redis 5.0.7 源碼閱讀——跳躍表skiplist

時間 2020-02-09

標籤 redis 5.0.7 源碼閱讀跳躍 skiplist 欄目 Redis 简体版

原文原文鏈接

redis中並無專門給跳躍表兩個文件。在5.0.7的版本中，結構體的聲明與定義、接口的聲明在server.h中，接口的定義在t_zset.c中，全部開頭爲zsl的函數。node

1、數據結構linux

單個節點：git

typedef struct zskiplistNode {
    //key，惟一
    sds ele;

    //分值，可重複
    double score;

    //後退指針
    struct zskiplistNode *backward;

    //層
    struct zskiplistLevel {
        //前進指針
        struct zskiplistNode *forward;
        //到本層下一節點的跨度，用於計算rank
        unsigned long span;
    } level[];
} zskiplistNode;

zskiplistNode定義了跳躍表中每一個節點的數據結構，它是一個變長結構體。github

 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 */

將用如下結構表示：redis

 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：數組

 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 */

跳錶：數據結構

1 typedef struct zskiplist {
2     //頭/尾節點
3     struct zskiplistNode *header, *tail;
4     //總長度
5     unsigned long length;
6     //總層數
7     int level;
8 } zskiplist;

因其頭節點固定爲空節點，固總體結構：dom

 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 */

每一個level層都是一條單身鏈表，其中level[0]中包含全部元素。函數

2、建立spa

根據指定的level，建立一個跳錶節點：

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 }

建立一個跳錶：

 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中定義的最大層數爲64層。且在剛建立時，會生成一個空的頭節點，這樣就能夠不用再考慮節點數從0至1或者從1至0時要處理的各類特殊狀況。

剛創完的跳錶結構（結構中以4作爲最大層數，後同）：

 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 */

3、插入節點

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中使用的決定新插入節點層數據的方法是拋硬幣法，且「硬幣」只有25%的概率是正面。

插入方法：

 1 zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) {
 2     //update數組，用於存儲查找路徑
 3     zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
 4 
 5     //rank數組，用於存儲每層路徑節點的排名
 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     //隨機一個level
28     level = zslRandomLevel();
29 
30     //若當前最大level不夠，則補齊update與rank數組
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     //建立一個節點，並插入
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數組中，比插入節點level更高的各成員的跨度增長
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 }

從註釋可知，redis的跳錶容許同score的狀況發生，可是不容許同ele，且是由調用者在外部保證。若插入順序爲e，b，c，d，則插入e時：

step一、定義update數組與rank數組。

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

實際在linux環境運行時，不會默認初始化，應該是一堆髒數據，此處是爲了方便處理結構

step二、查找位置後

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

step三、e的level爲2，比跳錶的大，故要補齊update與rank數組

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

step四、插入節點，與單身鏈表插入相同，將新節點e各層，插入到update數組中記錄的各層節點以後，並使用rank數組，計算跨度

 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 */

step五、處理新插入節點的backward指針，與跳錶的tail指針：

 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 */

此時插入b：

找到位置後的update與rank數組：

 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節點後：

 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 */

須要注意的是，update數組idx = 1的節點並無新的插入操做，span要自增，表示本層跨度增長了1。

插入c時的update與rank數組：

 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後：

 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 /*

最後插入d：

update與rank數組：

 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 /*

若是此時要新插入節點a，score爲4.5，則update與rank數組分別爲：

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

4、刪除節點

在已經查找到位置，與已知update數組時的刪除方法：

 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 }

刪除本節點以後，對應路徑相應得作處理。

從跳錶中刪除指定節點的操做：

 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與ele查找，生成update數組
 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     //跳錶容許同score，防止誤刪，作一下ele校驗
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 }

如如下跳錶：

 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 /*

要刪除節點d，生成的update數組爲：

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

因爲d的level爲1，故在level[0]層，使用從單向鏈表中刪除節點的操做，把d移出，再給高於level[0]的update數組中全部成員的span自減，節點少了，跨度要跟着下降。

刪除d以後的跳錶：

 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 /*

5、銷燬

 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 }