mysql> set @search_id := @found_id + 64;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+--------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+--------+
| 64 | 33.950 | 35.123 | keep |
+----+---------+----------------+--------+
在这里我们需要保持这个位(64),并计算找到的重量：
set @found_id := @search_id,@search_weight := @search_weight - 33.950;
然后继续下一个位：
mysql> set @search_id := @found_id + 32;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+---------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+---------+
| 96 | 16.260 | 1.173 | discard |
+----+---------+----------------+---------+
mysql> set @search_id := @found_id + 16;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+---------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+---------+
| 80 | 7.394 | 1.173 | discard |
+----+---------+----------------+---------+
mysql> set @search_id := @found_id + 8;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+---------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+---------+
| 72 | 3.995 | 1.173 | discard |
+----+---------+----------------+---------+
mysql> set @search_id := @found_id + 4;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+---------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+---------+
| 68 | 1.915 | 1.173 | discard |
+----+---------+----------------+---------+
mysql> set @search_id := @found_id + 2;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+--------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+--------+
| 66 | 1.146 | 1.173 | keep |
+----+---------+----------------+--------+
我们在这里找到了另一个
set @found_id := @search_id,@search_weight := @search_weight - 1.146;
mysql> set @search_id := @found_id + 1;
mysql> select id,"discard") as action
-> from entries where id = @search_id;
+----+---------+----------------+--------+
| id | fenwick | @search_weight | action |
+----+---------+----------------+--------+
| 67 | 0.010 | 0.027 | keep |
+----+---------+----------------+--------+
还有一个
set @found_id := @search_id,@search_weight := @search_weight - 0.010;
最终的搜索结果是：
mysql> select @found_id,@search_weight;
+-----------+----------------+
| @found_id | @search_weight |
+-----------+----------------+
| 67 | 0.017 |
+-----------+----------------+
验证
mysql> select sum(weight) from entries where id <= 67;
+-------------+
| sum(weight) |
+-------------+
| 35.106 |
+-------------+
mysql> select sum(weight) from entries where id <= 68;
+-------------+
| sum(weight) |
+-------------+
| 35.865 |
+-------------+
事实上,
35.106 (fenwick[67]) <= 35.123 (search) <= 35.865 (fenwick[68])
搜索查找值一次解析1位,每个查找结果决定要搜索的下一个ID的值.
此处给出的查询仅供参考.在实际应用程序中,代码应该只是一个包含以下内容的循环：
SELECT fenwick from entries where id = ?;
使用应用程序代码(或存储过程)实现与@ found_id,@ search_id和@search_weight相关的逻辑.
普通的留言
> Fenwick树用于前缀计算.如果要解决的问题首先涉及前缀,那么使用这些树才有意义.维基百科有一些应用程序的指针.不幸的是,OP没有描述fenwick树的用途.
> Fenwick树是查找复杂性和更新复杂性之间的权衡,因此它们只对非静态数据有意义.对于静态数据,计算一次完整前缀将更有效.
>执行的测试使用了一个INNODB表,主键索引被排序,因此计算max_id是一个简单的O(1)操作.如果max_id已在其他地方可用,我认为即使使用带有HASH索引ID的MEMORY表也可以,因为只使用主键查找.
附：
sqlfiddle今天已经关闭了,所以发布使用的原始数据(最初由concat提供),以便有兴趣的人可以重新运行测试.
INSERT INTO `entries` VALUES (1,0.480,0.480),(2,0.542,1.022),(3,0.269,0.269),(4,0.721,2.012),(5,0.798,0.798),(6,0.825,1.623),(7,0.731,0.731),(8,0.181,4.547),(9,0.711,0.711),(10,0.013,0.724),(11,0.930,0.930),(12,0.613,2.267),(13,0.276,0.276),(14,0.539,0.815),(15,0.867,0.867),(16,0.718,9.214),(17,0.991,0.991),(18,0.801,1.792),(19,0.033,0.033),(20,0.759,2.584),(21,0.698,0.698),(22,0.212,0.910),(23,0.965,0.965),(24,0.189,4.648),(25,0.049,0.049),(26,0.678,0.727),(27,0.245,0.245),(28,0.190,1.162),(29,0.214,0.214),(30,0.502,0.716),(31,0.868,0.868),(32,0.834,17.442),(33,0.566,0.566),(34,0.327,0.893),(35,0.939,0.939),(36,0.713,2.545),(37,0.747,0.747),(38,0.595,1.342),(39,0.733,0.733),(40,0.884,5.504),(41,0.218,0.218),(42,0.437,0.655),(43,0.532,0.532),(44,0.350,1.537),(45,0.154,0.154),(46,0.875),(47,0.140,0.140),(48,0.538,8.594),(49,0.271,0.271),(50,0.739,1.010),(51,0.884),(52,0.203,2.097),(53,0.361,0.361),(54,0.197,0.558),(55,0.903,0.903),(56,0.923,4.481),(57,0.906,0.906),(58,0.761,1.667),(59,0.089,0.089),(60,0.161,1.917),(61,0.537,0.537),(62,0.201,0.738),(63,0.397,0.397),(64,0.381,33.950),(65,0.715,0.715),(66,0.431,1.146),(67,0.010,0.010),(68,1.915),(69,0.763,0.763),(70,1.300),(71,0.399,0.399),(72,3.995),(73,0.709,0.709),(74,0.401,1.110),(75,0.880,0.880),(76,0.198,2.188),(77,0.348,0.348),(78,0.148,0.496),(79,0.693,0.693),(80,0.022,7.394),(81,0.031,0.031),(82,0.120),(83,0.353,0.353),(84,0.498,0.971),(85,0.428,0.428),(86,0.650,1.078),(87,0.963,0.963),(88,0.866,3.878),(89,0.442,0.442),(90,0.610,1.052),(91,0.725,0.725),(92,0.797,2.574),(93,0.808,0.808),(94,0.648,1.456),(95,0.817,0.817),(96,0.141,16.260),(97,0.256,0.256),(98,0.855,1.111),(99,0.508,0.508),(100,0.976,2.595),(101,(102,0.840,1.193),(103,0.139,0.139),(104,0.178,4.105),(105,0.469,0.469),(106,0.814,1.283),(107,0.664,0.664),(108,0.876,2.823),(109,0.390,0.390),(110,0.323,0.713),(111,(112,0.241,8.324),(113,0.881,0.881),(114,0.681,1.562),(115,0.760,0.760),(116,3.082),(117,0.518,0.518),(118,0.313,0.831),(119,0.008,0.008),(120,0.103,4.024),(121,0.488,0.488),(122,0.135,0.623),(123,0.207,0.207),(124,0.633,1.463),(125,0.542),(126,0.812,1.354),(127,0.433,0.433),(128,0.732,66.540),(129,0.358,0.358),(130,0.594,0.952),(131,0.897,0.897),(132,0.701,2.550),(133,0.815,(134,0.973,1.788),(135,0.419,0.419),(136,0.175,4.932),(137,0.620,0.620),(138,0.573,(139,0.004,0.004),(140,0.304,1.501),(141,(142,0.629,1.137),(143,0.618,0.618),(144,0.206,8.394),(145,0.175),(146,0.255,0.430),(147,0.750,0.750),(148,0.987,2.167),(149,0.683,0.683),(150,0.453,1.136),(151,0.219,0.219),(152,0.734,4.256),(153,0.016,0.016),(154,0.874,0.891),(155,0.325,0.325),(156,0.002,1.217);
附： 2
现在有一个完整的sqlfiddle：
http://sqlfiddle.com/#!9/d2c82/1
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