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  • redis 5.0.7 源码阅读——跳跃表skiplist

    redis中并没有专门给跳跃表两个文件。在5.0.7的版本中,结构体的声明与定义、接口的声明在server.h中,接口的定义在t_zset.c中,所有开头为zsl的函数。

    一、数据结构

    单个节点:

    typedef struct zskiplistNode {
        //key,唯一
        sds ele;
    
        //分值,可重复
        double score;
    
        //后退指针
        struct zskiplistNode *backward;
    
        //
        struct zskiplistLevel {
            //前进指针
            struct zskiplistNode *forward;
            //到本层下一节点的跨度,用于计算rank
            unsigned long span;
        } level[];
    } zskiplistNode;

    zskiplistNode定义了跳跃表中每个节点的数据结构,它是一个变长结构体。

     1 /*
     2 +------------------------+
     3 |sds ele                 |     /+-----------------------------+
     4 +------------------------+    / |struct zskiplistNode *forward|
     5 |double score            |   /  +-----------------------------+
     6 +------------------------+  /   |unsigned long span           |
     7 |zskiplistNode * backward| /    +-----------------------------+
     8 +------------------------+/     .                             .
     9 |zskiplistLevel  level[] |      .                             .
    10 +------------------------+     .                             .
    11                                +-----------------------------+
    12                                |struct zskiplistNode *forward|
    13                                +-----------------------------+
    14                                |unsigned long span           |
    15                                +-----------------------------+
    16 */

    将用以下结构表示:

     1 /*
     2 +--------+
     3 |level[1]|
     4 |1(span) |
     5 +--------+
     6 |level[0]|
     7 |1(span) |
     8 +--------+
     9 |backward|
    10 +--------+
    11 |score   |
    12 +--------+
    13 |ele     |
    14 +--------+
    15 */

    如:

     1 /*
     2 +--------+                +--------+                +--------+
     3 |level[1]|--------------->|level[1]|--------------->|level[1]|
     4 |2       |                |2       |                |0       |
     5 +--------+   +--------+   +--------+   +--------+   +--------+
     6 |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->|level[0]|
     7 |1       |   |1       |   |1       |   |1       |   |0       |
     8 +--------+   +--------+   +--------+   +--------+   +--------+
     9 |backward|<--|backward|<--|backward|<--|backward|<--|backward| 
    10 +--------+   +--------+   +--------+   +--------+   +--------+
    11 |1       |   |2       |   |3       |   |4       |   |5       |
    12 +--------+   +--------+   +--------+   +--------+   +--------+
    13 |a       |   |b       |   |c       |   |d       |   |e       |
    14 +--------+   +--------+   +--------+   +--------+   +--------+
    15 */

    跳表:

    1 typedef struct zskiplist {
    2     //头/尾节点
    3     struct zskiplistNode *header, *tail;
    4     //总长度
    5     unsigned long length;
    6     //总层数
    7     int level;
    8 } zskiplist;

    因其头节点固定为空节点,固整体结构:

     1 /*
     2     +--------+                +--------+                +--------+
     3     |level[1]|--------------->|level[1]|--------------->|level[1]|
     4     |2       |                |2       |                |0       |
     5     +--------+   +--------+   +--------+   +--------+   +--------+
     6     |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->|level[0]|
     7     |1       |   |1       |   |1       |   |1       |   |0       |
     8     +--------+   +--------+   +--------+   +--------+   +--------+
     9     |backward|<--|backward|<--|backward|<--|backward|<--|backward| 
    10     +--------+   +--------+   +--------+   +--------+   +--------+
    11     |0       |   |2       |   |3       |   |4       |   |5       |
    12     +--------+   +--------+   +--------+   +--------+   +--------+
    13     |NULL    |   |b       |   |c       |   |d       |   |e       |
    14 +-->+--------+   +--------+   +--------+   +--------+   +--------+<--+
    15 |                                                                    |
    16 |   +--------+                                                       |
    17 +---|header  |                                                       |
    18     +--------+                                                       |
    19     |tail    |-------------------------------------------------------+
    20     +--------+
    21     |length=4|
    22     +--------+
    23     |level=2 |
    24     +--------+
    25 */

    每个level层都是一条单身链表,其中level[0]中包含所有元素。

    二、创建

    根据指定的level,创建一个跳表节点:

    1 zskiplistNode *zslCreateNode(int level, double score, sds ele) {
    2     zskiplistNode *zn =
    3         zmalloc(sizeof(*zn)+level*sizeof(struct zskiplistLevel));
    4     zn->score = score;
    5     zn->ele = ele;
    6     return zn;
    7 }

    创建一个跳表:

     1 #define ZSKIPLIST_MAXLEVEL 64 /* Should be enough for 2^64 elements */
     2 
     3 zskiplist *zslCreate(void) {
     4     int j;
     5     zskiplist *zsl;
     6 
     7     zsl = zmalloc(sizeof(*zsl));
     8     zsl->level = 1;
     9     zsl->length = 0;
    10     zsl->header = zslCreateNode(ZSKIPLIST_MAXLEVEL,0,NULL);
    11     for (j = 0; j < ZSKIPLIST_MAXLEVEL; j++) {
    12         zsl->header->level[j].forward = NULL;
    13         zsl->header->level[j].span = 0;
    14     }
    15     zsl->header->backward = NULL;
    16     zsl->tail = NULL;
    17     return zsl;
    18 }

    redis中定义的最大层数为64层。且在刚创建时,会生成一个空的头节点,这样就可以不用再考虑节点数从0至1或者从1至0时要处理的各种特殊情况。

    刚创完的跳表结构(结构中以4做为最大层数,后同):

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+
     9       |level[1]|-->NULL
    10       |0       |
    11       +--------+
    12       |level[0]|-->NULL
    13       |0       |
    14       +--------+
    15 NULL<-|backward|
    16       +--------+
    17       |0       |
    18       +--------+
    19       |NULL    |
    20   +-->+--------+
    21   |           
    22   |   +--------+
    23   +---|header  |
    24       +--------+
    25       |tail    |-->NULL
    26       +--------+
    27       |length=0|
    28       +--------+
    29       |level=1 |
    30       +--------+
    31 */

    三、插入节点

    1 #define ZSKIPLIST_P 0.25      /* Skiplist P = 1/4 */
    2 
    3 int zslRandomLevel(void) {
    4     int level = 1;
    5     while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF))
    6         level += 1;
    7     return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL;
    8 }

    redis中使用的决定新插入节点层数据的方法是抛硬币法,且“硬币”只有25%的几率是正面。

    插入方法:

     1 zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) {
     2     //update数组,用于存储查找路径
     3     zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
     4 
     5     //rank数组,用于存储每层路径节点的排名
     6     unsigned int rank[ZSKIPLIST_MAXLEVEL];
     7     int i, level;
     8 
     9     serverAssert(!isnan(score));
    10     x = zsl->header;
    11 
    12     //先查找插入位置
    13     for (i = zsl->level-1; i >= 0; i--) {
    14         /* store rank that is crossed to reach the insert position */
    15         rank[i] = i == (zsl->level-1) ? 0 : rank[i+1];
    16         while (x->level[i].forward &&
    17                 (x->level[i].forward->score < score ||
    18                     (x->level[i].forward->score == score &&
    19                     sdscmp(x->level[i].forward->ele,ele) < 0)))
    20         {
    21             rank[i] += x->level[i].span;
    22             x = x->level[i].forward;
    23         }
    24         update[i] = x;
    25     }
    26 
    27     //随机一个level
    28     level = zslRandomLevel();
    29 
    30     //若当前最大level不够,则补齐update与rank数组
    31     if (level > zsl->level) {
    32         for (i = zsl->level; i < level; i++) {
    33             rank[i] = 0;
    34             update[i] = zsl->header;
    35             update[i]->level[i].span = zsl->length;
    36         }
    37         zsl->level = level;
    38     }
    39 
    40     //创建一个节点,并插入
    41     x = zslCreateNode(level,score,ele);
    42     for (i = 0; i < level; i++) {
    43         x->level[i].forward = update[i]->level[i].forward;
    44         update[i]->level[i].forward = x;
    45 
    46         x->level[i].span = update[i]->level[i].span - (rank[0] - rank[i]);
    47         update[i]->level[i].span = (rank[0] - rank[i]) + 1;
    48     }
    49 
    50     //update数组中,比插入节点level更高的各成员的跨度增加
    51     for (i = level; i < zsl->level; i++) {
    52         update[i]->level[i].span++;
    53     }
    54 
    55     x->backward = (update[0] == zsl->header) ? NULL : update[0];
    56     if (x->level[0].forward)
    57         x->level[0].forward->backward = x;
    58     else
    59         zsl->tail = x;
    60     zsl->length++;
    61     return x;
    62 }

    从注释可知,redis的跳表允许同score的情况发生,但是不允许同ele,且是由调用者在外部保证。若插入顺序为e,b,c,d,则插入e时:

    step1、定义update数组与rank数组。

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |NULL    |     |0       |
     9 +--------+     +--------+
    10 |NULL    |     |0       |
    11 +--------+     +--------+
    12 */

    实际在linux环境运行时,不会默认初始化,应该是一堆脏数据,此处是为了方便处理结构

    step2、查找位置后

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |NULL    |     |0       |
     9 +--------+     +--------+
    10 |header  |     |0       |
    11 +--------+     +--------+
    12 */

    step3、e的level为2,比跳表的大,故要补齐update与rank数组

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |header  |     |0       |
     9 +--------+     +--------+
    10 |header  |     |0       |
    11 +--------+     +--------+
    12 */

    step4、插入节点,与单身链表插入相同,将新节点e各层,插入到update数组中记录的各层节点之后,并使用rank数组,计算跨度

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+   +--------+
     9       |level[1]|-->|level[1]|-->NULL
    10       |1       |   |0       |
    11       +--------+   +--------+
    12       |level[0]|-->|level[0]|-->NULL
    13       |1       |   |0       |
    14       +--------+   +--------+
    15 NULL<-|backward|   |backward|
    16       +--------+   +--------+
    17       |0       |   |5       |
    18       +--------+   +--------+
    19       |NULL    |   |e       |
    20   +-->+--------+   +--------+
    21   |
    22   |   +--------+
    23   +---|header  |
    24       +--------+
    25       |tail    |
    26       +--------+
    27       |length=0|
    28       +--------+
    29       |level=1 |
    30       +--------+
    31 */

    step5、处理新插入节点的backward指针,与跳表的tail指针:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+   +--------+
     9       |level[1]|-->|level[1]|-->NULL
    10       |1       |   |0       |
    11       +--------+   +--------+
    12       |level[0]|-->|level[0]|-->NULL
    13       |1       |   |0       |
    14       +--------+   +--------+
    15 NULL<-|backward|   |backward|
    16       +--------+   +--------+
    17       |0       |   |5       |
    18       +--------+   +--------+
    19       |NULL    |   |e       |
    20   +-->+--------+   +--------+<--+
    21   |                             |
    22   |   +--------+                |
    23   +---|header  |                |
    24       +--------+                |
    25       |tail    |----------------+
    26       +--------+
    27       |length=1|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 
    32 */

    此时插入b:

    找到位置后的update与rank数组:

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |header  |     |0       |
     9 +--------+     +--------+
    10 |header  |     |0       |
    11 +--------+     +--------+
    12 */

    插入b节点后:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+                +--------+
     9       |level[1]|--------------->|level[1]|-->NULL
    10       |2       |                |0       |
    11       +--------+   +--------+   +--------+
    12       |level[0]|-->|level[0]|-->|level[0]|-->NULL
    13       |1       |   |1       |   |0       |
    14       +--------+   +--------+   +--------+
    15 NULL<-|backward|   |backward|<--|backward|
    16       +--------+   +--------+   +--------+
    17       |0       |   |2       |   |5       |
    18       +--------+   +--------+   +--------+
    19       |NULL    |   |b       |   |e       |
    20   +-->+--------+   +--------+   +--------+<--+
    21   |                                          |
    22   |   +--------+                             |
    23   +---|header  |                             |
    24       +--------+                             |
    25       |tail    |-----------------------------+
    26       +--------+
    27       |length=2|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 */

    需要注意的是,update数组idx = 1的节点并没有新的插入操作,span要自增,表示本层跨度增加了1。

    插入c时的update与rank数组:

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |header  |     |0       |
     9 +--------+     +--------+
    10 |b       |     |1       |
    11 +--------+     +--------+
    12 */

    插入c后:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+                +--------+   +--------+
     9       |level[1]|--------------->|level[1]|-->|level[1]|-->NULL
    10       |2       |                |1       |   |0       |
    11       +--------+   +--------+   +--------+   +--------+
    12       |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->NULL
    13       |1       |   |1       |   |1       |   |0       |
    14       +--------+   +--------+   +--------+   +--------+
    15 NULL<-|backward|   |backward|<--|backward|<--|backward|
    16       +--------+   +--------+   +--------+   +--------+
    17       |0       |   |2       |   |3       |   |5       |
    18       +--------+   +--------+   +--------+   +--------+
    19       |NULL    |   |b       |   |c       |   |e       |
    20   +-->+--------+   +--------+   +--------+   +--------+<--+
    21   |                                                       |
    22   |   +--------+                                          |
    23   +---|header  |                                          |
    24       +--------+                                          |
    25       |tail    |------------------------------------------+
    26       +--------+
    27       |length=3|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 /*

    最后插入d:

    update与rank数组:

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |c       |     |2       |
     9 +--------+     +--------+
    10 |c       |     |2       |
    11 +--------+     +--------+
    12 */

    插入d:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+                +--------+                +--------+
     9       |level[1]|--------------->|level[1]|--------------->|level[1]|-->NULL
    10       |2       |                |2       |                |0       |
    11       +--------+   +--------+   +--------+   +--------+   +--------+
    12       |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->NULL
    13       |1       |   |1       |   |1       |   |1       |   |0       |
    14       +--------+   +--------+   +--------+   +--------+   +--------+
    15 NULL<-|backward|   |backward|<--|backward|<--|backward|<--|backward|
    16       +--------+   +--------+   +--------+   +--------+   +--------+
    17       |0       |   |2       |   |3       |   |4       |   |5       |
    18       +--------+   +--------+   +--------+   +--------+   +--------+
    19       |NULL    |   |b       |   |c       |   |d       |   |e       |
    20   +-->+--------+   +--------+   +--------+   +--------+   +--------+<--+
    21   |                                                                    |
    22   |   +--------+                                                       |
    23   +---|header  |                                                       |
    24       +--------+                                                       |
    25       |tail    |-------------------------------------------------------+
    26       +--------+
    27       |length=4|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 /*

    如果此时要新插入节点a,score为4.5,则update与rank数组分别为:

     1 /*
     2 update         rank
     3 +--------+     +--------+
     4 |NULL    |     |0       |
     5 +--------+     +--------+
     6 |NULL    |     |0       |
     7 +--------+     +--------+
     8 |c       |     |2       |
     9 +--------+     +--------+
    10 |d       |     |3       |
    11 +--------+     +--------+
    12 */

    四、删除节点

    在已经查找到位置,与已知update数组时的删除方法:

     1 void zslDeleteNode(zskiplist *zsl, zskiplistNode *x, zskiplistNode **update) {
     2     int i;
     3     for (i = 0; i < zsl->level; i++) {
     4         if (update[i]->level[i].forward == x) {
     5             update[i]->level[i].span += x->level[i].span - 1;
     6             update[i]->level[i].forward = x->level[i].forward;
     7         } else {
     8             update[i]->level[i].span -= 1;
     9         }
    10     }
    11     if (x->level[0].forward) {
    12         x->level[0].forward->backward = x->backward;
    13     } else {
    14         zsl->tail = x->backward;
    15     }
    16     while(zsl->level > 1 && zsl->header->level[zsl->level-1].forward == NULL)
    17         zsl->level--;
    18     zsl->length--;
    19 }

    删除本节点之后,对应路径相应得做处理。

    从跳表中删除指定节点的操作:

     1 int zslDelete(zskiplist *zsl, double score, sds ele, zskiplistNode **node) {
     2     zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
     3     int i;
     4 
     5     //先用score与ele查找,生成update数组
     6     x = zsl->header;
     7     for (i = zsl->level-1; i >= 0; i--) {
     8         while (x->level[i].forward &&
     9                 (x->level[i].forward->score < score ||
    10                     (x->level[i].forward->score == score &&
    11                      sdscmp(x->level[i].forward->ele,ele) < 0)))
    12         {
    13             x = x->level[i].forward;
    14         }
    15         update[i] = x;
    16     }
    17 
    18     //跳表允许同score,防止误删,做一下ele校验
    19     if (x && score == x->score && sdscmp(x->ele,ele) == 0) {
    20         zslDeleteNode(zsl, x, update);
    21         if (!node)
    22             zslFreeNode(x);
    23         else
    24             *node = x;
    25         return 1;
    26     }
    27     return 0;
    28 }

    如以下跳表:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+                +--------+                +--------+
     9       |level[1]|--------------->|level[1]|--------------->|level[1]|-->NULL
    10       |2       |                |2       |                |0       |
    11       +--------+   +--------+   +--------+   +--------+   +--------+
    12       |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->NULL
    13       |1       |   |1       |   |1       |   |1       |   |0       |
    14       +--------+   +--------+   +--------+   +--------+   +--------+
    15 NULL<-|backward|   |backward|<--|backward|<--|backward|<--|backward|
    16       +--------+   +--------+   +--------+   +--------+   +--------+
    17       |0       |   |2       |   |3       |   |4       |   |5       |
    18       +--------+   +--------+   +--------+   +--------+   +--------+
    19       |NULL    |   |b       |   |c       |   |d       |   |e       |
    20   +-->+--------+   +--------+   +--------+   +--------+   +--------+<--+
    21   |                                                                    |
    22   |   +--------+                                                       |
    23   +---|header  |                                                       |
    24       +--------+                                                       |
    25       |tail    |-------------------------------------------------------+
    26       +--------+
    27       |length=4|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 /*

    要删除节点d,生成的update数组为:

     1 /*
     2 update       
     3 +--------+   
     4 |NULL    |   
     5 +--------+   
     6 |NULL    |   
     7 +--------+   
     8 |c       |   
     9 +--------+   
    10 |c       |   
    11 +--------+   
    12 */

    由于d的level为1,故在level[0]层,使用从单向链表中删除节点的操作,把d移出,再给高于level[0]的update数组中所有成员的span自减,节点少了,跨度要跟着降低。

    删除d之后的跳表:

     1 /*
     2       +--------+
     3       |level[3]|-->NULL
     4       |0       |
     5       +--------+
     6       |level[2]|-->NULL
     7       |0       |
     8       +--------+                +--------+   +--------+
     9       |level[1]|--------------->|level[1]|-->|level[1]|-->NULL
    10       |2       |                |1       |   |0       |
    11       +--------+   +--------+   +--------+   +--------+
    12       |level[0]|-->|level[0]|-->|level[0]|-->|level[0]|-->NULL
    13       |1       |   |1       |   |1       |   |0       |
    14       +--------+   +--------+   +--------+   +--------+
    15 NULL<-|backward|   |backward|<--|backward|<--|backward|
    16       +--------+   +--------+   +--------+   +--------+
    17       |0       |   |2       |   |3       |   |5       |
    18       +--------+   +--------+   +--------+   +--------+
    19       |NULL    |   |b       |   |c       |   |e       |
    20   +-->+--------+   +--------+   +--------+   +--------+<--+
    21   |                                                       |
    22   |   +--------+                                          |
    23   +---|header  |                                          |
    24       +--------+                                          |
    25       |tail    |------------------------------------------+
    26       +--------+
    27       |length=3|
    28       +--------+
    29       |level=2 |
    30       +--------+
    31 /*

    五、销毁

     1 void zslFreeNode(zskiplistNode *node) {
     2     sdsfree(node->ele);
     3     zfree(node);
     4 }
     5 
     6 void zslFree(zskiplist *zsl) {
     7     zskiplistNode *node = zsl->header->level[0].forward, *next;
     8 
     9     zfree(zsl->header);
    10     while(node) {
    11         next = node->level[0].forward;
    12         zslFreeNode(node);
    13         node = next;
    14     }
    15     zfree(zsl);
    16 }

    销毁操作本身只是在level[0]层遍历所有节点,依次销毁。

    redis 5.0.7 下载链接

    http://download.redis.io/releases/redis-5.0.7.tar.gz

    源码阅读顺序参考:

    https://github.com/huangz1990/blog/blob/master/diary/2014/how-to-read-redis-source-code.rst

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  • 原文地址:https://www.cnblogs.com/treeskyer/p/14030471.html
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