跳表与redis数据结构zset

跳表概念

跳表是链表的一种扩展
链表的查找性能低，复杂度为O(n)
通过设置多级索引的方法降低查找的复杂度

动态结构

跳表是一种动态的数据结构，对其插入删除时会自动调整，如不调整，可能退化成链表。
删除时，如果节点对应索引，也删除对应的索引
插入时，通过随机函数判定要不要添加索引以及添加索引到哪一级

Redis zset

集合中的元素不能重复，但是可以排序，是有序的。它给每个元素设置一个分数（score）作为排序的依据，有序集合提供了获取指定分数和元素范围查询，计算成员排名。

相关源码

zset 的数据结构由跳表和哈希表共同完成

数据结构

typedef struct zset {
    dict *dict;
    zskiplist *zsl;
} zset;

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

typedef struct zskiplistNode {
    sds ele;      
    double score; 
    struct zskiplistNode *backward;
    struct zskiplistLevel {
        struct zskiplistNode *forward;
        unsigned long span;
    } level[];
} zskiplistNode;

插入

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;
}

随机

/* Returns a random level for the new skiplist node we are going to create.
 * The return value of this function is between 1 and ZSKIPLIST_MAXLEVEL
 * (both inclusive), with a powerlaw-alike distribution where higher
 * levels are less likely to be returned. */
int zslRandomLevel(void) {
    int level = 1;
    while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF))
        level += 1;
    return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL;
}

参考资料：
https://juejin.im/post/6844904181900247053
https://juejin.im/post/6859134569703669774#heading-6