From 1f0b5ca94c62c7f2c11e19ce7d642ae089136b0e Mon Sep 17 00:00:00 2001 From: yanglbme Date: Mon, 5 Apr 2021 10:25:38 +0800 Subject: [PATCH] feat(big-data): topk problems and solutions Author @ChunelFeng --- README.md | 1 + docs/big-data/images/topk-trie.png | Bin 0 -> 179436 bytes docs/big-data/topk-problems-and-solutions.md | 172 +++++++++++++++++++ 3 files changed, 173 insertions(+) create mode 100644 docs/big-data/images/topk-trie.png create mode 100644 docs/big-data/topk-problems-and-solutions.md diff --git a/README.md b/README.md index fc9b64e..51dd1e7 100644 --- a/README.md +++ b/README.md @@ -169,6 +169,7 @@ - [如何从 5 亿个数中找出中位数?](./docs/big-data/find-mid-value-in-500-millions.md) - [如何按照 query 的频度排序?](./docs/big-data/sort-the-query-strings-by-counts.md) - [如何找出排名前 500 的数?](./docs/big-data/find-rank-top-500-numbers.md) +- [讲讲大数据中 TopK 问题的常用套路?](./docs/big-data/topk-problems-and-solutions.md) --- diff --git a/docs/big-data/images/topk-trie.png b/docs/big-data/images/topk-trie.png 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个人微信:ChunelFeng
个人博客:[一面之猿网](http://www.chunel.cn)
开源项目:[Caiss 智能相似搜索引擎](https://github.com/ChunelFeng/caiss) + + + +Doocs 社区的朋友们,大家好。我是你们的新朋友 [Chunel Feng](https://github.com/ChunelFeng)。今天想跟大家聊一些**常见的 topK 问题**。 + +对于海量数据到处理经常会涉及到 topK 问题。在设计数据结构和算法的时候,主要需要考虑的应该是当前算法(包括数据结构)跟给定情境(比如数据量级、数据类型)的适配程度,和当前问题最核心的瓶颈(如降低时间复杂度,还是降低空间复杂度)是什么。 + +首先,我们来举几个常见的 topK 问题的例子: + + +1. 给定 100 个 int 数字,在其中找出最大的 10 个; +1. 给定 10 亿个 int 数字,在其中找出最大的 10 个(这 10 个数字可以无序); +1. 给定 10 亿个 int 数字,在其中找出最大的 10 个(这 10 个数字依次排序); +1. 给定 10 亿个不重复的 int 数字,在其中找出最大的 10 个; +1. 给定 10 个数组,每个数组中有 1 亿个 int 数字,在其中找出最大的 10 个; +1. 给定 10 亿个 string 类型的数字,在其中找出最大的 10 个(仅需要查 1 次); +1. 给定 10 亿个 string 类型的数字,在其中找出最大的 k 个(需要反复多次查询,其中 k 是一个随机数字)。 + + +上面这些问题看起来很相似,但是解决的方式却千差万别。稍有不慎,就可能使得 topK 问题成为系统的瓶颈。不过也不用太担心,接下来我会总结几种常见的解决思路,遇到问题的时候,大家把这些基础思路融会贯通并且杂糅组合,即可做到见招拆招。 +
+ +### 1. 堆排序法 + +这里说的是堆排序法,而不是快排或者希尔排序。虽然理论时间复杂度都是 `O(nlogn)`,但是堆排在做 topK 的时候有一个优势,就是可以维护一个仅包含 k 个数字的小顶堆(想清楚,为啥是小顶堆哦),当新加入的数字大于堆顶数字的时候,将堆顶元素剔除,并加入新的数字。 + +用 C++ 来说明,堆在 stl 中是 priority_queue(不是 set)。 + +```cpp +int main() { + const int topK = 3; + vector vec = {4,1,5,8,7,2,3,0,6,9}; + priority_queue, greater<>> pq; // 小顶堆 + for (const auto& x : vec) { + pq.push(x); + if (pq.size() > topK) { + // 如果超出个数,则弹出堆顶(最小的)数据 + pq.pop(); + } + } + + while (!pq.empty()) { + cout << pq.top() << endl; // 输出依次为7,8,9 + pq.pop(); + } + + return 0; +} +``` + +> Java 中同样提供了 PriorityQueue 的数据结构。 + +### 2. 类似快排法 + +快排大家都知道,针对 topK 问题,可以对快排进行改进。仅对部分数据进行递归计算。比如,在 100 个数字中,找最大的 10 个,第一次循环的时候,povit 被移动到了 80 的位置,则接下来仅需要在后面的 20 个数字中找最大的 10 个即可。 + +这样做的优势是,理论最优时间复杂度可以达到 `O(n)`,不过平均时间复杂度还是 `O(nlogn)`。需要说明的是,通过这种方式,找出来的最大的 k 个数字之间,是无序的。 + +```cpp +int partition(vector& arr, int begin, int end) { + int left = begin; + int right = end; + int povit = arr[begin]; + + while (left < right) { + while (left < right && arr[right] >= povit) {right--;} + while (left < right && arr[left] <= povit) {left++;} + if (left < right) {swap(arr[left], arr[right]);} + } + + swap(arr[begin], arr[left]); + return left; +} + +void partSort(vector& arr, int begin, int end, int target) { + if (begin >= end) { + return; + } + + int povit = partition(arr, begin, end); + if (target < povit) { + partSort(arr, begin, povit - 1, target); + } else if (target > povit) { + partSort(arr, povit + 1, end, target); + } +} + +vector getMaxNumbers(vector& arr, int k) { + int size = (int)arr.size(); + // 把求最大的k个数,转换成求最小的size-k个数字 + int target = size - k; + partSort(arr, 0, size - 1, target); + vector ret(arr.end() - k, arr.end()); + return ret; +} + +int main() { + vector vec = {4,1,5,8,7,2,3,0,6,9}; + auto ret = getMaxNumbers(vec, 3); + + for (auto x : ret) { + cout << x << endl; // 输出7,8,9(理论上无序) + } + + return 0; +} +``` + +
+ +### 3. 使用 bitmap + +有时候 topK 问题会遇到数据量过大,内存无法全部加载。这个时候,可以考虑将数据存放至 bitmap 中,方便查询。 + +比如,给出 10 个 int 类型的数据,分别是【13,12,11,1,2,3,4,5,6,7】,int 类型的数据每个占据 4 个字节,那这个数组就占据了 40 个字节。现在,把它们放到一个 16 个长度 bool 的 bitmap 中,结果就是【0,1,1,1,1,1,1,1,0,0,0,1,1,1,0,0】,在将空间占用降低至 4 字节的同时,也可以很方便的看出,最大的 3 个数字,分别是 11,12 和 13。 + +需要说明的是,bitmap 结合跳表一起使用往往有奇效。比如以上数据还可以记录成:从第 1 位开始,有连续 7 个 1;从第 11 位开始,有连续 3 个 1。这样做,空间复杂度又得到了进一步的降低。 + +这种做法的优势,当然是降低了空间复杂度。不过需要注意一点,bitmap 比较适合不重复且有范围(比如,数据均在 0 ~ 10 亿之间)的数据的查询。至于有重复数据的情况,可以考虑与 hash 等结构的混用。 +
+ +### 4. 使用 hash + +如果遇到了查询 string 类型数据的大小,可以考虑 hash 方法。 + +举个例子,10 个 string 数字【"1001","23","1002","3003","2001","1111","65","834","5","987"】找最大的 3 个。我们先通过长度进行 hash,得到长度最大为 4,且有 5 个长度为 4 的 string。接下来再通过最高位值做 hash,发现有 1 个最高位为"3"的,1 个为"2"的,3 个为"1"的。接下来,可以通过再设计 hash 函数,或者是循环的方式,在 3 个最高位为"1"的 string 中找到最大的一个,即可找到 3 个最值大的数据。 + +这种方法比较适合网址或者电话号码的查询。缺点就是如果需要多次查询的话,需要多次计算 hash,并且需要根据实际情况设计多个 hash 函数。 +
+ +### 5. 字典树 + +字典树(trie)的具体结构和查询方式,不在这里赘述了,自行百度一下就有很多。这里主要说一下优缺点。 + +![](./images/topk-trie.png) + + +字典树的思想,还是通过前期建立索引信息,后期可以反复多次查询,并且后期增删数据也很方便。比较适合于需要反复多次查询的情况。 + +比如,反复多次查询字符序(例如:z>y>...>b>a)最大的 k 个 url 这种,使用字典树把数据存储一遍,就非常适合。既减少了空间复杂度,也加速了查询效率。 +
+ +### 6. 混合查询 + +以上几种方法,都是比较独立的方法。其实,在实际工作中,遇到更多的问题还是混合问题,这就需要我们对相关的内容,融会贯通并且做到活学活用。 + +我举个例子:我们的分布式服务跑在 10 台不同机器上,每台机器上部署的服务均被请求 10000 次,并且记录了个这 10000 次请求的耗时(耗时值为 int 数据),找出这 10\*10000 次请求中,从高到低的找出耗时最大的 50 个。看看这个问题,很现实吧。我们试着用上面介绍的方法,组合一下来求解。 + +#### 方法一 + +首先,对每台机器上的 10000 个做类似快排,找出每台机器上 top50 的耗时信息。此时,单机上的这 50 条数据是无序的。 + +然后,再将 10 台机器上的 50 条数据(共 500 条)放到一起,再做一次类似快排,找到最大的 50 个(此时应该这 50 个应该是无序的)。 + +最后,对这 50 个数据做快排,从而得到最终结果。 + +#### 方法二 + +首先通过堆排,分别找出 10 台机器上耗时最高的 50 个数据,此时的这 50 个数据,已经是从大到小有序的了。 + +然后,我们依次取出 10 台机器中,耗时最高的 5 条放入小顶堆中。 + +最后,遍历 10 台机器上的数据,每台机器从第 6 个数据开始往下循环,如果这个值比堆顶的数据大,则抛掉堆顶数据并且把它加入,继续用下一个值进行同样比较。如果这个值比堆顶的值小,则结束当前循环,并且在下一台机器上做同样操作。 + +以上我介绍了两种方法,并不是为了说明哪种方法更好,或者时间复杂度更低。而是想说同样的事情有多种不同的解决方法,而且随着数据量的增加,可能会需要更多组合形式。在这个领域,数据决定了数据结构,数据结构决定了算法。 + +**没有最好的方法,只有不断找寻更好的方法的程序员。适合的,才会是最好的。** + +嗯,加油,你可以找到更好的!!!