收集每层level 小于score的最后一个节点
x = zsl->header;
for (i = zsl->level-1; i >= 0; i--) {
/* store rank that is crossed to reach the insert position */
#rank[level-]的初始值为0 ,是因为 当前是计算的第一个元素,需要从header.level[i]中取出来
rank[i] = i == (zsl->level-1) ? 0 : rank[i+1];
while (x->level[i].forward &&
(x->level[i].forward->score < score ||
(x->level[i].forward->score == score &&
sdscmp(x->level[i].forward->ele,ele) < 0)))
{
rank[i] += x->level[i].span;
x = x->level[i].forward;
}
update[i] = x;
}
/* we assume the element is not already inside, since we allow duplicated
* scores, reinserting the same element should never happen since the
* caller of zslInsert() should test in the hash table if the element is
* already inside or not. */
#生成当前新节点的level值,如果当前值大于当前list的level值,需要初始化[当前level,level)之间的level元素
level = zslRandomLevel();
if (level > zsl->level) {
for (i = zsl->level; i < level; i++) {
rank[i] = 0;
update[i] = zsl->header;
update[i]->level[i].span = zsl->length;
}
zsl->level = level;
}
#构造新节点的元素
x = zslCreateNode(level,score,ele);
//从下到上,修改每层小雨score的最后一个元素 ,与当前元素level[i]的链接关系以及span数值
for (i = 0; i < level; i++) {
x->level[i].forward = update[i]->level[i].forward;
update[i]->level[i].forward = x;
/* update span covered by update[i] as x is inserted here */
x->level[i].span = update[i]->level[i].span - (rank[0] - rank[i]);
update[i]->level[i].span = (rank[0] - rank[i]) + 1;
}
/* increment span for untouched levels */
#修改每一层小于score的最后一个元素的span值,在这里再执行一次是因为当前节点的level如果小于list的level,则大于当前节点level到list level之间的level的span值还没有被处理,而这些数值只是单纯的增加1
for (i = level; i < zsl->level; i++) {
update[i]->level[i].span++;
}
#修改向后遍历指针
x->backward = (update[0] == zsl->header) ? NULL : update[0];
if (x->level[0].forward)
x->level[0].forward->backward = x;
else
zsl->tail = x;
#修改当前list 元素个数
zsl->length++;
return x;
}
跳表level函数:
#define ZSKIPLIST_P 0.25
#define ZSKIPLIST_MAXLEVEL 64 /* Should be enough for 2^64 elements */
int zslRandomLevel(void) {
int level = 1;
while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF))
level += 1;
return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL;
}
redis中规定,level最多只能有64层
三、跳表java实现
3.1、数据结构
java实现时去掉了dict结构,主要演示node的插入
@Data
public class ZSkipListNode {
private String ele;
private double score;
private ZSkipListNode backward;
private ZSkipListLevel[] level;
public ZSkipListNode(String ele, double score) {
this.ele = ele;
this.score = score;
this.level = new ZSkipListLevel[ZSkipList.MAX_LEVEL];
for(int j = 0;j< ZSkipList.MAX_LEVEL;j++){
level[j] = new ZSkipListLevel();
}
}
@Override
public String toString() {
return "ZSkipListNode{}";
}
}
@Data
public class ZSkipListLevel {
private ZSkipListNode forword;
private long span;
@Override
public String toString() {
return "ZSkipListLevel{}";
}
}
@Data
public class ZSkipList {
public static final int MAX_LEVEL = 32;
public static final double LEVEL_FACTOR = 0.25;
private ZSkipListNode header;
private ZSkipListNode tail;
private long length;
private int level;
public ZSkipList() {
this.level = 1;
this.length = 0;
this.header = new ZSkipListNode(null,0);
for(int j = 0;j<MAX_LEVEL;j++){
this.getHeader().getLevel()[j].setForword(null);
this.getHeader().getLevel()[j].setSpan(0);
}
this.getHeader().setBackward(null);
this.setTail(null);
}
}
3.2、insert和delete方法实现
@Data
public class ZSkipList {
public static final int MAX_LEVEL = 32;
public static final double LEVEL_FACTOR = 0.25;
private ZSkipListNode header;
private ZSkipListNode tail;
private long length;
private int level;
public ZSkipList() {
this.level = 1;
this.length = 0;
this.header = new ZSkipListNode(null,0);
for(int j = 0;j<MAX_LEVEL;j++){
this.getHeader().getLevel()[j].setForword(null);
this.getHeader().getLevel()[j].setSpan(0);
}
this.getHeader().setBackward(null);
this.setTail(null);
}
public ZSkipListNode insert(double score, String ele) {
long[] rank = new long[MAX_LEVEL];
ZSkipListNode[] update = new ZSkipListNode[MAX_LEVEL];
ZSkipListNode h = this.getHeader();
for(int i=getLevel()-1;i>=0;i--){
rank[i] = i == getLevel()-1 ? 0 : rank[i+1];
while (h.getLevel()[i].getForword()!=null
&& (h.getLevel()[i].getForword().getScore()<score
|| (h.getLevel()[i].getForword().getScore() == score && valCmp(h.getLevel()[i].getForword().getEle(),ele)<0))){
rank[i]+= h.getLevel()[i].getSpan();
h = h.getLevel()[i].getForword();
}
update[i] = h;
}
int level = zslRandomLevel();
if(level>getLevel()){
for(int l = getLevel();l<level;l++){
update[l] = getHeader();
update[l].getLevel()[l].setSpan(getLength());
rank[l]= 0;
}
}
ZSkipListNode cur = new ZSkipListNode(ele,score);
for(int i = 0;i<level;i++){
cur.getLevel()[i].setForword(update[i].getLevel()[i].getForword());
update[i].getLevel()[i].setForword(cur);
cur.getLevel()[i].setSpan(update[i].getLevel()[i].getSpan()-(rank[0]-rank[i]));
update[i].getLevel()[i].setSpan(rank[0]-rank[i]+1);
}
for (int i = level;i<this.getLevel()-1; i++){
update[i].getLevel()[i].setSpan(update[i].getLevel()[i].getSpan()+1);
}
cur.setBackward(update[0] == getHeader() ? null : update[0]);
if(cur.getLevel()[0].getForword()!=null){
cur.getLevel()[0].getForword().setBackward(cur);
}else {
this.setTail(cur);
}
if(level>getLevel()){
this.setLevel(level);
}
this.setLength(this.getLength()+1);
return cur;
}
/**
* 删除成功 返回1 ，删除失败，或者没有找到返回0
* 删除元素
* 并修改剩下的level中的 span信息
* @return
*/
public int delete(ZSkipListNode node,ZSkipListNode[] update){
for(int i=0;i<getLevel();i++){
ZSkipListLevel level =update[i].getLevel()[i];
if(level.getForword() == node){
level.setSpan(level.getSpan()+node.getLevel()[i].getSpan()-1);
level.setForword(node.getLevel()[i].getForword());
}else {
level.setSpan(level.getSpan()-1);
}
}
/**
* 修改返回指针
*/
if(node.getLevel()[0].getForword()==null){
this.setTail(node.getBackward());
}else {
node.getLevel()[0].getForword().setBackward(node.getBackward());
}
/**
* 修改level
*/
while (getLevel()>0 && getHeader().getLevel()[getLevel()-1].getForword()==null){
setLevel(getLevel()-1);
}
setLength(getLength()-1);
return 1;
}
/**
* int zslDelete(zskiplist *zsl, double score, sds ele, zskiplistNode **node)
* @param score
* @param ele
* @return
*/
public int deleteWithScore(double score,String ele){
ZSkipListNode[] update = new ZSkipListNode[MAX_LEVEL];
ZSkipListNode h = getHeader();
ZSkipListNode x = null;
for(int i= getLevel()-1;i>=0;i--){
while (h.getLevel()[i].getForword() != null
&& (h.getLevel()[i].getForword().getScore() < score
|| (h.getLevel()[i].getForword().getScore() == score && valCmp(h.getLevel()[i].getForword().getEle(), ele) < 0))
) {
h = h.getLevel()[i].getForword();
}
update[i]=h;
}
x = h.getLevel()[0].getForword();
if(x!=null && x.getScore() == score && valCmp(x.getEle(),ele) == 0){
return delete(x,update);
}
return 0;
}
private int zslRandomLevel() {
int level = 1;
Random random = new Random();
while(random.nextInt(20)<20*LEVEL_FACTOR){
level+=1;
}
return level<MAX_LEVEL ? level : MAX_LEVEL;
}
public int valCmp(String t, String target) {
return t.compareTo(target);
}
public static void main(String[] args) {
ZSkipList list = new ZSkipList();
Map<String,Integer> eleMap = new HashMap<>();
Random random = new Random();
int max = 0;
for (int i = 0;i<10;i++){
int score =1+random.nextInt(20);
max +=score;
String ele = "a"+i;
list.insert(max,ele);
eleMap.put(ele,max);
}
printZsl(list);
/**
* 删除元素测试
*/
for (Map.Entry<String,Integer> entry : eleMap.entrySet()){
list.deleteWithScore(entry.getValue(),entry.getKey());
System.out.printf("delete,ele:"+entry.getKey()+",score:"+entry.getValue());
printZsl(list);
}
}
public static void printZsl(ZSkipList list){
ZSkipListNode header = list.getHeader();
System.out.println("---------------------------------------");
for(int i = list.getLevel()-1;i>=0;i--){
System.out.println("level = "+i);
ZSkipListNode h = header.getLevel()[i].getForword();
while (h!=null){
System.out.printf("[node:"+h.getEle()+":"+h.getScore()+",span:"+h.getLevel()[i].getSpan()+"]-");
h = h.getLevel()[i].getForword();
}
System.out.println();
}
System.out.println("---------------------------------------");
}
@Override
public String toString() {
return "ZSkipList{";
}
}
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