0%

skiplist

skiplist

结构

skiplist提供了平均$O(log n)$的查找、插入和删除。zskiplistNode中使用柔性数组设计,每个节点存储了sds,level数组存储了各层指向其他节点的指针,最大层数为ZSKIPLIST_MAXLEVEL = 64

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
/* ZSETs use a specialized version of Skiplists */
typedef struct zskiplistNode {
sds ele;
double score;
struct zskiplistNode *backward;
struct zskiplistLevel {
struct zskiplistNode *forward;
unsigned long span;
} level[];
} zskiplistNode;

typedef struct zskiplist {
struct zskiplistNode *header, *tail;
unsigned long length;
int level;
} zskiplist;

插入

先找到待插入的位置,查找的时候从顶层开始,在当前层尽可能的往前移动,每层都满足[header, update[i]]:(< score) or (== score and < ele))。最终的插入位置在update[i]之后。

要提的一点是redis的skiplist还维护了,

  • span,记录了两个节点间的距离。

    • 寻找插入位置时,需要在每层都累加节点的span

    • 插入时,

      1
      2
      x->level[i].span = update[i]->level[i].span - (rank[0] - rank[i]);
      update[i]->level[i].span = (rank[0] - rank[i]) + 1;
  • forward,记录了节点的prev指针。

    在插入时,如果新节点的random level > zsl->level,则需要将update中多出来的level设置为header。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) {
zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
unsigned int rank[ZSKIPLIST_MAXLEVEL];
int i, level;

serverAssert(!isnan(score));
x = zsl->header;
for (i = zsl->level-1; i >= 0; i--) {
/* store rank that is crossed to reach the insert position */
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. */
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;
}
x = zslCreateNode(level,score,ele);
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 */
for (i = level; i < zsl->level; i++) {
update[i]->level[i].span++;
}

x->backward = (update[0] == zsl->header) ? NULL : update[0];
if (x->level[0].forward)
x->level[0].forward->backward = x;
else
zsl->tail = x;
zsl->length++;
return x;
}

删除

和以插入相同的方式查找待删除节点。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
int zslDelete(zskiplist *zsl, double score, sds ele, zskiplistNode **node) {
zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
int i;

x = zsl->header;
for (i = zsl->level-1; i >= 0; i--) {
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)))
{
x = x->level[i].forward;
}
update[i] = x;
}
/* We may have multiple elements with the same score, what we need
* is to find the element with both the right score and object. */
x = x->level[0].forward;
if (x && score == x->score && sdscmp(x->ele,ele) == 0) {
zslDeleteNode(zsl, x, update);
if (!node)
zslFreeNode(x);
else
*node = x;
return 1;
}
return 0; /* not found */
}

删除时需要维护spanforward

  • 如果当前层update[i]->level[i].forward == x

    • span

      累加上x的,并减1。

    • forward

      在每层指向待删除节点的下一个节点,update[i]->level[i].forward = x->level[i].forward

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

Reference

  1. Redis内部数据结构详解(6)——skiplist