Exercise 1: The Inverted Index, the Book-Index Analogy, and the Worked Example — Possible Solution
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WHAT AN INVERTED INDEX IS, USING THE BOOK-INDEX ANALOGY
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Per this chapter, "a 'forward' index maps a document to its own
content — the way a book's table of contents maps a chapter to a
page. An inverted index does the opposite: it maps each individual
term to the list of documents containing it — exactly like a book's
own back-of-book index, mapping a word to the page numbers it appears
on." A book's table of contents lets you look up "Chapter 3" and find
out it starts on page 45 — going FROM a known chapter TO its location.
A book's own back-of-book index works the opposite direction: given a
specific WORD (say, "photosynthesis"), it tells you every page number
that word appears on — going FROM a term TO its locations. An inverted
index in a search engine works exactly like that back-of-book index:
given a search term, it directly returns every document containing
that term, rather than requiring a scan through every document to
check.

WALKING THROUGH THE WORKED EXAMPLE
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Per this chapter, indexing "the quick brown fox" (doc 1) and "the lazy
dog" (doc 2) produces:

  the    -> [doc 1, doc 2]
  quick  -> [doc 1]
  brown  -> [doc 1]
  fox    -> [doc 1]
  lazy   -> [doc 2]
  dog    -> [doc 2]

Each unique term across both documents becomes its own entry (its own
"row," in a loose sense) in this structure. The word "the" appears in
BOTH documents, so its entry lists both doc 1 and doc 2. Each of the
other words ("quick," "brown," "fox," "lazy," "dog") appears in only
ONE of the two documents, so each of their entries lists just that one
document. A search for "fox" is then answered by directly looking up
the "fox" entry in this table, immediately returning [doc 1] — no
scanning of either document's actual raw text was required to answer
the query.

WHY THIS WORKS AS AN ANSWER
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It states the book-index analogy precisely, contrasting it against the
forward-index/table-of-contents comparison the chapter also makes, and
walks through the worked example term by term, explaining specifically
why "the" ends up mapped to both documents while the other terms map
to only one each.