Redis基础-跳表
一、跳表原理
1.1、什么是跳表
跳跃表是一种随机化的数据结构,在查找、插入和删除这些字典操作上,其效率可比拟于平衡二叉树(如红黑树),大多数操作只需要O(log n)平均时间,但它的代码以及原理更简单。跳跃表的定义如下:
“Skip lists are data structures that use probabilistic balancing rather than strictly enforced balancing. As a result, the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees.”
译文:跳跃表使用概率平衡,而不是强制平衡,因此,对于插入和删除结点比传统上的平衡树算法更为简洁高效。
1.2、理想跳表
在理想情况下:
- 最底层元素是一个单链表
- 从最底层往上,每一层的元素个数是之前一层的1/2
二、跳表redis实现
Base:redis version: 5.0.8
2.1、redis跳表原理和数据结构
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2.2、Redis跳表代码
2.2.1、Redis跳表数据结构
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | #跳表节点 typedef struct zskiplistNode { sds ele; double score; struct zskiplistNode *backward; #跳表表示level的数据 struct zskiplistLevel { struct zskiplistNode *forward; unsigned long span; } level[]; } zskiplistNode; #跳表 list结构 typedef struct zskiplist { struct zskiplistNode *header, *tail; unsigned long length; int level; } zskiplist; #zset 结构 typedef struct zset { dict *dict; zskiplist *zsl; } zset; |
2.2.2、跳表执行流程
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 | #zset 添加/更新操作入口 int zsetAdd(robj *zobj, double score, sds ele, int *flags, double *newscore) { /* Turn options into simple to check vars. */ int incr = (*flags & ZADD_INCR) != 0; int nx = (*flags & ZADD_NX) != 0; int xx = (*flags & ZADD_XX) != 0; *flags = 0; /* We'll return our response flags. */ double curscore; /* NaN as input is an error regardless of all the other parameters. */ if (isnan(score)) { *flags = ZADD_NAN; return 0; } /* Update the sorted set according to its encoding. */ if (zobj->encoding == OBJ_ENCODING_ZIPLIST) { unsigned char *eptr; if ((eptr = zzlFind(zobj->ptr,ele,&curscore)) != NULL) { /* NX? Return, same element already exists. */ if (nx) { *flags |= ZADD_NOP; return 1; } /* Prepare the score for the increment if needed. */ if (incr) { score += curscore; if (isnan(score)) { *flags |= ZADD_NAN; return 0; } if (newscore) *newscore = score; } /* Remove and re-insert when score changed. */ if (score != curscore) { zobj->ptr = zzlDelete(zobj->ptr,eptr); zobj->ptr = zzlInsert(zobj->ptr,ele,score); *flags |= ZADD_UPDATED; } return 1; } else if (!xx) { /* Optimize: check if the element is too large or the list * becomes too long *before* executing zzlInsert. */ zobj->ptr = zzlInsert(zobj->ptr,ele,score); if (zzlLength(zobj->ptr) > server.zset_max_ziplist_entries || sdslen(ele) > server.zset_max_ziplist_value) zsetConvert(zobj,OBJ_ENCODING_SKIPLIST); if (newscore) *newscore = score; *flags |= ZADD_ADDED; return 1; } else { *flags |= ZADD_NOP; return 1; } } else if (zobj->encoding == OBJ_ENCODING_SKIPLIST) { #当前zset编码是 skipList zset *zs = zobj->ptr; zskiplistNode *znode; dictEntry *de; #根据 ele从dict中获取元素,如果获取到直接更新该节点value,如果获取不到就插入 de = dictFind(zs->dict,ele); if (de != NULL) { /* NX? Return, same element already exists. */ if (nx) { *flags |= ZADD_NOP; return 1; } curscore = *( double *)dictGetVal(de); /* Prepare the score for the increment if needed. */ if (incr) { score += curscore; if (isnan(score)) { *flags |= ZADD_NAN; return 0; } if (newscore) *newscore = score; } /* Remove and re-insert when score changes. */ if (score != curscore) { //更新znode节点 znode = zslUpdateScore(zs->zsl,curscore,ele,score); /* Note that we did not removed the original element from * the hash table representing the sorted set, so we just * update the score. */ dictGetVal(de) = &znode->score; /* Update score ptr. */ *flags |= ZADD_UPDATED; } return 1; } else if (!xx) { ele = sdsdup(ele); //插入新的节点 znode = zslInsert(zs->zsl,score,ele); serverAssert(dictAdd(zs->dict,ele,&znode->score) == DICT_OK); *flags |= ZADD_ADDED; if (newscore) *newscore = score; return 1; } else { *flags |= ZADD_NOP; return 1; } } else { serverPanic( "Unknown sorted set encoding" ); } return 0; /* Never reached. */ } |
插入新的节点流程
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | zskiplistNode *zslInsert(zskiplist *zsl, double score, sds ele) { zskiplistNode *update[ZSKIPLIST_MAXLEVEL], *x; unsigned int rank[ZSKIPLIST_MAXLEVEL]; int i, level; serverAssert(!isnan(score)); #初始化遍历初始值 #rank 数组收集每层level从header到小于score的最后一个节点的span值 #update 数组收集每层level 小于score的最后一个节点 x = zsl->header; for (i = zsl->level-1; i >= 0; i--) { /* store rank that is crossed to reach the insert position */ #rank[level-]的初始值为0 ,是因为 当前是计算的第一个元素,需要从header.level[i]中取出来 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; x = x->level[i].forward; } 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. */ #生成当前新节点的level值,如果当前值大于当前list的level值,需要初始化[当前level,level)之间的level元素 level = zslRandomLevel(); 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; } #构造新节点的元素 x = zslCreateNode(level,score,ele); //从下到上,修改每层小雨score的最后一个元素 ,与当前元素level[i]的链接关系以及span数值 for (i = 0; i < level; i++) { 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 */ #修改每一层小于score的最后一个元素的span值,在这里再执行一次是因为当前节点的level如果小于list的level,则大于当前节点level到list level之间的level的span值还没有被处理,而这些数值只是单纯的增加1 for (i = level; i < zsl->level; i++) { update[i]->level[i].span++; } #修改向后遍历指针 x->backward = (update[0] == zsl->header) ? NULL : update[0]; if (x->level[0].forward) x->level[0].forward->backward = x; else zsl->tail = x; #修改当前list 元素个数 zsl->length++; return x; } |
跳表level函数:
1 2 3 4 5 6 7 8 | #define ZSKIPLIST_P 0.25 #define ZSKIPLIST_MAXLEVEL 64 /* Should be enough for 2^64 elements */ int zslRandomLevel( void ) { int level = 1; while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF)) level += 1; return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL; } |
redis中规定,level最多只能有64层
三、跳表java实现
3.1、数据结构
java实现时去掉了dict结构,主要演示node的插入
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | @Data public class ZSkipListNode { private String ele; private double score; private ZSkipListNode backward; private ZSkipListLevel[] level; public ZSkipListNode(String ele, double score) { this .ele = ele; this .score = score; this .level = new ZSkipListLevel[ZSkipList.MAX_LEVEL]; for ( int j = 0 ;j< ZSkipList.MAX_LEVEL;j++){ level[j] = new ZSkipListLevel(); } } @Override public String toString() { return "ZSkipListNode{}" ; } } @Data public class ZSkipListLevel { private ZSkipListNode forword; private long span; @Override public String toString() { return "ZSkipListLevel{}" ; } } @Data public class ZSkipList { public static final int MAX_LEVEL = 32 ; public static final double LEVEL_FACTOR = 0.25 ; private ZSkipListNode header; private ZSkipListNode tail; private long length; private int level; public ZSkipList() { this .level = 1 ; this .length = 0 ; this .header = new ZSkipListNode( null , 0 ); for ( int j = 0 ;j<MAX_LEVEL;j++){ this .getHeader().getLevel()[j].setForword( null ); this .getHeader().getLevel()[j].setSpan( 0 ); } this .getHeader().setBackward( null ); this .setTail( null ); } } |
3.2、insert和delete方法实现
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 | @Data public class ZSkipList { public static final int MAX_LEVEL = 32 ; public static final double LEVEL_FACTOR = 0.25 ; private ZSkipListNode header; private ZSkipListNode tail; private long length; private int level; public ZSkipList() { this .level = 1 ; this .length = 0 ; this .header = new ZSkipListNode( null , 0 ); for ( int j = 0 ;j<MAX_LEVEL;j++){ this .getHeader().getLevel()[j].setForword( null ); this .getHeader().getLevel()[j].setSpan( 0 ); } this .getHeader().setBackward( null ); this .setTail( null ); } public ZSkipListNode insert( double score, String ele) { long [] rank = new long [MAX_LEVEL]; ZSkipListNode[] update = new ZSkipListNode[MAX_LEVEL]; ZSkipListNode h = this .getHeader(); for ( int i=getLevel()- 1 ;i>= 0 ;i--){ rank[i] = i == getLevel()- 1 ? 0 : rank[i+ 1 ]; while (h.getLevel()[i].getForword()!= null && (h.getLevel()[i].getForword().getScore()<score || (h.getLevel()[i].getForword().getScore() == score && valCmp(h.getLevel()[i].getForword().getEle(),ele)< 0 ))){ rank[i]+= h.getLevel()[i].getSpan(); h = h.getLevel()[i].getForword(); } update[i] = h; } int level = zslRandomLevel(); if (level>getLevel()){ for ( int l = getLevel();l<level;l++){ update[l] = getHeader(); update[l].getLevel()[l].setSpan(getLength()); rank[l]= 0 ; } } ZSkipListNode cur = new ZSkipListNode(ele,score); for ( int i = 0 ;i<level;i++){ cur.getLevel()[i].setForword(update[i].getLevel()[i].getForword()); update[i].getLevel()[i].setForword(cur); cur.getLevel()[i].setSpan(update[i].getLevel()[i].getSpan()-(rank[ 0 ]-rank[i])); update[i].getLevel()[i].setSpan(rank[ 0 ]-rank[i]+ 1 ); } for ( int i = level;i< this .getLevel()- 1 ; i++){ update[i].getLevel()[i].setSpan(update[i].getLevel()[i].getSpan()+ 1 ); } cur.setBackward(update[ 0 ] == getHeader() ? null : update[ 0 ]); if (cur.getLevel()[ 0 ].getForword()!= null ){ cur.getLevel()[ 0 ].getForword().setBackward(cur); } else { this .setTail(cur); } if (level>getLevel()){ this .setLevel(level); } this .setLength( this .getLength()+ 1 ); return cur; } /** * 删除成功 返回1 ,删除失败,或者没有找到返回0 * 删除元素 * 并修改剩下的level中的 span信息 * @return */ public int delete(ZSkipListNode node,ZSkipListNode[] update){ for ( int i= 0 ;i<getLevel();i++){ ZSkipListLevel level =update[i].getLevel()[i]; if (level.getForword() == node){ level.setSpan(level.getSpan()+node.getLevel()[i].getSpan()- 1 ); level.setForword(node.getLevel()[i].getForword()); } else { level.setSpan(level.getSpan()- 1 ); } } /** * 修改返回指针 */ if (node.getLevel()[ 0 ].getForword()== null ){ this .setTail(node.getBackward()); } else { node.getLevel()[ 0 ].getForword().setBackward(node.getBackward()); } /** * 修改level */ while (getLevel()> 0 && getHeader().getLevel()[getLevel()- 1 ].getForword()== null ){ setLevel(getLevel()- 1 ); } setLength(getLength()- 1 ); return 1 ; } /** * int zslDelete(zskiplist *zsl, double score, sds ele, zskiplistNode **node) * @param score * @param ele * @return */ public int deleteWithScore( double score,String ele){ ZSkipListNode[] update = new ZSkipListNode[MAX_LEVEL]; ZSkipListNode h = getHeader(); ZSkipListNode x = null ; for ( int i= getLevel()- 1 ;i>= 0 ;i--){ while (h.getLevel()[i].getForword() != null && (h.getLevel()[i].getForword().getScore() < score || (h.getLevel()[i].getForword().getScore() == score && valCmp(h.getLevel()[i].getForword().getEle(), ele) < 0 )) ) { h = h.getLevel()[i].getForword(); } update[i]=h; } x = h.getLevel()[ 0 ].getForword(); if (x!= null && x.getScore() == score && valCmp(x.getEle(),ele) == 0 ){ return delete(x,update); } return 0 ; } private int zslRandomLevel() { int level = 1 ; Random random = new Random(); while (random.nextInt( 20 )< 20 *LEVEL_FACTOR){ level+= 1 ; } return level<MAX_LEVEL ? level : MAX_LEVEL; } public int valCmp(String t, String target) { return t.compareTo(target); } public static void main(String[] args) { ZSkipList list = new ZSkipList(); Map<String,Integer> eleMap = new HashMap<>(); Random random = new Random(); int max = 0 ; for ( int i = 0 ;i< 10 ;i++){ int score = 1 +random.nextInt( 20 ); max +=score; String ele = "a" +i; list.insert(max,ele); eleMap.put(ele,max); } printZsl(list); /** * 删除元素测试 */ for (Map.Entry<String,Integer> entry : eleMap.entrySet()){ list.deleteWithScore(entry.getValue(),entry.getKey()); System.out.printf( "delete,ele:" +entry.getKey()+ ",score:" +entry.getValue()); printZsl(list); } } public static void printZsl(ZSkipList list){ ZSkipListNode header = list.getHeader(); System.out.println( "---------------------------------------" ); for ( int i = list.getLevel()- 1 ;i>= 0 ;i--){ System.out.println( "level = " +i); ZSkipListNode h = header.getLevel()[i].getForword(); while (h!= null ){ System.out.printf( "[node:" +h.getEle()+ ":" +h.getScore()+ ",span:" +h.getLevel()[i].getSpan()+ "]-" ); h = h.getLevel()[i].getForword(); } System.out.println(); } System.out.println( "---------------------------------------" ); } @Override public String toString() { return "ZSkipList{" ; } } |
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