$4\mathrm{.}3[20$ points$]$ The map$-$reduce framework is quite useful for creating inverted indices on a set of documents. An inverted index stores for each word a list of all document IDs that it appears in $($offsets in the documents are also normally stored, but we shall ignore them in this question$).$

For example, if the input document IDs and contents are as follows:

$1$: data clean

$2$: data base

$3$: clean base

then the inverted lists would

data: $1,2$

clean: $1,3$

base: $2,3$

Give pseudocode for$$Map$$and reduce functions to create inverted indices on a given set of files $($each file is a document$).$ Assume the document ID is available using a function$$context$.$getDocumentID$(),$ and the$$Map$$function is invoked once per line of the document. The output inverted list for each word should be a list of document IDs separated by commas. The document IDs are normally sorted, but for the purpose of this question you do not need to bother to sort them.