redis-zset数据结构探索

redis用的人比较多，其中zset大家都熟悉，主要用于排名场景。
zset数据结构，分成两部分，一部分是用于排序，一部分用于缓存键值。
先看看结构：

typedef struct zset {
    dict *dict;         //缓存
    zskiplist *zsl;     //排序结构
} zset;

上面，跳跃表用于排序结构，可以按照名次，积分查找对应键, 时间复杂度: log(n)。
按照名次，积分范围查找一系列键时, 先查询满足条件的第一个键，然后当前键查找后续键， 时间复杂度: log(n) + o(m), n=总键数, m=查询结果键数。

跳跃表结构:

typedef struct zskiplist {
    struct zskiplistNode *header, *tail;        //头结点:用于顺序查询，常用方式; 尾结点:用于倒序简单查询。
    unsigned long length;                       //结点数
    int level;                                  //跳跃层级
} zskiplist;

结点结构：

typedef struct zskiplistNode {
    robj *obj;                                  //键
    double score;                               //积分
    struct zskiplistNode *backward;             //前一个结点, 和level[0]可看作双链表
    struct zskiplistLevel {                     //跳跃层关系, 每层都是单链表
        struct zskiplistNode *forward;          //此层下一个结点
        unsigned int span;                      //此层下一个结点和当前结点距离(两者隔了多少结点)
    } level[];                                  //最多32层
} zskiplistNode; 

查询：
根据名次范围查询

void zrangeGenericCommand(client *c, int reverse) {
        ......

        zset *zs = zobj->ptr;           //zset结构变量
        zskiplist *zsl = zs->zsl;       //跳跃表
        zskiplistNode *ln;
        robj *ele;

        /* Check if starting point is trivial, before doing log(N) lookup. */
        if (reverse) {                  //是否倒序查询
            ln = zsl->tail;             //默认取尾结点
            if (start > 0)
                ln = zslGetElementByRank(zsl,llen-start);       //如果start>0, 则取对应结点
        } else {
            ln = zsl->header->level[0].forward; //默认取第一个结点
            if (start > 0)
                ln = zslGetElementByRank(zsl,start+1);
        }

        while(rangelen--) {             //取rangelen个结点
            serverAssertWithInfo(c,zobj,ln != NULL);
            ele = ln->obj;
            addReplyBulk(c,ele);        //响应键名
            if (withscores)
                addReplyDouble(c,ln->score);    //响应键值
            ln = reverse ? ln->backward : ln->level[0].forward; //设置下一个结点
        }

        ......
}

/* Finds an element by its rank. The rank argument needs to be 1-based. */
zskiplistNode* zslGetElementByRank(zskiplist *zsl, unsigned long rank) {
    zskiplistNode *x;
    unsigned long traversed = 0;                //当前名次
    int i;

    x = zsl->header;                            //头结点, 从头结点的下一个结点遍历
    for (i = zsl->level-1; i >= 0; i--) {       //从高层到低层链表遍历
        while (x->level[i].forward && (traversed + x->level[i].span) <= rank)   //如果有下一个结点，且下一个结点的名次<=rank
        {
            traversed += x->level[i].span;
            x = x->level[i].forward;
        }
        if (traversed == rank) {                //找到对应名次的结点
            return x;
        }
    }
    return NULL;
}

 zslGetElementByRank()时间复杂度理想值 = log(n)

 
如果有删除，添加操作，和查询类似，需要额外维护跳跃表关系。

/* Delete all the elements with score between min and max from the skiplist.
 * Min and max are inclusive, so a score >= min || score <= max is deleted.
 * Note that this function takes the reference to the hash table view of the
 * sorted set, in order to remove the elements from the hash table too. 
 * 根据积分范围删除结点
 */
unsigned long zslDeleteRangeByScore(zskiplist *zsl, zrangespec *range, dict *dict) {
    zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;      //update维护跳跃表层级关系,用于zslDeleteNode()
    unsigned long removed = 0;
    int i;

    x = zsl->header;
    for (i = zsl->level-1; i >= 0; i--) {
        while (x->level[i].forward && (range->minex ?   //不満足积分条件时，循环
            x->level[i].forward->score <= range->min :
            x->level[i].forward->score < range->min))
                x = x->level[i].forward;
        update[i] = x;                                  //此层最接近于条件的结点
    }

    /* Current node is the last with score < or <= min. */
    x = x->level[0].forward;                            //第一个最可能满足条件的结点

    /* Delete nodes while in range. */
    while (x &&
           (range->maxex ? x->score < range->max : x->score <= range->max))     //满足条件的结点
    {
        zskiplistNode *next = x->level[0].forward;
        zslDeleteNode(zsl,x,update);                    //更新层级关系
        dictDelete(dict,x->obj);                        //删除缓存
        zslFreeNode(x);
        removed++;
        x = next;
    }
    return removed;
}

/* Internal function used by zslDelete, zslDeleteByScore and zslDeleteByRank */
void zslDeleteNode(zskiplist *zsl, zskiplistNode *x, zskiplistNode **update) {
    int i;
    for (i = 0; i < zsl->level; i++) {                  //更新层级关系
        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) {                          //维护当前结点的下一个结点
        x->level[0].forward->backward = x->backward;
    } else {
        zsl->tail = x->backward;                        //维护尾结点
    }
    while(zsl->level > 1 && zsl->header->level[zsl->level-1].forward == NULL)
        zsl->level--;                                   //维护层数
    zsl->length--;                                      //维护结点数
}

根据键名查找积分, 有了zset->dict这个键值缓存，只需要时间复杂度0(1)

int zsetScore(robj *zobj, robj *member, double *score) {
    if (!zobj || !member) return C_ERR;

    if (zobj->encoding == OBJ_ENCODING_ZIPLIST) {       //ziplit实现
        if (zzlFind(zobj->ptr, member, score) == NULL) return C_ERR;
    } else if (zobj->encoding == OBJ_ENCODING_SKIPLIST) {
        zset *zs = zobj->ptr;
        dictEntry *de = dictFind(zs->dict, member);     //找到缓存entry
        if (de == NULL) return C_ERR;
        *score = *(double*)dictGetVal(de);              //获取对应积分  
    } else {
        serverPanic("Unknown sorted set encoding");
    }
    return C_OK;
}

如果zset对象用ziplist实现，则查询和删除操作时间复杂度 = o(n)

...