Redis之SkipList數據結構

0.前言

Redis中有序集合zset須要使用skiplist做爲存儲數據結構, 關於skiplist數據結構描述能夠查詢wiki, 本文主要介紹Redis實現的skiplist的細節.

1.數據結構定義

typedef struct zskiplistNode {
     /*成員object對象*/
    robj *obj;
     /*分數字段依賴此值對skiplist進行排序*/
    double score;
     /*插入層中指向上一個元素level數組*/
    struct zskiplistNode *backward;
    struct zskiplistLevel {
          /*每層中指向下一個元素指針*/
        struct zskiplistNode *forward;
          /*距離下一個元素之間元素數量, 即forward指向的元素*/
        unsigned int span;
    } level[];
} zskiplistNode;

typedef struct zskiplist {
     /*跳躍表頭節點和尾節點*/
    struct zskiplistNode *header, *tail;
     /*跳躍表中元素個數*/
    unsigned long length;
     /*跳躍表當前最大層數*/
    int level;
} zskiplist;

2.建立跳躍表

建立跳躍表過程比較簡單, 初始化zskiplist數據結構, 跳躍表默認最大層數32層, 跳躍表是按score進行升序排列.

/*建立跳躍表*/
zskiplist *zslCreate(void) {
    int j;
    zskiplist *zsl;

    zsl = zmalloc(sizeof(*zsl));
    zsl->level = 1;
    zsl->length = 0;
     /*初始化建立一個頭節點, 初始化節點信息*/
    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;
}
/*建立一個跳躍表節點*/
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;
     /*從頭節點開始搜索, 一層一層向下搜索, 直到直到最後一層, update數組中保存着每層應該插入的位置*/
    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))) {
               /*記錄每層距離頭部位置的距離*/
            rank[i] += x->level[i].span;
            x = x->level[i].forward;
        }
        update[i] = x;
    }
    /* 隨機一個層數, 若是隨機的層數是新的層數, 則須要給update數組中新的層數賦值*/
    level = zslRandomLevel();
    if (level > zsl->level) {
        for (i = zsl->level; i < level; i++) {
            rank[i] = 0;
               /*新的一層上一個指針確定是header*/
            update[i] = zsl->header;
            update[i]->level[i].span = zsl->length;
        }
        zsl->level = level;
    }
     /*建立新的節點插入到update數組對應的層*/
    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數組中span值和新插入元素span值, rank[0]存儲的是x元素距離頭部的距離, rank[i]存儲的是update[i]距離頭部的距離, 上面給出了示意圖
          */
        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, 無變更的元素span依次增長1*/
    for (i = level; i < zsl->level; i++) {
        update[i]->level[i].span++;
    }
     /*上一個元素level數組, 從新賦值*/
    x->backward = (update[0] == zsl->header) ? NULL : update[0];
    if (x->level[0].forward)
        x->level[0].forward->backward = x;
    else
          /*下一個元素爲空,則表示x爲尾部元素*/
        zsl->tail = x;
    zsl->length++;
    return x;
}

4.獲取排名

排名其實就是元素在skiplist中排列的序號, 獲取排名須要給出分數和成員member, 經過score查找, 匹配member成員, 時間複雜度log(N). 因爲skiplist是升序排列的,所以函數返回的rank是score按升序排列的rank, 若是想獲取降序rank應該是(length-rank).

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

    x = zsl->header;
     /*循環遍歷並累加每層的span值, 獲取總的排名*/
    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;
        }

        /* 判斷成員是否相等 */
        if (x->obj && equalStringObjects(x->obj,o)) {
              /*升序排列的排名*/
            return rank;
        }
    }
    return 0;
}

5.根據排名查找元素

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

     /*遍歷每一層,並記錄排名, 與待查rank比較, 相等則找到, 找不到則返回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.刪除元素

刪除元素須要精確匹配到分數和member

/*刪除一個元素*/
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;
    }
    /* 因爲score值可能相等, 所以須要精確匹配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 */
}

/* 具體進行刪除元素所在節點*/
void zslDeleteNode(zskiplist *zsl, zskiplistNode *x, zskiplistNode **update) {
    int i;
     /*刪除元素須要更新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) {
          /*非尾部元素則須要重置backforward指針*/
        x->level[0].forward->backward = x->backward;
    } else {
          /*刪除x多是最後一個元素, 須要重置尾部指針*/
        zsl->tail = x->backward;
    }
     /*刪除元素位於最上層, 而且僅有此一個元素, 刪除以後,須要下降跳躍表層數*/
    while(zsl->level > 1 && zsl->header->level[zsl->level-1].forward == NULL)
        zsl->level--;
    zsl->length--;
}