跳表（skiplist）是一個非常優秀的數據結構，實現簡單，插入、刪除、查找的復雜度均為O(logN)。LevelDB的核心數據結構是用跳表實現的，redis的sorted set數據結構也是有跳表實現的。
其結構如下所示：
所有操作均從上向下逐層查找，越上層一次next操作跨度越大。其實現是典型的空間換時間。
具體的細節，可參考維基百科http://en.wikipedia.org/wiki/Skip_list
本文作者將redis的sorted set代碼進行整理，將跳表部分的實現抽取出來，供參考。
skiplist.h
#ifndef __SKIPLIST_H
#define __SKIPLIST_H
#define SKIPLIST_MAXLEVEL 8
typedef struct skiplistNode {
double score;
struct skiplistNode *backward;
struct skiplistLevel {
struct skiplistNode *forward;
}level[];
}skiplistNode;
typedef struct skiplist {
struct skiplistNode *header, *tail;
unsigned long length;
int level;
}skiplist;
#endif
skiplist.c
#include "skiplist.h"
#include <stdlib.h>
#include <stdio.h>
skiplistNode *slCreateNode(int level, double score) {
skiplistNode * sn = malloc(sizeof(*sn) + level*sizeof(struct skiplistLevel));
sn->score = score;
return sn;
}
skiplist *slCreate(void) {
int j;
skiplist *sl;
sl = malloc(sizeof(*sl));
sl->level = 1;
sl->length = 0;
sl->header = slCreateNode(SKIPLIST_MAXLEVEL, 0);
for(j = 0; j < SKIPLIST_MAXLEVEL; j++) {
sl->header->level[j].forward = NULL;
}
sl->header->backward = NULL;
sl->tail = NULL;
return sl;
}
void slFreeNode(skiplistNode *sn) {
free(sn);
}
void slFree(skiplist *sl) {
skiplistNode *node = sl->header->level[0].forward, *next;
free(sl->header);
while(node) {
next = node->level[0].forward;
slFreeNode(node);
node = next;
}
free(sl);
}
int slRandomLevel(void) {
int level = 1;
while((rand()&0xFFFF) < (0.5 * 0xFFFF))
level += 1;
return (level < SKIPLIST_MAXLEVEL) ? level : SKIPLIST_MAXLEVEL;
}
skiplistNode *slInsert(skiplist *sl, double score) {
skiplistNode *update[SKIPLIST_MAXLEVEL];
skiplistNode *node;
node = sl->header;
int i, level;
for ( i = sl->level-1; i >= 0; i--) {
while(node->level[i].forward && node->level[i].forward->score < score) {
node = node->level[i].forward;
}
update[i] = node;
}
level = slRandomLevel();
if (level > sl->level) {
for (i = sl->level; i< level ;i++) {
update[i] = sl->header;
}
sl->level = level;
}
node = slCreateNode(level, score);
for (i = 0; i < level; i++) {
node->level[i].forward = update[i]->level[i].forward;
update[i]->level[i].forward = node;
}
node->backward = (update[0] == sl->header? NULL : update[0]);
if (node->level[0].forward)
node->level[0].forward->backward = node;
else
sl->tail = node;
sl->length++;
return node;
}
void slDeleteNode(skiplist *sl, skiplistNode *x, skiplistNode **update){
int i;
for (i = 0; i < sl->level; i++) {
if (update[i]->level[i].forward == x) {
update[i]->level[i].forward = x->level[i].forward;
}
}
if (x->level[0].forward) {
x->level[0].forward->backward = x->backward;
} else {
sl->tail = x->backward;
}
while (sl->level > 1 && sl->header->level[sl->level-1].forward == NULL)
sl->level--;
sl->length--;
}
int slDelete(skiplist *sl, double score) {
skiplistNode *update[SKIPLIST_MAXLEVEL], *node;
int i;
node = sl->header;
for(i = sl->level-1; i >= 0; i--) {
while (node->level[i].forward && node->level[i].forward->score < score) {
node = node->level[i].forward;
}
update[i] = node;
}
node = node->level[0].forward;
if (node && score == node->score) {
slDeleteNode(sl, node, update);
slFreeNode(node);
return 1;
} else {
return 0;
}
return 0;
}
int slSearch(skiplist *sl, double score) {
skiplistNode *node;
int i;
node = sl->header;
for (i = sl->level-1; i >= 0 ;i--) {
while(node->level[i].forward && node->level[i].forward->score < score) {
node = node->level[i].forward;
}
}
node = node->level[0].forward;
if (node && score == node->score) {
printf("Found %d\n",(int)node->score);
return 1;
} else {
printf("Not found %d\n", (int)score);
return 0;
}
}
void slPrint(skiplist *sl) {
skiplistNode *node;
int i;
for (i = 0; i < SKIPLIST_MAXLEVEL; i++) {
printf("LEVEL[%d]: ", i);
node = sl->header->level[i].forward;
while(node) {
printf("%d -> ", (int)(node->score));
node = node->level[i].forward;
}
printf("NULL\n");
}
}
#ifdef SKIP_LIST_TEST_MAIN
int main() {
srand((unsigned)time(0));
int count = 20, i;
printf("### Function Test ###\n");
printf("=== Init Skip List ===\n");
skiplist * sl = slCreate();
for ( i = 0; i < count; i++) {
slInsert(sl,i);
}
printf("=== Print Skip List ===\n");
slPrint(sl);
printf("=== Search Skip List ===\n");
for (i = 0; i < count; i++) {
int value = rand()%(count+10);
slSearch(sl, value);
}
printf("=== Delete Skip List ===\n");
for (i = 0; i < count+10; i+=2) {
printf("Delete[%d]: %s\n", i, slDelete(sl, i)?"SUCCESS":"NOT FOUND");
}
slPrint(sl);
slFree(sl);
sl = NULL;
}
#endif
測試結果如下所示：
### Function Test ###
=== Init Skip List ===
=== Print Skip List ===
LEVEL[0]: 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 10 -> 11 -> 12 -> 13 -> 14 -> 15 -> 16 -> 17 -> 18 -> 19 -> NULL
LEVEL[1]: 0 -> 2 -> 4 -> 7 -> 9 -> 10 -> 11 -> 12 -> 14 -> 15 -> 17 -> 18 -> NULL
LEVEL[2]: 7 -> 10 -> 12 -> 14 -> 15 -> NULL
LEVEL[3]: 10 -> 14 -> 15 -> NULL
LEVEL[4]: 10 -> 14 -> NULL
LEVEL[5]: NULL
LEVEL[6]: NULL
LEVEL[7]: NULL
=== Search Skip List ===
Found 1
Found 18
Not found 21
Not found 24
Found 10
Not found 20
Found 14
Found 10
Found 19
Found 18
Not found 27
Found 5
Found 0
Found 0
Found 18
Not found 26
Found 13
Not found 28
Not found 29
Not found 23
=== Delete Skip List ===
Delete[0]: SUCCESS
Delete[2]: SUCCESS
Delete[4]: SUCCESS
Delete[6]: SUCCESS
Delete[8]: SUCCESS
Delete[10]: SUCCESS
Delete[12]: SUCCESS
Delete[14]: SUCCESS
Delete[16]: SUCCESS
Delete[18]: SUCCESS
Delete[20]: NOT FOUND
Delete[22]: NOT FOUND
Delete[24]: NOT FOUND
Delete[26]: NOT FOUND
Delete[28]: NOT FOUND
LEVEL[0]: 1 -> 3 -> 5 -> 7 -> 9 -> 11 -> 13 -> 15 -> 17 -> 19 -> NULL
LEVEL[1]: 7 -> 9 -> 11 -> 15 -> 17 -> NULL
LEVEL[2]: 7 -> 15 -> NULL
LEVEL[3]: 15 -> NULL
LEVEL[4]: NULL
LEVEL[5]: NULL
LEVEL[6]: NULL
LEVEL[7]: NULL