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(/home/vip/.miktex/texmfs/install/tex/latex/hyperref/nameref.sty Package: nameref 2019/09/16 v2.46 Cross-referencing by name of section (/home/vip/.miktex/texmfs/install/tex/latex/refcount/refcount.sty Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO) ) (/home/vip/.miktex/texmfs/install/tex/generic/gettitlestring/gettitlestring.sty Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO) ) \c@section@level=\count304 ) LaTeX Info: Redefining \ref on input line 0. LaTeX Info: Redefining \pageref on input line 0. LaTeX Info: Redefining \nameref on input line 0. (texput.out) (texput.out) \@outlinefile=\write3 \openout3 = `texput.out'. *{\Large *\begin{center}{CS5800: Algorithms} --- --- \instructor \end{center}} *{\large *\vspace{10pt} *\noindent Homework~\hwnum \vspace{2pt}\\ *Due :~\hwdue} ! Undefined control sequence. <*> Due :~\hwdue } ? *\bigskip *{\large \noindent Name: \yourname } * (Please type a command or say `\end') *\vspace{15pt} * (Please type a command or say `\end') *{\large \noindent Instructions:} * (Please type a command or say `\end') *\begin{itemize} * (Please type a command or say `\end') *\item Make sure to put your name on the first page. If you are using the \LaT eX~template we provided, then you can make sure it appears by filling in the \t exttt{yourname} command. LaTeX Font Info: Trying to load font information for TS1+ppl on input line 0 . (/home/vip/.miktex/texmfs/install/tex/latex/psnfss/ts1ppl.fd File: ts1ppl.fd 2001/06/04 font definitions for TS1/ppl. ) LaTeX Font Info: Trying to load font information for OT1+jkp on input line 0 . (/home/vip/.miktex/texmfs/install/tex/latex/kpfonts/ot1jkp.fd File: ot1jkp.fd 2007/08/30 Fontinst v1.928 font definitions for OT1/jkp. ) Package microtype Info: Loading generic protrusion settings for font family (microtype) `jkp' (encoding: OT1). (microtype) For optimal results, create family-specific settings. (microtype) See the microtype manual for details. LaTeX Font Info: Trying to load font information for U+jkpsya on input line 0. (/home/vip/.miktex/texmfs/install/tex/latex/kpfonts/ujkpsya.fd File: ujkpsya.fd 2006/08/15 v1.0 ) LaTeX Font Info: Trying to load font information for U+jkpsyb on input line 0. (/home/vip/.miktex/texmfs/install/tex/latex/kpfonts/ujkpsyb.fd File: ujkpsyb.fd 2006/08/15 v1.0 ) LaTeX Font Info: Trying to load font information for U+jkpmia on input line 0. (/home/vip/.miktex/texmfs/install/tex/latex/kpfonts/ujkpmia.fd File: ujkpmia.fd 2006/08/15 v1.0 ) LaTeX Font Info: Trying to load font information for U+jkpsyc on input line 0. (/home/vip/.miktex/texmfs/install/tex/latex/kpfonts/ujkpsyc.fd File: ujkpsyc.fd 2006/08/15 v1.0 ) Package microtype Info: Loading generic protrusion settings for font family (microtype) `cmtt' (encoding: OT1). (microtype) For optimal results, create family-specific settings. (microtype) See the microtype manual for details. * (Please type a command or say `\end') *\item Please review the grading policy outlined in the course information page . * (Please type a command or say `\end') *\item You must also write down with whom you worked on the assignment. If thi s changes from problem to problem, then you should write down this information separately with each problem. * (Please type a command or say `\end') *\item Problem numbers (like Exercise 3.1-1) are corresponding to CLRS $3^{rd}$ edition. While the $2^{nd}$ edition has similar problems with similar numbers, the actual exercises and their solutions are different, so make su re you are using the $3^{rd}$ edition. * (Please type a command or say `\end') *\end{itemize} * (Please type a command or say `\end') *\newpage [1 {/home/vip/.miktex/texmfs/data/pdftex/config/pdftex.map}] * (Please type a command or say `\end') *\begin{prob} \textbf{(20 points)} *\end{prob} * (Please type a command or say `\end') *Two linked lists (simple link, not double link) heads are given:headA, andhead B;it is also given that the two lists intersect, thus after the intersection t hey have thesame elements to the end. Find the first common element, without m odifying the listselements or using additional datastructures. * (Please type a command or say `\end') *\begin{enumerate}[label=(\alph*)] * (Please type a command or say `\end') *\item A linear algorithm is discussed in the lecture: count the lis ts first, then use the count difference as an offset in the longer list, before traversing the lists together. Write a formal pseudocode (the pseudocode in the lecture is vague), using “next” as a method/pointer to a dvance to the next element in a list. * (Please type a command or say `\end') *\solution * (Please type a command or say `\end') *\item Write the actual code in a programming language (C/C++, Java, Python etc ) of your choice and run it on a made-up test pair of two lists. A good idea is to use pointers to represent the list linkage. * (Please type a command or say `\end') *\solution * (Please type a command or say `\end') *\end{enumerate} * (Please type a command or say `\end') *\begin{prob} \textbf{(10 points)} Exercise 3.1-1 *\end{prob} * (Please type a command or say `\end') *\begin{prob} \textbf{(5 points)} Exercise 3.1-4 *\end{prob} * (Please type a command or say `\end') *\begin{prob} \textbf{(15 points)} *\end{prob} * (Please type a command or say `\end') *Rank the following functions in terms of asymptotic growth. In othe r words, find an arrangement of the functions $f_1, f_2, . . .$ such that for all i, $f_i = \Omega(f_{i+1})$. * Overfull \hbox (2.17874pt too wide) detected at line 0 []\OT1/ppl/m/n/10.95 (-20) Rank the following functions in terms of asymptotic growth. In other words, find an arrangement [] (Please type a command or say `\end') *\begin{center} *\begin{tabular}{ccccccc} *$\sqrt{n}\ln n$ & $\ln \ln n^2$ & $2^{\ln^2 n}$ & $n!$ & $n^{0.001}$ & $2^{2\l n n}$ & $(\ln n)!$ \\ *\end{tabular} *\end{center} * (Please type a command or say `\end') *\begin{prob} \textbf{(40 points)} Problem 4-1 (page 107) *\end{prob} * (Please type a command or say `\end') *Give asymptotic upper and lower bounds for T(n) in each of the following recur rences. Assume that T(n) is constant for $n \leq 2$. Make your bounds as tight as possible, and justify your answers. * (Please type a command or say `\end') *\begin{enumerate}[label=(\alph*)] * (Please type a command or say `\end') *\item $T(n) = 2T(n/2) + n^4$ * (Please type a command or say `\end') *\item $T(n) = T(7n/10) + n$ * (Please type a command or say `\end') *\item $T(n) = 16T(n/4) + n^2$ * (Please type a command or say `\end') *\item $T(n) = 7T(n/3) + n^2$ * (Please type a command or say `\end') *\item $T(n) = 7T(n/2) + n^2$ * (Please type a command or say `\end') *\item $T(n) = 7T(n/4) + \sqrt{n}$ * (Please type a command or say `\end') *\item $T(n) = T(n-2) + n^2$ * (Please type a command or say `\end') *\end{enumerate} * (Please type a command or say `\end') *\begin{prob} \textbf{(30 points)} Problem 4-3 from (a) to (f) (page 108) *\end{prob} * (Please type a command or say `\end') *Give asymptotic upper and lower bounds for T(n) in each of the following recur rences. Assume that T(n) is constant for sufficiently small n. Make your bounds as tight as possible, and justify your answers. * (Please type a command or say `\end') *\begin{enumerate}[label=(\alph*)] * (Please type a command or say `\end') *\item $T(n) = 4T(n/3) + n\lg n$ * (Please type a command or say `\end') *\item $T(n) = 3T(n/3) + n / \lg n$ * (Please type a command or say `\end') *\item $T(n) = 4T(n/2) + n^2 \sqrt{n}$ * (Please type a command or say `\end') *\item $T(n) = 3T(n/3 - 2) + n/2$ [2] * (Please type a command or say `\end') *\item $T(n) = 2T(n/2) + n / \lg n$ * (Please type a command or say `\end') *\item $T(n) = T(n/2) + T(n/4) + T(n/8) + n$ * (Please type a command or say `\end') *\end{enumerate} * (Please type a command or say `\end') *\end{document} [3] (texput.aux) Package rerunfilecheck Info: File `texput.out' has not changed. (rerunfilecheck) Checksum: D41D8CD98F00B204E9800998ECF8427E;0. 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