Redis之SkipList数据结构

0.前言

Redis中有序集合zset需要使用skiplist作为存储数据结构, 关于skiplist数据结构描述可以查询wiki, 本文主要介绍Redis实现的skiplist的细节.

1.数据结构定义

typedef struct zskiplistNode {
     /*成员object对象*/
    robj *obj;
     /*分数字段依赖此值对skiplist进行排序*/
    double score;
     /*插入层中指向上一个元素level数组*/
    struct zskiplistNode *backward;
    struct zskiplistLevel {
          /*每层中指向下一个元素指针*/
        struct zskiplistNode *forward;
          /*距离下一个元素之间元素数量, 即forward指向的元素*/
        unsigned int span;
    } level[];
} zskiplistNode;

typedef struct zskiplist {
     /*跳跃表头节点和尾节点*/
    struct zskiplistNode *header, *tail;
     /*跳跃表中元素个数*/
    unsigned long length;
     /*跳跃表当前最大层数*/
    int level;
} zskiplist;

2.创建跳跃表

创建跳跃表过程比较简单, 初始化zskiplist数据结构, 跳跃表默认最大层数32层, 跳跃表是按score进行升序排列.

/*创建跳跃表*/
zskiplist *zslCreate(void) {
    int j;
    zskiplist *zsl;

    zsl = zmalloc(sizeof(*zsl));
    zsl->level = 1;
    zsl->length = 0;
     /*初始化创建一个头节点, 初始化节点信息*/
    zsl->header = zslCreateNode(ZSKIPLIST_MAXLEVEL,0,NULL);
    for (j = 0; j < ZSKIPLIST_MAXLEVEL; j++) {
        zsl->header->level[j].forward = NULL;
        zsl->header->level[j].span = 0;
    }
    zsl->header->backward = NULL;
    zsl->tail = NULL;
    return zsl;
}
/*创建一个跳跃表节点*/
zskiplistNode *zslCreateNode(int level, double score, robj *obj) {
    zskiplistNode *zn = zmalloc(sizeof(*zn)+level*sizeof(struct zskiplistLevel));
    zn->score = score;
    zn->obj = obj;
    return zn;
}

3.添加元素

zskiplistNode *zslInsert(zskiplist *zsl, double score, robj *obj) {
    zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x;
    unsigned int rank[ZSKIPLIST_MAXLEVEL];
    int i, level;

    redisAssert(!isnan(score));
    x = zsl->header;
     /*从头节点开始搜索, 一层一层向下搜索, 直到直到最后一层, update数组中保存着每层应该插入的位置*/
    for (i = zsl->level-1; i >= 0; i--) {
        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 &&
                compareStringObjects(x->level[i].forward->obj,obj) < 0))) {
               /*记录每层距离头部位置的距离*/
            rank[i] += x->level[i].span;
            x = x->level[i].forward;
        }
        update[i] = x;
    }
    /* 随机一个层数, 如果随机的层数是新的层数, 则需要给update数组中新的层数赋值*/
    level = zslRandomLevel();
    if (level > zsl->level) {
        for (i = zsl->level; i < level; i++) {
            rank[i] = 0;
               /*新的一层上一个指针肯定是header*/
            update[i] = zsl->header;
            update[i]->level[i].span = zsl->length;
        }
        zsl->level = level;
    }
     /*创建新的节点插入到update数组对应的层*/
    x = zslCreateNode(level,score,obj);
    for (i = 0; i < level; i++) {
        x->level[i].forward = update[i]->level[i].forward;
        update[i]->level[i].forward = x;
        /*
         header                update[i]     x    update[i]->forward         
          |-----------|-----------|-----------|-----------|-----------|-----------|
                                  |<---update[i].span---->|
          |<-------rank[i]------->|                      
          |<-------------------rank[0]------------------->|
         
          更新update数组中span值和新插入元素span值, rank[0]存储的是x元素距离头部的距离, rank[i]存储的是update[i]距离头部的距离, 上面给出了示意图
          */
        x->level[i].span = update[i]->level[i].span - (rank[0] - rank[i]);
        update[i]->level[i].span = (rank[0] - rank[i]) + 1;
    }

    /* level可能小zsl->level, 无变动的元素span依次增加1*/
    for (i = level; i < zsl->level; i++) {
        update[i]->level[i].span++;
    }
     /*上一个元素level数组, 重新赋值*/
    x->backward = (update[0] == zsl->header) ? NULL : update[0];
    if (x->level[0].forward)
        x->level[0].forward->backward = x;
    else
          /*下一个元素为空,则表示x为尾部元素*/
        zsl->tail = x;
    zsl->length++;
    return x;
}

4.获取排名

排名其实就是元素在skiplist中排列的序号, 获取排名需要给出分数和成员member, 通过score查找, 匹配member成员, 时间复杂度log(N). 由于skiplist是升序排列的,因此函数返回的rank是score按升序排列的rank, 如果想获取降序rank应该是(length-rank).

unsigned long zslGetRank(zskiplist *zsl, double score, robj *o) {
    zskiplistNode *x;
    unsigned long rank = 0;
    int i;

    x = zsl->header;
     /*循环遍历并累加每层的span值, 获取总的排名*/
    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 &&
                compareStringObjects(x->level[i].forward->obj,o) <= 0))) {
            rank += x->level[i].span;
            x = x->level[i].forward;
        }

        /* 判断成员是否相等 */
        if (x->obj && equalStringObjects(x->obj,o)) {
              /*升序排列的排名*/
            return rank;
        }
    }
    return 0;
}

5.根据排名查找元素

/*通过排名查找元素, rank是从1开始, rank是升序排列的rank值*/
zskiplistNode* zslGetElementByRank(zskiplist *zsl, unsigned long rank) {
    zskiplistNode *x;
    unsigned long traversed = 0;
    int i;

     /*遍历每一层,并记录排名, 与待查rank比较, 相等则找到, 找不到则返回NULL*/
    x = zsl->header;
    for (i = zsl->level-1; i >= 0; i--) {
        while (x->level[i].forward && (traversed + x->level[i].span) <= rank)
        {
            traversed += x->level[i].span;
            x = x->level[i].forward;
        }
          /*找到直接返回*/
        if (traversed == rank) {
            return x;
        }
    }
    return NULL;
}

6.删除元素

删除元素需要精确匹配到分数和member

/*删除一个元素*/
int zslDelete(zskiplist *zsl, double score, robj *obj) {
    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 &&
                compareStringObjects(x->level[i].forward->obj,obj) < 0)))
            x = x->level[i].forward;
        update[i] = x;
    }
    /* 由于score值可能相等, 因此需要精确匹配score和obj值 */
    x = x->level[0].forward;
    if (x && score == x->score && equalStringObjects(x->obj,obj)) {
        zslDeleteNode(zsl, x, update);
        zslFreeNode(x);
        return 1;
    }
    return 0; /* not found */
}

/* 具体进行删除元素所在节点*/
void zslDeleteNode(zskiplist *zsl, zskiplistNode *x, zskiplistNode **update) {
    int i;
     /*删除元素需要更新update元素的span值*/
    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) {
          /*非尾部元素则需要重置backforward指针*/
        x->level[0].forward->backward = x->backward;
    } else {
          /*删除x可能是最后一个元素, 需要重置尾部指针*/
        zsl->tail = x->backward;
    }
     /*删除元素位于最上层, 并且仅有此一个元素, 删除之后,需要降低跳跃表层数*/
    while(zsl->level > 1 && zsl->header->level[zsl->level-1].forward == NULL)
        zsl->level--;
    zsl->length--;
}