From 13030cc6bc407532b85447730fa60e68d2fdfb47 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Sun, 24 Mar 2019 17:29:32 +0100 Subject: [PATCH] Added Graded Assignment 2 exercise 2 in Latex --- .gitignore | 263 ++++++++++++++++++++++++++++++++++++++++++++++++++++ GA2/ga2.pdf | Bin 0 -> 206761 bytes GA2/ga2.tex | 145 +++++++++++++++++++++++++++++ 3 files changed, 408 insertions(+) create mode 100644 GA2/ga2.pdf create mode 100644 GA2/ga2.tex diff --git a/.gitignore b/.gitignore index 2195e64..eea356a 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,266 @@ +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Generated if empty string is given at "Please type another file name for output:" +.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Comment the next line if you want to keep your tikz graphics files +*.tikz +*-tikzDictionary + +# listings +*.lol + +# luatexja-ruby +*.ltjruby + +# makeidx +*.idx +*.ilg +*.ind +*.ist + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices +*.xyc + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# KBibTeX +*~[0-9]* + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + # Created by https://www.gitignore.io/api/python # Edit at https://www.gitignore.io/?templates=python diff --git a/GA2/ga2.pdf b/GA2/ga2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e0c5c92e4c2bfcfda683686aae7627e32abfc31c GIT binary patch literal 206761 zcma%iV{m9e(`Ibjc5ZCjwr%Iewr$(Co!r>AZJV2|-LJN4->us3{F+lUJ=Le@>F#Hy z=a9+^i_$RAvOtl}E)K0iF%i%c*cn$-%_H2Fh*yC|O2slO7@D=7ZX+sd#<$;D)%^FDODed{Z9Y zz^EZ!vSr;EROQEO#Q8bUQfja5F(G_7$Mtd~r=El+{?LK!$AC|@F%kL*QhX0bU2zK; zwaOkLj7hd_S7Iqn%cH#_bCJG=bauhubp4y~2?htZQBHwEh%fTZ$#J|#Rjmvsj8PC9 zTw_fG5q57K3OWBY$GdVxrge~hv7=_AMeA87hEx{-0ZxFzVq){cgT-w3tY8xC!Qeff 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has a time cost of $O(n)$ in the worst case (if no elements +are found), and the loop of \textsc{search} has an added cost of $O(n)$. The +total cost in the worst case then, including mergesort, is $n^2 + n log(n) += \theta(n^2)$. + +\begin{lstlisting}[caption=Sum of three in pseudocode, label={lst:sum3}] +FUNCTION SEARCH-TWO(A, sum2, i_skip): + i $\gets$ 1 + j $\gets$ A.length + + while i < j: + if i = i_skip: + i $\gets$ i + 1 + elif j = i_skip: + j $\gets$ j - 1 + else: + sum $\gets$ $A_i$ + $A_j$ + if sum = sum2: + return TRUE + elif sum > sum2: + j $\gets$ j - 1 + else: + i $\gets$ i + 1 + + return FALSE + +FUNCTION SUM-OF-THREE(A, s): + A $\gets$ mergesort(A) + l $\gets$ A.length + + for i from 1 to l: + if SEARCH-TWO(A, s - $A_i$, i): + return TRUE + + return FALSE +\end{lstlisting} + +\subsection{Exercise c} +The \textit{Python} code used to implement \textit{Sum of three} can be found in +the listing \ref{lst:sum3py}. + +\begin{lstlisting}[caption=Sum of three in Python, label={lst:sum3py},% +language=python] +#!/usr/bin/env python3 + +import sys + +def search_two(A, sum2, i_skip): + i = 0 + j = len(A) - 1 + + while i < j: + if i == i_skip: + i = i + 1 + elif j == i_skip: + j = j - 1 + else: + cs = A[i] + A[j] + if cs == sum2: + return True + elif cs > sum2: + j = j - 1 + else: + i = i + 1 + + return False + +def sum_of_three(A, sum3): + A.sort() # assume using mergesort for worst case of O(n*log(n)) + l = len(A) + + for i in range(l): + if search_two(A, sum3 - A[i], i): + return True + + return False + +if __name__ == "__main__": + args = [int(x) for x in sys.argv[1:]] + print(sum_of_three(args[1:], args[0])) +\end{lstlisting} +\end{document}