redis 数据结构之跳跃表

数据结构

跳跃表

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

length 节点数量
level 表的最大层

跳跃表节点

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

score 分值
forward 前进指针
span 间隔的节点数量，当前节点和下一个节点的距离，初始span为0，level[0]的span都为1

demo

源码API分析

创建skiplist

/* Create a new skiplist. */
zskiplist *zslCreate(void) {
    int j;
    zskiplist *zsl;
    zsl = zmalloc(sizeof(*zsl));
    zsl->level = 1;
    zsl->length = 0;
    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;
}

头节点的层是ZSKIPLIST_MAXLEVEL 32

zslFree 释放给定跳跃表

/* Free the specified skiplist node. The referenced SDS string representation
 * of the element is freed too, unless node->ele is set to NULL before calling
 * this function. */
void zslFreeNode(zskiplistNode *node) {
    sdsfree(node->ele);
    zfree(node);
}

/* Free a whole skiplist. */
void zslFree(zskiplist *zsl) {
    zskiplistNode *node = zsl->header->level[0].forward, *next;//逗号表达式 声明了一个 zskiplistNode * 变量

    zfree(zsl->header);
    while(node) {
        next = node->level[0].forward;
        zslFreeNode(node);
        node = next;
    }
    zfree(zsl);
}

从头节点依次释放，时间复杂度O(N)

zslCreateNode创建skiplistNode

/* Create a skiplist node with the specified number of levels.
 * The SDS string 'ele' is referenced by the node after the call. */
zskiplistNode *zslCreateNode(int level, double score, sds ele) {
    zskiplistNode *zn =
        zmalloc(sizeof(*zn)+level*sizeof(struct zskiplistLevel));
    zn->score = score;
    zn->ele = ele;
    return zn;
}

生成随机level

int zslRandomLevel(void) {
    int level = 1;
    while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF))
        level += 1;
    return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL;
}

ZSKIPLIST_P的值是0.25，random()生成的数，转换成32位表示，高三位只有001、000满足，也就是说，k层的概率是k+1层概率的4倍

查找member的rank(ZRANK)

/* Find the rank for an element by both score and key.
 * Returns 0 when the element cannot be found, rank otherwise.
 * Note that the rank is 1-based due to the span of zsl->header to the
 * first element. */
unsigned long zslGetRank(zskiplist *zsl, double score, sds ele) {
    zskiplistNode *x;
    unsigned long rank = 0;
    int i;

    //起始位置是从header开始
    x = zsl->header;
    //从跳跃表的level-1的位置开始，向下遍历
    for (i = zsl->level-1; i >= 0; i--) {
        //当前进指针不为null && 要查找的节点值在forward节点的前面（也就是说还需要往前查找）
        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加上这一层的span
            rank += x->level[i].span;

            //x前移
            x = x->level[i].forward;
        }

        /* x might be equal to zsl->header, so test if obj is non-NULL */
        if (x->ele && sdscmp(x->ele,ele) == 0) {
            return rank;
        }
    }
    return 0;
}

查找的过程类似树的查找，从K层开始查找，查找的score大于当前的score，指针前移，小于就从指针指向的位置的K-1层开始查找

插入新的Node

/* Insert a new node in the skiplist. Assumes the element does not already
 * exist (up to the caller to enforce that). The skiplist takes ownership
 * of the passed SDS string 'ele'. */
zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) {
    //update记录的是插入节点的每一层的上一个节点
    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;//rank[i]记录的是i层到从表头到update[i]的距离
            x = x->level[i].forward;
        }
        //x为待插入节点的每一层的最后一个位置
        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. */

    //新节点的level长度random是随机数
    level = zslRandomLevel();
    //如果random 大于 skiplist的最大层max，更新头节点的max到random层中的span，更新skiplist的最大层
    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;//表头i层的span等于length
        }
        zsl->level = level;
    }
    x = zslCreateNode(level,score,ele);
    for (i = 0; i < level; i++) {
        //第i层 节点插入update[i]的后面
        x->level[i].forward = update[i]->level[i].forward;
        update[i]->level[i].forward = x;//i层x的前后节点都初始化

        /* update span covered by update[i] as x is inserted here */
        // update[i]->level[i].span  i层x上一个节点到x下一个节点的距离
        // rank[i] i层上一个节点到表头的距离
        // rank[0]+1 是x到表头的距离
        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 */
    //从random到max的这些层span进行更新
    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;
}

时间复杂度 平均O（logN)，最差O(N) ps（i+1层是i层数的1／2，0层的平均耗时为N/2)

zslDelete 删除，和插入类似，忽略。

注意

跳跃表允许重复的score值
查找的时候需要检查score值和member，查找的时候是从跳跃表的最大层在头节点开始查找，依次往下次查找，查找都是用的forward
头节点的最大层是32，跳跃表的最大层为节点的最大层
每层保存的span可以用来快速计算最后的rank，跳跃表的查找性能很高