Problem $2$: $(5$ points$)$ You are asked to process pairs of words that appear together $($one after the other$)$ in

the document: how often this given pair occurs, compared to any other pairs starting with word: $$word$1?$

Write pseudo$-$code, showing Map and Reduce functions to address the above problem. If a second Map Reduce

iteration is required, then write again the new Map and Reduce functions. Please answer Question $1$ and Question

$2$ below:

Co$-$occurrence of word$1$ and word $2,$ as you will read next, means that in a document we must find the

frequency$/$probability that word$2$ comes right after word $1$ in a document and$/$or vice$-$versa.

Input: text documents

key: document id

value: text document

Output: key$/$value pairs where

key: pair$($word$1,$ word$2)$

value: #co$-$occurrences$($word$1,$ word$2)/$#co$-$occurrences$($word$1,$ any word$)$

Solve the problem when for the co$-$occurrence of word$1-$word$2$ we impose that word $1$ must come first and word $2$

must come second in the document.

Solution: