跳跃表是一种有序数据结构，他是通过在每个节点中维持多个指向其他节点的指针，从而达到快速访问节点的目的。在的插入和删除都可以在O(lgN)时间复杂度内搞定

　　Redis在两个地方用到跳跃表，一个是实现有序集合键，另一个是在集群节点中用作内部数据结构。

　　　　1.跳跃表的实现

/* ZSETs use a specialized version of Skiplists */
typedef struct zskiplistNode {
    robj *obj;
    //分值
    double score;
    //后退指针
    struct zskiplistNode *backward;
    //层
    struct zskiplistLevel {
        //前进指针
        struct zskiplistNode *forward;
        //跨度
        unsigned int span;
    } level[];
} zskiplistNode;

typedef struct zskiplist {
    struct zskiplistNode *header, *tail;
    unsigned long length; //记录跳跃表内，层数最大的节点的层数
    int level;     //记录跳跃表的长度 也就是目前包含节点的数量
} zskiplist;

跳跃表的结构如图:图片来源

 

 

　　跳跃表节点每个元素都包含一个指向其他节点的指针，程序可以通过这些层来加快访问其他节点的速度，并且层数越多，访问节点的速度就越快。

　　每次创建一个新跳跃表节点的时候，程序都会根据幂次定律（越大的数出现的概率越小）随机生成一个1～32之间的值作为level。

　　2.跳跃表的实现

　　　　1.跳跃表的结构

/* ZSETs use a specialized version of Skiplists */
typedef struct zskiplistNode {
    robj *obj;
    //分值
    double score;
    //后退指针
    struct zskiplistNode *backward;
    //层
    struct zskiplistLevel {
        //前进指针
        struct zskiplistNode *forward;
        //跨度
        unsigned int span;
    } level[];
} zskiplistNode;

typedef struct zskiplist {
    struct zskiplistNode *header, *tail;
    unsigned long length; //记录跳跃表内，层数最大的节点的层数
    int level;     //记录跳跃表的长度 也就是目前包含节点的数量
} zskiplist;

　　　　2.跳跃表的创建

//创建一个跳表的节点
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;
}

zskiplist *zslCreate(void) {
    int j;
    //表头
    zskiplist *zsl;

    zsl = zmalloc(sizeof(*zsl));
    zsl->level = 1;   //初始化节点层数为1
    zsl->length = 0;   //初始化节点数为0
    //ZSKIPLIST_MAXLEVEL = 32  头节点默认32层 所有节点层数不能超过32
    zsl->header = zslCreateNode(ZSKIPLIST_MAXLEVEL,0,NULL);
    //初始化 表头的32个level层
    for (j = 0; j < ZSKIPLIST_MAXLEVEL; j++) {
        zsl->header->level[j].forward = NULL;  //初始化头节点层结构数组
        zsl->header->level[j].span = 0;
    }
    zsl->header->backward = NULL;
    zsl->tail = NULL;
    return zsl;
}

　　　　3.跳跃表的插入

//插入元素
zskiplistNode *zslInsert(zskiplist *zsl, double score, robj *obj) {
    zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x; //update节点数组  保存插入节点每一层的前驱节点
    unsigned int rank[ZSKIPLIST_MAXLEVEL]; //rank 用于保存 插入位置在每一层中跨过的节点数
    int i, level;

    redisAssert(!isnan(score));
    x = zsl->header;  //设置头节点
    for (i = zsl->level-1; i >= 0; i--) {
        /* store rank that is crossed to reach the insert position */
        //如果是最高层 则表示扩过0个节点 否则 记录跨过的节点数 与上一层相同
        rank[i] = i == (zsl->level-1) ? 0 : rank[i+1];
        //每次遍历从上一层的前驱节点开始遍历
        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))) {
            rank[i] += x->level[i].span;
            x = x->level[i].forward;
        }
        update[i] = x; //记录第i层的前驱节点
    }
    /* we assume the key is not already inside, since we allow duplicated
     * scores, and the re-insertion of score and redis object should never
     * happen since the caller of zslInsert() should test in the hash table
     * if the element is already inside or not. */
    level = zslRandomLevel(); //随机生成层数
    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,obj);  //生成x node
    for (i = 0; i < level; i++) { //插入node节点 并更新前驱节点和跨度
        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;
}

　　　　4.跳跃表的删除

//逐层遍历 删除x节点 update 记录x节点每一层的前驱节点
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--;
}

/* Delete an element with matching score/object from the skiplist. */
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; //记录节点的前驱节点
    }
    /* 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 && equalStringObjects(x->obj,obj)) {
        zslDeleteNode(zsl, x, update);
        zslFreeNode(x);
        return 1;
    }
    return 0; /* not found */
}

　　　　5.跳跃表查找：会给定一个range，然后在跳跃表中查找相应的值，可用于查找删除操作。

　　　　range的数据结构

/* Struct to hold a inclusive/exclusive range spec by score comparison. */
typedef struct {
    double min, max;  //最大值 最小值
    int minex, maxex; /* are min or max exclusive? */ //是否为开闭空间 1为开 0为闭
} zrangespec;

/* Struct to hold an inclusive/exclusive range spec by lexicographic comparison. */
//一个字典顺序的范围
typedef struct {
    robj *min, *max;  /* May be set to shared.(minstring|maxstring) */
    int minex, maxex; /* are min or max exclusive? */
} zlexrangespec;

　　例如返回区间的最小值

static int zslValueGteMin(double value, zrangespec *spec) {
    return spec->minex ? (value > spec->min) : (value >= spec->min);
}

static int zslValueLteMax(double value, zrangespec *spec) {
    return spec->maxex ? (value < spec->max) : (value <= spec->max);
}

/* Returns if there is a part of the zset is in range. */
//判断是否有(range->min,range->max)在哈希表中
int zslIsInRange(zskiplist *zsl, zrangespec *range) {
    zskiplistNode *x;

    /* Test for ranges that will always be empty. */
    if (range->min > range->max ||
            (range->min == range->max && (range->minex || range->maxex)))
        return 0;
    x = zsl->tail;
    if (x == NULL || !zslValueGteMin(x->score,range))
        return 0;
    x = zsl->header->level[0].forward;
    if (x == NULL || !zslValueLteMax(x->score,range))
        return 0;
    return 1;
}

/* Find the first node that is contained in the specified range.
 * Returns NULL when no element is contained in the range. */
//返回满足区间最小值
zskiplistNode *zslFirstInRange(zskiplist *zsl, zrangespec *range) {
    zskiplistNode *x;
    int i;

    /* If everything is out of range, return early. */
    if (!zslIsInRange(zsl,range)) return NULL;

    x = zsl->header;
    for (i = zsl->level-1; i >= 0; i--) {
        /* Go forward while *OUT* of range. */
        while (x->level[i].forward &&
            !zslValueGteMin(x->level[i].forward->score,range))
                x = x->level[i].forward;
    }

    /* This is an inner range, so the next node cannot be NULL. */
    x = x->level[0].forward;
    redisAssert(x != NULL);

    /* Check if score <= max. */
    if (!zslValueLteMax(x->score,range)) return NULL;
    return x;
}