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Esercizi per il terzo tutorato
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‎latex/esercitazioni/es_tutorato_2.pdf

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‎latex/esercitazioni/es_tutorato_2.tex

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\documentclass[11pt,a4]{article}
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\usepackage[margin=2cm]{geometry}
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\usepackage{multicol}
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\usepackage{amsmath}
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\usepackage{url}
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\usepackage{amsmath}
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\usepackage{url}
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\usepackage[utf8]{inputenc}
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% Default fixed font does not support bold face
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\DeclareFixedFont{\ttb}{T1}{txtt}{bx}{n}{10} % for bold
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\DeclareFixedFont{\ttm}{T1}{txtt}{m}{n}{10} % for normal
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% Custom colors
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\usepackage{color}
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\definecolor{deepblue}{rgb}{0,0,0.5}
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\definecolor{deepred}{rgb}{0.6,0,0}
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\definecolor{deepgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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% Python style for highlighting
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\newcommand\pythonstyle{\lstset{
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language=Python,
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basicstyle=\ttm,
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otherkeywords={self}, % Add keywords here
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keywordstyle=\ttb\color{deepblue},
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emph={MyClass,__init__}, % Custom highlighting
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emphstyle=\ttb\color{deepred}, % Custom highlighting style
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stringstyle=\color{deepgreen},
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frame=tb, % Any extra options here
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showstringspaces=false %
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}}
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% Python environment
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\lstnewenvironment{python}[1][]
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{
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\pythonstyle
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\lstset{#1}
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}
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{}
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% Python for external files
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\newcommand\pythonexternal[2][]{{
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\pythonstyle
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\lstinputlisting[#1]{#2}}}
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% Python for inline
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\newcommand\pythoninline[1]{{\pythonstyle\lstinline!#1!}}
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\usepackage{collectbox}
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\newcommand{\mybox}[2]{$\quad$\fbox{
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\begin{minipage}{#1cm}
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\hfill\vspace{#2cm}
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\end{minipage}
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}}
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\usepackage{fancyhdr}
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\pagestyle{fancy}
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\rhead{Programmazione 1 - Esercitazione 5}
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\include{book_header}
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\begin{document}
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\thispagestyle{empty}
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\hrule
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\begin{center}
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{\Large {\bf Programmazione 1 \hspace{3cm} $\quad \quad \quad$ Tutorato 3}}
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\end{center}
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\hrule
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{}
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\begin{enumerate}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\item Scrivere due funzioni {\tt MapFR(x)} e {\tt FilterFR(x)} che implementano la $map$ e la $filter$ utilizzando la FoldRight.
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\begin{python}
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def FoldRight(P, As, v):
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if IsEmpty(As):
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return v
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return P(Head(As), FoldRight(P, Tail(As), v))
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\end{python}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\item Scrivere due funzioni {\tt MapFL(x)} e {\tt FilterFL(x)} che implementano la $map$ e la $filter$ utilizzando la FoldLeft.
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\begin{python}
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def FoldLeft(P, As, v):
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if IsEmpty(As):
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return v
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return FoldLeft(P,Tail(As),P(z,Head(As))
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\end{python}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\item Ricordando le strutture viste:
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\begin{multicols}{2}
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\small
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\fbox{\parbox[t][3.5cm][t]{7.4cm}{
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\vspace{0.2cm}
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\textbf{def} $F(X_1, \dots, X_n):$\\
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$\hspace*{0.5cm}$ \textbf{def} $Fiter(Y_1,...,Y_m):$\\
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$\hspace*{1.0cm}$ \textbf{if} $Proposizione(Y_1,...,Y_m)==True:$\\
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\vspace{0.2cm}
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$\hspace*{1.5cm}$ \textbf{return} $Y_1,...,Y_{m'}$ $(m'\le m)$\\
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\vspace{0.2cm}
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$\hspace*{1.0cm}$ \textbf{return} $Fiter(\tilde{Y_1},...,\tilde{Y_m})$\\
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$\hspace*{0.5cm}$ $\textbf{return}$ $Fiter(\tilde{X_1},...,\tilde{X_m})$\\}}
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\columnbreak
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\fbox{\parbox[t][3.5cm][t]{7.4cm}{
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\vspace{0.2cm}
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\textbf{def} $F(X_1, \dots, X_n):$\\
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$\hspace*{0.5cm}$ $Y_i=\tilde{X_i}$ per $i=0,\dots,m$\\
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$\hspace*{0.5cm}$ (le $\tilde{X_i}$ sono costruite a partire dalle $X_i$)\\
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$\hspace*{0.5cm}$ \textbf{while} $Proposizione(Y_1,...,Y_m)==False:$\\
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$\hspace*{1.4cm}$ $Y_i=\tilde{Y_i}$ per $i=0,\dots,m$\\
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\\
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$\hspace*{0.5cm}$ \textbf{return} $Y_1,...,Y_{m'}$}}
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\end{multicols}
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Si scrivano in entrambi i modi le funzioni seguenti:
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\begin{enumerate}
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\item {\tt Fib(n)}: prende in input un numero intero $n$ e restituisce l'n-esimo elemento della successione di Fibonacci.
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\item {\tt Fn(n)}: prende in input un numero intero $n$ e restituisce l'n-esimo elemento della successione $Fn$ definita ricorsivamente:
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\begin{equation*}
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\mbox{Fn}(x) = \left\{ \begin{array}{ll}
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n & \mbox{ se } n<3, \\
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f(n-1)f(n-2)+nf(n-3) & \mbox{ se } n\ge3.
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\end{array} \right.
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\end{equation*}
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\item {\tt Equal(As,Bs)}: prende in input due liste e restituisce {True} se sono uguali, {False} altrimenti.
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\item {\tt PrimiPrimi(n)}: prende in input un numero intero $n$ e restituisce una lista dei primi n numeri primi.
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\end{enumerate}
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Dando una stima in termini di O-grande della complessità dell'algoritmo.
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\end{enumerate}
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\end{document}

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