Added Graded Assignment 2 exercise 2 in Latex

.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
 

GA2/ga2.tex

@@ -0,0 +1,145 @@
+% vim: set ts=2 sw=2 tw=80 et:
+\documentclass[12pt]{article}
+
+\usepackage[margin=3cm]{geometry}
+\usepackage{xcolor}
+\usepackage{lmodern}
+\usepackage{listings}
+
+\title{Graded Assignment 2 -- DSA}
+\author{Claudio Maggioni}
+
+% listings configuration
+\lstset{
+  basicstyle=\small\ttfamily,
+  frame=shadowbox,
+  rulesepcolor=\color{black},
+  columns=fullflexible,
+  commentstyle=\color{gray},
+  keywordstyle=\bfseries,
+  keywords={,while,if,elif,else,FUNCTION,return,for,from,to,TRUE,FALSE},
+  mathescape=true,
+  aboveskip=2em,
+  captionpos=b,
+  abovecaptionskip=1em,
+  belowcaptionskip=1em
+}
+
+\begin{document}
+
+\maketitle
+\tableofcontents
+\lstlistoflistings
+\newpage
+
+\section{Exercise 2}
+
+\subsection{Exercise a}
+The pseudocode for \textit{Sum of two} can be found in listing \ref{lst:sum2}.
+The total cost of this algorithm in the worst case is the sum of the worst case
+of mergesort ($O(n log(n))$) and the cost of the worst case in the partition
+done afterwards (which is equivalent to not finding the sum, i.e. $2 n =
+O(n)$). Therefore, the total cost is $\theta(n log(n))$.
+
+\begin{lstlisting}[caption=Sum of two in pseudocode, label={lst:sum2}]
+FUNCTION SUM-OF-TWO(A, s):
+  A $\gets$ mergesort(A)
+  i $\gets$ 1
+  j $\gets$ A.length
+
+  while i < j:
+    sum $\gets$ $A_i$ + $A_j$
+    if sum = s:
+      return TRUE
+    elif sum > s:
+      j $\gets$ j - 1
+    else:
+      i $\gets$ i + 1
+
+ return FALSE
+\end{lstlisting}
+
+\subsection{Exercise b}
+The pseudocode for \textit{Sum of three} can be found in listing \ref{lst:sum3}.
+\textsc{search-two} 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}