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Redis 3.0.4 跳跃表
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内容图文
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;
}
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