$[5$pts$]$ Given the following $4$ documents retrieved from the collection of $10,000,000$ documents in response to query $"\backslash ($ N P $\backslash$wedge $\backslash )$ Turing $\backslash (\backslash$wedge $\backslash )$ circuits":

D$1=$"deterministic Turing machines are special non$-$deterministic Turing machines, it is easily observed that each problem in P is also member of the class NP$."$

D$2=$"also known that if $\backslash ($ P$=$N P $\backslash ),$ then EXPTIME $\backslash (=\backslash )$ NEXPTIME, the class of problems solvable in exponential time by a nondeterministic Turing machine"

D$3="$In computational complexity theory, an advice string is an extra input to a Turing machine. A circuit $\backslash ($ A$($n$)\backslash )$ is deciding the problem, or we can use a Turing machine that interprets the advice string as a description of the circuit'

D$4=$"The fact that Circuit$-$SAT is in NP is easy. Given a circuit C in the standard basis"

We know that document frequency of terms NP$,$ circuit and Turing in this collection are $100,000$ and $50,000$ and $200,000$ respectively.

Use sublinear scaling weighted term frequency $\backslash ($ w f$\_\{$t$,$ d$\}\backslash ),$ wf$-$idf metric and cosine similarity measure to compute ranking of each document w$.$r$.$t the query. Then order documents according to the rank.

Use the format of Table $6\mathrm{.}1$ from the text $($copied below$)$

$[5$pts$]$ When discussing champion lists, we simply used the r documents with the largest tf values to create the champion list for $\backslash ($ t $\backslash ).$ But when considering global champion lists, we used idf as between these two cases?

$[5$pts$]$ Compute the gamma encoding for the posting list: