Reservoir Sampling

Refs:

1. https://gregable.com/2007/10/reservoir-sampling.html
2. http://blog.jobbole.com/42550/

Problem:

Reservoir Sampling is an algorithm for sampling elements from a stream of data. Imagine you are given a really large stream of data elements, for example:

• Queries on google searches in May
• Products bought at Walmart during the Christmas season
• Names in a phone book
  Your goal is to efficiently return a random sample of 1,000 elements evenly distributed from the original stream. How would you do it?

简而言之就是data stream,最好是one pass，只遍历数据一遍就抽样。

解法：stream里面抽k个样，维持一个reservoir （k大小），之后每进（k+i）一个数A，以 k/(k+i)的比例抽样留下A，然后再在reservoir里面均匀抽样某一个数被A替换。这样子无论是新树A还是之前的所有数，在reservoir中survive的probability都是 k/(k+i). (之前的数： 1/(k+i-1) * k/(k+i) )

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