From ad284e54bfc102f6c33410824c27d8de929fbb61 Mon Sep 17 00:00:00 2001 From: Peter Gerwinski <peter.gerwinski@hs-bochum.de> Date: Thu, 24 Jan 2019 18:30:24 +0100 Subject: [PATCH] =?UTF-8?q?=C3=9Cbungsaufgaben=20und=20Musterl=C3=B6sung?= =?UTF-8?q?=2021.1.2019?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 20190121/aufgabe-2.c | 47 ++ 20190121/hp-musterloesung-20190121.pdf | Bin 0 -> 80157 bytes 20190121/hp-musterloesung-20190121.tex | 598 +++++++++++++++++++++++++ 20190121/hp-uebung-20190121.pdf | Bin 66372 -> 66263 bytes 20190121/hp-uebung-20190121.tex | 22 +- 20190121/loesung-1.c | 62 +++ 20190121/loesung-1b-1.c | 58 +++ 20190121/loesung-1b-2.c | 58 +++ 20190121/loesung-1c.c | 72 +++ 20190121/loesung-1d.c | 86 ++++ 20190121/loesung-2a.c | 69 +++ 20190121/loesung-2b.c | 97 ++++ 20190121/loesung-3c.c | 68 +++ 13 files changed, 1226 insertions(+), 11 deletions(-) create mode 100644 20190121/aufgabe-2.c create mode 100644 20190121/hp-musterloesung-20190121.pdf create mode 100644 20190121/hp-musterloesung-20190121.tex create mode 100644 20190121/loesung-1.c create mode 100644 20190121/loesung-1b-1.c create mode 100644 20190121/loesung-1b-2.c create mode 100644 20190121/loesung-1c.c create mode 100644 20190121/loesung-1d.c create mode 100644 20190121/loesung-2a.c create mode 100644 20190121/loesung-2b.c create mode 100644 20190121/loesung-3c.c diff --git a/20190121/aufgabe-2.c b/20190121/aufgabe-2.c new file mode 100644 index 0000000..f26ce5d --- /dev/null +++ b/20190121/aufgabe-2.c @@ -0,0 +1,47 @@ +#include <stdio.h> +#include <stdlib.h> + +typedef struct node +{ + int content; + struct node *next; +} node; + +void output_list (node *first) +{ + for (node *p = first; p; p = p->next) + printf ("%d ", p->content); + printf ("\n"); +} + +void insert_into_list (node *what, node *where) +{ + what->next = where->next; + where->next = what; +} + +int main (void) +{ + node *element3 = malloc (sizeof (node)); + node *element7 = malloc (sizeof (node)); + node *element137 = malloc (sizeof (node)); + + element3->content = 3; + element7->content = 7; + element137->content = 137; + + node *first = element3; + element3->next = element7; + element7->next = element137; + element137->next = NULL; + + output_list (first); + + node *element5 = malloc (sizeof (node)); + element5->content = 5; + insert_into_list (element5, element3); + + output_list (first); + + return 0; +} diff --git a/20190121/hp-musterloesung-20190121.pdf b/20190121/hp-musterloesung-20190121.pdf new file mode 100644 index 0000000000000000000000000000000000000000..57b065d7ede6125a1452a0021a7f49b6a62997ef GIT binary patch literal 80157 zcmY!laB<T$)HCH$y>R8|4K7Os1BLvgEG`=xeV^34^pXq(BTGXg1u)Qe%giZBEz)<( zNi0cqNlngANwu@%DlREXP0Z!0xV1JaI{)!8(Yo*J1%gZ_Jh=PvPWxnE?j>iJ-OcUJ zNfu|^WhS=8)!Rqql<3MEuNVB^o1Q1qzDUFC)Zuj*MdxN3KmT`@NA9d!#h2^ccYgi- z{Pn2(zQrXj7D+LeE`B}Sae$rYzq-i9mcA*+JiH8d#r4_s{hzi@U8H}xu+lOAmsZ-B 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Free Software +% Foundation, either version 3 of the License, or (at your option) +% any later version. +% +% This document is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this document. If not, see <http://www.gnu.org/licenses/>. +% +% You should have received a copy of the Creative Commons +% Attribution-ShareAlike 3.0 Unported License along with this +% document. If not, see <http://creativecommons.org/licenses/>. + +% README: Stack-Operationen, einfach und doppelt verkettete Listen, ternärer Baum + +\documentclass[a4paper]{article} + +\usepackage{pgscript} +\usepackage{tikz} + +\begin{document} + + \section*{Hardwarenahe Programmierung\\ + Musterlösung zu den Übungsaufgaben -- 21.\ Januar 2019} + + \exercise{Stack-Operationen} + + Wir betrachten das folgende Programm (\gitfile{hp}{20190121}{aufgabe-1.c}): + + \begin{minipage}[t]{0.5\textwidth} + \begin{lstlisting}[gobble=6] + #include <stdio.h> + + #define STACK_SIZE 10 + + int stack[STACK_SIZE]; + int stack_pointer = 0; + + void push (int x) + { + stack[stack_pointer++] = x; + } + + int pop (void) + { + return stack[--stack_pointer]; + } + + void show (void) + { + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); + } + \end{lstlisting} + \end{minipage}\hfill + \begin{minipage}[t]{0.5\textwidth} + \begin{lstlisting}[gobble=6] + void insert (int x, int pos) + { + for (int i = pos; i < stack_pointer; i++) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; + } + + void insert_sorted (int x) + { + int i = 0; + while (i < stack_pointer && x < stack[i]) + i++; + insert (x, i); + } + + int main (void) + { + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + return 0; + } + \end{lstlisting} + \end{minipage} + + \begin{enumerate}[\quad(a)] + \item + Ändern Sie das Programm so, + daß die Funktion \lstinline{insert()} ihren Parameter \lstinline{x} + an der Stelle \lstinline{pos} in den Stack einfügt, + und den sonstigen Inhalt des Stacks verschiebt, aber nicht zerstört. + \points{3} + \item + Ändern Sie das Programm so, + daß die Funktion \lstinline{insert_sorted()} ihren Parameter \lstinline{x} + an derjenigen Stelle einfügt, an die er von der Sortierung her gehört. + (Der Stack wird hierbei vor dem Funktionsaufruf als sortiert vorausgesetzt.) + \points{2} + \item + Schreiben Sie eine zusätzliche Funktion \lstinline{int search (int x)}, + die die Position (Index) des Elements \lstinline{x} + innerhalb des Stack zurückgibt + -- oder \lstinline{-1}, wenn \lstinline{x} nicht im Stack enthalten ist. + Der Rechenaufwand darf höchstens $\mathcal{O}(n)$ betragen. + \points{3} + \item + Wie (c), aber der Rechenaufwand darf höchstens $\mathcal{O}(\log n)$ betragen. + \points{4} + \end{enumerate} + + \solution + + \begin{enumerate}[\quad(a)] + \item + \textbf{Ändern Sie das Programm so, + daß die Funktion \lstinline{insert()} ihren Parameter \lstinline{x} + an der Stelle \lstinline{pos} in den Stack einfügt, + und den sonstigen Inhalt des Stacks verschiebt, aber nicht zerstört.} + + Die \lstinline{for}-Schleife in der Funktion \lstinline{insert()} + durchläuft das Array von unten nach oben. + Um den Inhalt des Arrays von unten nach oben zu verschieben, + muß man die Schleife jedoch von oben nach unten durchlaufen. + + \goodbreak + Um die Funktion zu reparieren, ersetze man also + \begin{lstlisting}[gobble=8] + for (int i = pos; i < stack_pointer; i++) + \end{lstlisting} + durch: + \begin{lstlisting}[gobble=8] + for (int i = stack_pointer - 1; i >= pos; i--) + \end{lstlisting} + (Siehe auch: \gitfile{hp}{20190121}{loesung-1.c}) + + \item + \textbf{Ändern Sie das Programm so, + daß die Funktion \lstinline{insert_sorted()} ihren Parameter \lstinline{x} + an derjenigen Stelle einfügt, an die er von der Sortierung her gehört. + (Der Stack wird hierbei vor dem Funktionsaufruf als sortiert vorausgesetzt.)} + + Der Vergleich \lstinline{x < stack[i]} + als Bestandteil der \lstinline{while}-Bedingung + paßt nicht zur Durchlaufrichtung der Schleife (von unten nach oben). + + Um die Funktion zu reparieren, kann man daher entweder + das Kleinerzeichen durch ein Größerzeichen ersetzen + (\lstinline{x > stack[i]} -- siehe \gitfile{hp}{20190121}{loesung-1b-1.c}) + oder die Schleife von oben nach unten durchlaufen + (siehe \gitfile{hp}{20190121}{loesung-1b-2.c}). + + Eine weitere Möglichkeit besteht darin, + das Suchen nach der Einfügeposition + mit dem Verschieben des Arrays zu kombinieren + (siehe \gitfile{hp}{20190121}{loesung-1.c}). + Hierdurch spart man sich eine Schleife; das Programm wird schneller. + (Es bleibt allerdings bei $\mathcal{O}(n)$.) + + \item + \textbf{Schreiben Sie eine zusätzliche Funktion \lstinline{int search (int x)}, + die die Position (Index) des Elements \lstinline{x} + innerhalb des Stack zurückgibt + -- oder \lstinline{-1}, wenn \lstinline{x} nicht im Stack enthalten ist. + Der Rechenaufwand darf höchstens $\mathcal{O}(n)$ betragen.} + + Man geht in einer Schleife den Stack (= den genutzten Teil des Arrays) durch. + Bei Gleichheit gibt man direkt mit \lstinline{return} den Index zurück. + Nach dem Schleifendurchlauf steht fest, + daß \lstinline{x} nicht im Stack vorhanden ist; + man kann dann direkt \lstinline{-1} zurückgeben + (siehe \gitfile{hp}{20190121}{loesung-1c.c}). + + Da es sich um eine einzelne Schleife handelt, + ist die Ordnung $\mathcal{O}(n)$. + + \item + \textbf{Wie (c), aber der Rechenaufwand darf höchstens $\mathcal{O}(\log n)$ betragen.} + + Um $\mathcal{O}(\log n)$ zu erreichen, + halbiert man fortwährend das Intervall von (einschließlich) \lstinline{0} + bis (ausschließlich) \lstinline{stack_pointer} + (siehe \gitfile{hp}{20190121}{loesung-1d.c}) -- + wie in der Funktion \lstinline{push_sorted()} + im Beispiel-Programm \gitfile{hp}{20190121}{stack-11.c}. + + Ein wichtiger Unterschied besteht darin, + daß man nach dem Durchlauf der Schleife noch auf die Gleichheit + \lstinline{x == stack[left]} (insbesondere nicht: \lstinline{stack[right]}) + prüfen und ggf.\ \lstinline{left} bzw.\ \lstinline{-1} zurückgeben muß. + \end{enumerate} + + \goodbreak + + \exercise{Einfach und doppelt verkettete Listen} + + Das Beispiel-Programm \gitfile{hp}{20190121}{aufgabe-2.c} + demonstriert zwei Funktionen zur Verwaltung einfach verketteter Listen: + \lstinline{output_list()} zum Ausgeben der Liste auf den Bildschirm und + \lstinline{insert_into_list()} zum Einfügen in die Liste. + + \begin{enumerate}[\quad(a)] + \item + Ergänzen Sie eine Funktion \lstinline{delete_from_list()} + zum Löschen eines Elements aus der Liste + mit Freigabe des Speicherplatzes. + \points{5} + \item + Ergänzen Sie eine Funktion \lstinline{reverse_list()} + die die Reihenfolge der Elemente in der Liste umdreht.\\ + \points{3} + \end{enumerate} + + Eine doppelt verkettete Liste hat in jedem Knotenpunkt (\lstinline{node}) + \emph{zwei\/} Zeiger -- einen auf das nächste Element (\lstinline{next}) + und einen auf das vorherige Element (z.\,B.\ \lstinline{prev} für "`previous"'). + Dadurch ist es leichter als bei einer einfach verketteten Liste, + die Liste in umgekehrter Reihenfolge durchzugehen. + + \begin{quote} + \begin{tikzpicture} + \color{blendedblue} + \node(first) at (0,3.5) {first}; + \node(NULL1) at (-1,1.25) {NULL}; + \node[shape=rectangle,draw,line width=1pt](3) at (1,2) {3}; + \node[shape=rectangle,draw,line width=1pt](7) at (3,2) {7}; + \node[shape=rectangle,draw,line width=1pt](137) at (5,2) {137}; + \node(NULL2) at (7,2.75) {NULL}; + \draw[-latex](first)--(3); + \draw[-latex](3) to[out=45,in=135] (7); + \draw[-latex](3) to[out=-135,in=0] (NULL1); + \draw[-latex](7) to[out=-135,in=-45] (3); + \draw[-latex](7) to[out=45,in=135] (137); + \draw[-latex](137) to[out=-135,in=-45] (7); + \draw[-latex](137) to[out=45,in=180] (NULL2); + \end{tikzpicture} + \end{quote} + + Der Rückwärts-Zeiger (\lstinline{prev}) des ersten Elements zeigt, + genau wie der Vorwärts-Zeiger (\lstinline{next}) des letzten Elements, + auf \emph{nichts}, hat also den Wert \lstinline{NULL}. + + \begin{enumerate}[\quad(a)]\setcounter{enumi}{2} + \item + Schreiben Sie das Programm um für doppelt verkettete Listen. + \points{5} + \end{enumerate} + + \solution + + \begin{enumerate}[\quad(a)] + \item + \textbf{Ergänzen Sie eine Funktion \lstinline{delete_from_list()} + zum Löschen eines Elements aus der Liste + mit Freigabe des Speicherplatzes.} + + Siehe: \gitfile{hp}{20190121}{loesung-2a.c} + + Um ein Element aus einer verketteten Liste zu löschen, + müssen zuerst die Zeiger umgestellt werden, + um das Element von der Liste auszuschließen. + Erst danach darf der Speicherplatz für das Element freigegeben werden. + +% Da das Beispielprogramm (\gitfile{hp}{20190121}{lists-5.c}) +% nicht mit dynamischem Speicher arbeitet, +% stellen wir dieses zunächst auf dynamischen Speicher um, z.\,B.: +% \begin{lstlisting}[gobble=8] +% node *element5 = malloc (sizeof (node)); +% \end{lstlisting} +% Danach bezeichnet \lstinline{element5} +% die Adresse der \lstinline{struct}-Variablen; +% es wird also \lstinline{element5} an die Funktionen übergeben +% und nicht \lstinline{&element5} (die Adresse des Zeigers). + +% Um nun ein Element aus der Liste zu entfernen, +% benötigt man + Man benötigt also + \emph{das vorherige Element}, + dessen \lstinline{next}-Zeiger man dann auf + das übernächste Element \lstinline{next->next} weitersetzt. + + Bei jedem Zeiger muß man vor dem Zugriff prüfen, + daß dieser nicht auf \lstinline{NULL} zeigt. + (Die Musterlösung ist in dieser Hinsicht nicht konsequent. + Für den Produktiveinsatz müßte z.\,B.\ \lstinline{delete_from_list()} + auch den übergebenen Zeiger \lstinline{what} auf \lstinline{NULL} prüfen.) + + Ein Spezialfall tritt ein, wenn das erste Element einer Liste + entfernt werden soll. In diesem Fall tritt \lstinline{first} + an die Stelle des \lstinline{next}-Zeigers + des (nicht vorhandenen) vorherigen Elements. + Da \lstinline{delete_from_list()} \emph{schreibend\/} auf \lstinline{first} + zugreift, muß \lstinline{first} \emph{als Zeiger\/} übergeben werden + (\lstinline{node **first}). + + Um alle Spezialfälle zu testen (am Anfang, am Ende und in der Mitte der Liste), + wurden die Testfälle im Hauptprogramm erweitert. + + \item + \textbf{Schreiben Sie das Programm um für doppelt verkettete Listen.} + + Siehe: \gitfile{hp}{20190121}{loesung-2b.c} + + Bei allen Einfüge- und Löschaktionen müssen \emph{jeweils zwei\/} + \lstinline{next}- und \lstinline{prev}-Zeiger neu gesetzt werden. + + Zum Debuggen empfiehlt es sich sehr, + eine Funktion zu schreiben, die die Liste auf Konsistenz prüft + (hier: \lstinline{check_list()}). + + Das Testprogramm macht von der Eigenschaft der doppelt verketteten Liste, + daß man sie auch rückwärts effizient durchgehen kann, keinen Gebrauch. + Um diese Eigenschaft als Vorteil nutzen zu können, empfiehlt es sich, + zusätzlich zu \lstinline{first} + auch einen Zeiger auf das letzte Element (z.\,B.\ \lstinline{last}) + einzuführen. Dieser muß dann natürlich bei allen Operationen + (Einfügen, Löschen, \dots) auf dem aktuellen Stand gehalten werden. + + \end{enumerate} + + \exercise{Ternärer Baum} + + Der in der Vorlesung vorgestellte \newterm{binäre Baum\/} + ist nur ein Spezialfall; + im allgemeinen können Bäume auch mehr als zwei Verzweigungen + pro Knotenpunkt haben. + Dies ist nützlich bei der Konstruktion \emph{balancierter Bäume}, + also solcher, die auch im \emph{Worst Case\/} + nicht zu einer linearen Liste entarten, + sondern stets eine -- möglichst flache -- Baumstruktur behalten. + + Wir betrachten einen Baum mit bis zu drei Verzweigungen pro Knotenpunkt, + einen sog.\ \newterm{ternären Baum}. + Jeder Knoten enthält dann nicht nur einen, + sondern \emph{zwei\/} Werte als Inhalt: + + \begin{lstlisting} + typedef struct node + { + int content_left, content_right; + struct node *left, *middle, *right; + } node; + \end{lstlisting} + + Wir konstruieren nun einen Baum nach folgenden Regeln: + \vspace{-\medskipamount} + \begin{itemize}\itemsep0pt + \item + Innerhalb eines Knotens sind die Werte sortiert: + \lstinline{content_left} muß stets kleiner sein als \lstinline{content_right}. + \item + Der Zeiger \lstinline{left} zeigt auf Knoten, + deren enthaltene Werte durchweg kleiner sind als \lstinline{content_left}. + \item + Der Zeiger \lstinline{right} zeigt auf Knoten, + deren enthaltene Werte durchweg größer sind als \lstinline{content_right}. + \item + Der Zeiger \lstinline{middle} zeigt auf Knoten, + deren enthaltene Werte durchweg größer sind als \lstinline{content_left}, + aber kleiner als \lstinline{content_right}. + \item + Ein Knoten muß nicht immer mit zwei Werten voll besetzt sein; + er darf auch \emph{nur einen\/} gültigen Wert enthalten. + + Der Einfachheit halber lassen wir in diesem Beispiel + nur positive Zahlen als Werte zu. + Wenn ein Knoten nur einen Wert enthält, + setzen wir \lstinline{content_right = -1}, + und der Zeiger \lstinline{middle} wird nicht verwendet. + \item + Wenn wir neue Werte in den Baum einfügen, + werden \emph{zuerst\/} die nicht voll besetzten Knoten aufgefüllt + und \emph{danach erst\/} neue Knoten angelegt und Zeiger gesetzt. + \item + Beim Auffüllen eines Knotens darf nötigenfalls \lstinline{content_left} + nach \lstinline{content_right} verschoben werden. + Ansonsten werden einmal angelegte Knoten nicht mehr verändert. + \end{itemize} + \vspace*{-\medskipamount} + (In der Praxis dürfen Knoten gemäß speziellen Regeln + nachträglich verändert werden, + um Entartungen gar nicht erst entstehen zu lassen -- + siehe z.\,B.\ \url{https://de.wikipedia.org/wiki/2-3-4-Baum}.) + + \begin{enumerate}[\quad(a)] + \item + Zeichnen Sie ein Schaubild, das veranschaulicht, + wie die Zahlen 7, 137, 3, 5, 6, 42, 1, 2 und 12 + nacheinander und in dieser Reihenfolge + in den oben beschriebenen Baum eingefügt werden + -- analog zu den Vortragsfolien (\gitfile{hp}{20190121}{hp-20190121.pdf}), + Seite 43. + \points{3} + % + % Lösung: + % + % 7 137 + % / | + % 3 5 12 42 + % / \ + % 1 2 6 + % + % (NULL-Zeiger sind hier nicht dargestellt, + % gehören aber dazu.) + % + \goodbreak + \item + Dasselbe, aber in der Reihenfolge + 2, 7, 42, 12, 1, 137, 5, 6, 3. + \points{3} + % + % Lösung: + % + % 2 7 + % / | \ + % 1 5 6 12 42 + % / \ + % 3 137 + % + % (NULL-Zeiger sind hier wieder nicht dargestellt, + % gehören aber dazu.) + % + \item + Beschreiben Sie in Worten und/oder als C-Quelltext-Fragment, + wie eine Funktion aussehen müßte, um den auf diese Weise entstandenen Baum + sortiert auszugeben. + \points{4} + \end{enumerate} + + \solution + + \begin{enumerate}[\quad(a)] + \item + \textbf{Zeichnen Sie ein Schaubild, das veranschaulicht, + wie die Zahlen 7, 137, 3, 5, 6, 42, 1, 2 und 12 + nacheinander und in dieser Reihenfolge + in den oben beschriebenen Baum eingefügt werden + -- analog zu den Vortragsfolien (\gitfile{hp}{20190121}{hp-20190121.pdf}), + Seite 21.} + % + % Lösung: + % + % 7 137 + % / | + % 3 5 12 42 + % / \ + % 1 2 6 + % + % (NULL-Zeiger sind hier nicht dargestellt, + % gehören aber dazu.) + % + \begin{center} + \newcommand{\x}{~\makebox(0,0){\raisebox{0.7em}{\rule{1pt}{1.4em}}}~} + \begin{tikzpicture} + \color{blendedblue} + \node(root) at (0,0) {\lstinline{node *root;}}; + \node[shape=rectangle,draw,line width=1pt](7-137) at (0,-1.5) {7\x 137}; + \draw[-latex](root)--(7-137); + \node[shape=rectangle,draw,line width=1pt](3-5) at (-2,-3) {3\x 5}; + \draw[-latex](7-137)--(3-5); + \node[shape=rectangle,draw,line width=1pt](12-42) at (0,-3) {12\x 42}; + \draw[-latex](7-137)--(12-42); + \node[shape=rectangle,draw,line width=1pt](1-2) at (-4,-4.5) {1\x 2}; + \draw[-latex](3-5)--(1-2); + \node[shape=rectangle,draw,line width=1pt](6) at (0,-4.5) {6}; + \draw[-latex](3-5)--(6); + \end{tikzpicture} + \end{center} + Bemerkungen: + \begin{itemize} + \item + Zeiger mit dem Wert \lstinline{NULL} sind nicht dargestellt: + \lstinline{right}-Zeiger von 7/137, + \lstinline{middle}-Zeiger von 3/5, + sämtliche Zeiger von 1/2, 12/42 und 6. + \item + Beim Einfügen der 12 wird die sich bereits vorher in diesem + \lstinline{node} befindliche 42 zu \lstinline{content_right}, + und die 12 wird das neue \lstinline{content_left}. + \item + Dieser Baum hat sehr einfache Regeln und ist daher \emph{nicht\/} + balanciert. Insbesondere unsere Regel, daß einmal angelegte Knoten + nicht mehr verändert werden dürfen, steht dem im Wege. + Ein einfaches Beispiel für einen \emph{balancierten\/} ternären + Baum ist der 2-3-Baum -- siehe z.\,B.\ \url{https://en.wikipedia.org/wiki/2-3_tree}. + \end{itemize} + \goodbreak + \item + \textbf{Dasselbe, aber in der Reihenfolge + 2, 7, 42, 12, 1, 137, 5, 6, 3.} + % + % Lösung: + % + % 2 7 + % / | \ + % 1 5 6 12 42 + % / \ + % 3 137 + % + % (NULL-Zeiger sind hier wieder nicht dargestellt, + % gehören aber dazu.) + % + \begin{center} + \newcommand{\x}{~\makebox(0,0){\raisebox{0.7em}{\rule{1pt}{1.4em}}}~} + \begin{tikzpicture} + \color{blendedblue} + \node(root) at (0,0) {\lstinline{node *root;}}; + \node[shape=rectangle,draw,line width=1pt](2-7) at (0,-1.5) {2\x 7}; + \draw[-latex](root)--(7-137); + \node[shape=rectangle,draw,line width=1pt](1) at (-2,-3) {1}; + \draw[-latex](2-7)--(1); + \node[shape=rectangle,draw,line width=1pt](5-6) at (0,-3) {5\x 6}; + \draw[-latex](2-7)--(5-6); + \node[shape=rectangle,draw,line width=1pt](3) at (-2,-4.5) {3}; + \draw[-latex](5-6)--(3); + \node[shape=rectangle,draw,line width=1pt](12-42) at (2,-3) {12\x 42}; + \draw[-latex](2-7)--(12-42); + \node[shape=rectangle,draw,line width=1pt](137) at (4,-4.5) {137}; + \draw[-latex](12-42)--(137); + \end{tikzpicture} + \end{center} + Bemerkungen: + \begin{itemize} + \item + Wieder sind Zeiger mit dem Wert \lstinline{NULL} nicht dargestellt: + \lstinline{middle}- und \lstinline{right}-Zeiger von 5/6, + \lstinline{left}- und \lstinline{middle}-Zeiger von 12/42, + sämtliche Zeiger von 1, 3 und 137. + \item + Beim Einfügen der 12 wird wieder die sich bereits vorher in diesem + \lstinline{node} befindliche 42 zu \lstinline{content_right}, + und die 12 wird das neue \lstinline{content_left}. + \end{itemize} + \item + \textbf{Beschreiben Sie in Worten und/oder als C-Quelltext-Fragment, + wie eine Funktion aussehen müßte, um den auf diese Weise entstandenen Baum + sortiert auszugeben.} + + Die entscheidende Idee ist \textbf{Rekursion}. + + Eine Funktion, die den gesamten Baum ausgibt, + müßte einmalig für den Zeiger \lstinline{root} aufgerufen werden + und folgendes tun: + \begin{enumerate}[\quad 1.] + \item + falls der übergebene Zeiger den Wert \lstinline{NULL} hat, + nichts ausgeben, sondern die Funktion direkt beenden, + \item + sich selbst für den \lstinline{left}-Zeiger aufrufen, + \item + den Wert von \lstinline{content_left} ausgeben, + \item + sich selbst für den \lstinline{middle}-Zeiger aufrufen, + \item + sofern vorhanden (also ungleich \lstinline{-1}), + den Wert von \lstinline{content_right} ausgeben, + \item + sich selbst für den \lstinline{right}-Zeiger aufrufen. + \end{enumerate} + Als C-Fragment: + \begin{lstlisting}[gobble=8] + void output_tree (node *root) + { + if (root) + { + output_tree (root->left); + printf ("%d\n", root->content_left); + output_tree (root->middle); + if (root->content_right >= 0) + printf ("%d\n", root->content_right); + output_tree (root->right); + } + } + \end{lstlisting} + Die Datei \gitfile{hp}{20190121}{loesung-3c.c} erweitert dieses Fragment + zu einem vollständigen C-Programm zum Erstellen und sortierten Ausgeben + eines ternären Baums mit den Zahlenwerten von Aufgabenteil (a). + \end{enumerate} + +\end{document} diff --git a/20190121/hp-uebung-20190121.pdf b/20190121/hp-uebung-20190121.pdf index 849e6d1c2736862258d0b4799e6419c6ce8726c3..aeaa67f68317c7df03a89caf1af5a411374ab342 100644 GIT binary patch delta 35088 zcmX@o#&W%tMNl=s#ZA{x&y-8`!j+>pxC{*@3WzWoPd~`Ws5;T>V*M`dslqBNJ_YSR zo%6EfnoZDw`x`4w_ovO#*ZRKQ!*0#zc<tHGdb2*9a!&iZS?A7%$UN@)*X^#m^sXO` zn85P0{eR4_`}*1ckC`6*b8XtxxwmD+PU`)6{M0mfkIr76i7|Pp4DTy<?fAOBRxWtr znx>eh!d!-k4KMX(NU4Z?<^E@_QSX(|JJnq8hQa!*)`y?slYNDwZFY#~*nKTyNIq<I z>SWEtNP~${DU){!cP5G&@AjBGkGJ{#=A*GY&#XG7_lI}UpY_}4sP8_;lpo6eEi&$0 z&P+Y+|8qDink%fLMZ})mlwo~uRUnkoqL9UJwUp6eBEt&%e#tePk4>EJ9QX77X|1{S 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a/20190121/hp-uebung-20190121.tex b/20190121/hp-uebung-20190121.tex index d0a8b62..a658160 100644 --- a/20190121/hp-uebung-20190121.tex +++ b/20190121/hp-uebung-20190121.tex @@ -20,7 +20,7 @@ % Attribution-ShareAlike 3.0 Unported License along with this % document. If not, see <http://creativecommons.org/licenses/>. -% README: Stack-Operationen, doppelt verkettete Liste, ternärer Baum +% README: Stack-Operationen, einfach und doppelt verkettete Listen, ternärer Baum \documentclass[a4paper]{article} @@ -35,13 +35,13 @@ Übungsaufgaben -- 21.\ Januar 2019} Diese Übung enthält Punkteangaben wie in einer Klausur. - Um zu "`bestehen"', müssen Sie innerhalb von 90 Minuten + Um zu "`bestehen"', müssen Sie innerhalb von 100 Minuten unter Verwendung ausschließlich zugelassener Hilfsmittel - 16 Punkte (von insgesamt \totalpoints) erreichen. + 17 Punkte (von insgesamt \totalpoints) erreichen. \exercise{Stack-Operationen} - Wir betrachten das folgende Programm (\gitfile{hp}{20180122}{aufgabe-1.c}): + Wir betrachten das folgende Programm (\gitfile{hp}{20190121}{aufgabe-1.c}): \begin{minipage}[t]{0.5\textwidth} \begin{lstlisting}[gobble=6] @@ -136,19 +136,19 @@ \goodbreak - \exercise{Doppelt verkettete Liste} + \exercise{Einfach und doppelt verkettete Listen} - In der Vorlesung wurde ein Beispiel-Programm -% (\gitfile{hp}{20180122}{lists-11.c}) - zur Verwaltung einfach verketteter Listen erstellt - (an die Liste anhängen, in die Liste einfügen, Liste ausgeben usw.). + Das Beispiel-Programm \gitfile{hp}{20190121}{aufgabe-2.c} + demonstriert zwei Funktionen zur Verwaltung einfach verketteter Listen: + \lstinline{output_list()} zum Ausgeben der Liste auf den Bildschirm und + \lstinline{insert_into_list()} zum Einfügen in die Liste. \begin{enumerate}[\quad(a)] \item Ergänzen Sie eine Funktion \lstinline{delete_from_list()} zum Löschen eines Elements aus der Liste mit Freigabe des Speicherplatzes. - \points{3} + \points{5} \item Ergänzen Sie eine Funktion \lstinline{reverse_list()} die die Reihenfolge der Elemente in der Liste umdreht.\\ @@ -260,7 +260,7 @@ wie die Zahlen 7, 137, 3, 5, 6, 42, 1, 2 und 12 nacheinander und in dieser Reihenfolge in den oben beschriebenen Baum eingefügt werden - -- analog zu den Vortragsfolien (\gitfile{hp}{20190121}{hp-20980121.pdf}), + -- analog zu den Vortragsfolien (\gitfile{hp}{20190121}{hp-20190121.pdf}), Seite 43. \points{3} % diff --git a/20190121/loesung-1.c b/20190121/loesung-1.c new file mode 100644 index 0000000..9b87d6c --- /dev/null +++ b/20190121/loesung-1.c @@ -0,0 +1,62 @@ +#include <stdio.h> + +#define STACK_SIZE 10 + +int stack[STACK_SIZE]; +int stack_pointer = 0; + +void push (int x) +{ + stack[stack_pointer++] = x; +} + +int pop (void) +{ + return stack[--stack_pointer]; +} + +void show (void) +{ + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); +} + +void insert (int x, int pos) +{ + for (int i = stack_pointer - 1; i >= pos; i--) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; +} + +void insert_sorted (int x) +{ + int i = stack_pointer - 1; + while (i >= 0 && x < stack[i]) + { + stack[i + 1] = stack[i]; + i--; + } + stack[i + 1] = x; + stack_pointer++; +} + +int main (void) +{ + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + return 0; +} diff --git a/20190121/loesung-1b-1.c b/20190121/loesung-1b-1.c new file mode 100644 index 0000000..cbbe370 --- /dev/null +++ b/20190121/loesung-1b-1.c @@ -0,0 +1,58 @@ +#include <stdio.h> + +#define STACK_SIZE 10 + +int stack[STACK_SIZE]; +int stack_pointer = 0; + +void push (int x) +{ + stack[stack_pointer++] = x; +} + +int pop (void) +{ + return stack[--stack_pointer]; +} + +void show (void) +{ + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); +} + +void insert (int x, int pos) +{ + for (int i = stack_pointer - 1; i >= pos; i--) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; +} + +void insert_sorted (int x) +{ + int i = 0; + while (i < stack_pointer && x > stack[i]) + i++; + insert (x, i); +} + +int main (void) +{ + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + return 0; +} diff --git a/20190121/loesung-1b-2.c b/20190121/loesung-1b-2.c new file mode 100644 index 0000000..b1e1ae8 --- /dev/null +++ b/20190121/loesung-1b-2.c @@ -0,0 +1,58 @@ +#include <stdio.h> + +#define STACK_SIZE 10 + +int stack[STACK_SIZE]; +int stack_pointer = 0; + +void push (int x) +{ + stack[stack_pointer++] = x; +} + +int pop (void) +{ + return stack[--stack_pointer]; +} + +void show (void) +{ + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); +} + +void insert (int x, int pos) +{ + for (int i = stack_pointer - 1; i >= pos; i--) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; +} + +void insert_sorted (int x) +{ + int i = stack_pointer - 1; + while (i >= 0 && x < stack[i]) + i--; + insert (x, i + 1); +} + +int main (void) +{ + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + return 0; +} diff --git a/20190121/loesung-1c.c b/20190121/loesung-1c.c new file mode 100644 index 0000000..79d061e --- /dev/null +++ b/20190121/loesung-1c.c @@ -0,0 +1,72 @@ +#include <stdio.h> + +#define STACK_SIZE 10 + +int stack[STACK_SIZE]; +int stack_pointer = 0; + +void push (int x) +{ + stack[stack_pointer++] = x; +} + +int pop (void) +{ + return stack[--stack_pointer]; +} + +void show (void) +{ + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); +} + +void insert (int x, int pos) +{ + for (int i = stack_pointer - 1; i >= pos; i--) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; +} + +void insert_sorted (int x) +{ + int i = stack_pointer - 1; + while (i >= 0 && x < stack[i]) + { + stack[i + 1] = stack[i]; + i--; + } + stack[i + 1] = x; + stack_pointer++; +} + +int search (int x) +{ + for (int i = 0; i < stack_pointer; i++) + if (stack[i] == x) + return i; + return -1; +} + +int main (void) +{ + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + printf ("%d\n", search (42)); + printf ("%d\n", search (1117)); + return 0; +} diff --git a/20190121/loesung-1d.c b/20190121/loesung-1d.c new file mode 100644 index 0000000..9079d8d --- /dev/null +++ b/20190121/loesung-1d.c @@ -0,0 +1,86 @@ +#include <stdio.h> + +#define STACK_SIZE 10 + +int stack[STACK_SIZE]; +int stack_pointer = 0; + +void push (int x) +{ + stack[stack_pointer++] = x; +} + +int pop (void) +{ + return stack[--stack_pointer]; +} + +void show (void) +{ + printf ("stack content:"); + for (int i = 0; i < stack_pointer; i++) + printf (" %d", stack[i]); + if (stack_pointer) + printf ("\n"); + else + printf (" (empty)\n"); +} + +void insert (int x, int pos) +{ + for (int i = stack_pointer - 1; i >= pos; i--) + stack[i + 1] = stack[i]; + stack[pos] = x; + stack_pointer++; +} + +void insert_sorted (int x) +{ + int i = stack_pointer - 1; + while (i >= 0 && x < stack[i]) + { + stack[i + 1] = stack[i]; + i--; + } + stack[i + 1] = x; + stack_pointer++; +} + +int search (int x) +{ + int left = 0; + int right = stack_pointer; + while (left < right - 1) + { + int middle = (left + right) / 2; + if (x < stack[middle]) + right = middle; + else + left = middle; + } + if (x == stack[left]) + return left; + else + return -1; +} + +int main (void) +{ + push (3); + push (7); + push (137); + show (); + insert (5, 1); + show (); + insert_sorted (42); + show (); + insert_sorted (2); + show (); + printf ("%d\n", search (2)); + printf ("%d\n", search (4)); + printf ("%d\n", search (42)); + printf ("%d\n", search (67)); + printf ("%d\n", search (137)); + printf ("%d\n", search (1117)); + return 0; +} diff --git a/20190121/loesung-2a.c b/20190121/loesung-2a.c new file mode 100644 index 0000000..93f5e56 --- /dev/null +++ b/20190121/loesung-2a.c @@ -0,0 +1,69 @@ +#include <stdio.h> +#include <stdlib.h> + +typedef struct node +{ + int content; + struct node *next; +} node; + +void output_list (node *first) +{ + for (node *p = first; p; p = p->next) + printf ("%d ", p->content); + printf ("\n"); +} + +void insert_into_list (node *what, node *where) +{ + what->next = where->next; + where->next = what; +} + +void delete_from_list (node *what, node **first) +{ + if (what == *first) + *first = what->next; + else + { + node *p = *first; + while (p && p->next != what) + p = p->next; + if (p) + p->next = what->next; + } + free (what); +} + +int main (void) +{ + node *element3 = malloc (sizeof (node)); + node *element7 = malloc (sizeof (node)); + node *element137 = malloc (sizeof (node)); + + element3->content = 3; + element7->content = 7; + element137->content = 137; + + node *first = element3; + element3->next = element7; + element7->next = element137; + element137->next = NULL; + + output_list (first); + + node *element5 = malloc (sizeof (node)); + element5->content = 5; + insert_into_list (element5, element3); + + output_list (first); + + delete_from_list (element5, &first); + output_list (first); + delete_from_list (element3, &first); + output_list (first); + delete_from_list (element137, &first); + output_list (first); + + return 0; +} diff --git a/20190121/loesung-2b.c b/20190121/loesung-2b.c new file mode 100644 index 0000000..811b99b --- /dev/null +++ b/20190121/loesung-2b.c @@ -0,0 +1,97 @@ +#include <stdio.h> +#include <stdlib.h> + +typedef struct node +{ + int content; + struct node *next, *prev; +} node; + +void check_list (node *first) +{ + for (node *p = first; p; p = p->next) + { + if (p->next && p->next->prev != p) + fprintf (stderr, "List inconsistency!\n"); + if (p->prev && p->prev->next != p) + fprintf (stderr, "List inconsistency!\n"); + } +} + +void output_list (node *first) +{ + for (node *p = first; p; p = p->next) + printf ("%d ", p->content); + printf ("\n"); +} + +void insert_into_list (node *what, node *where) +{ + what->next = where->next; + if (where->next) + where->next->prev = what; + what->prev = where; + where->next = what; +} + +void delete_from_list (node *what, node **first) +{ + if (what == *first) + { + *first = what->next; + if (*first) + (*first)->prev = NULL; + } + else + { + node *p = *first; + while (p && p->next != what) + p = p->next; + if (p) + p->next = what->next; + if (what->next) + what->next->prev = p; + } + free (what); +} + +int main (void) +{ + node *element3 = malloc (sizeof (node)); + node *element7 = malloc (sizeof (node)); + node *element137 = malloc (sizeof (node)); + + element3->content = 3; + element7->content = 7; + element137->content = 137; + + node *first = element3; + element3->prev = NULL; + element3->next = element7; + element7->prev = element3; + element7->next = element137; + element137->prev = element7; + element137->next = NULL; + + output_list (first); + check_list (first); + + node *element5 = malloc (sizeof (node)); + element5->content = 5; + insert_into_list (element5, element3); + + output_list (first); + check_list (first); + + delete_from_list (element5, &first); + output_list (first); + check_list (first); + delete_from_list (element3, &first); + output_list (first); + check_list (first); + delete_from_list (element137, &first); + output_list (first); + check_list (first); + + return 0; +} diff --git a/20190121/loesung-3c.c b/20190121/loesung-3c.c new file mode 100644 index 0000000..a6dea99 --- /dev/null +++ b/20190121/loesung-3c.c @@ -0,0 +1,68 @@ +#include <stdio.h> +#include <stdlib.h> + +typedef struct node +{ + int content_left, content_right; + struct node *left, *middle, *right; +} node; + +void insert_into_tree (node **root, int value) +{ + if (*root) + { + if ((*root)->content_right >= 0) + if (value < (*root)->content_left) + insert_into_tree (&(*root)->left, value); + else if (value < (*root)->content_right) + insert_into_tree (&(*root)->middle, value); + else + insert_into_tree (&(*root)->right, value); + else + if (value < (*root)->content_left) + { + (*root)->content_right = (*root)->content_left; + (*root)->content_left = value; + } + else + (*root)->content_right = value; + } + else + { + *root = malloc (sizeof (node)); + (*root)->left = NULL; + (*root)->content_left = value; + (*root)->middle = NULL; + (*root)->content_right = -1; + (*root)->right = NULL; + } +} + +void output_tree (node *root) +{ + if (root) + { + output_tree (root->left); + printf ("%d\n", root->content_left); + output_tree (root->middle); + if (root->content_right >= 0) + printf ("%d\n", root->content_right); + output_tree (root->right); + } +} + +int main (void) +{ + node *root = NULL; + insert_into_tree (&root, 7); + insert_into_tree (&root, 137); + insert_into_tree (&root, 3); + insert_into_tree (&root, 5); + insert_into_tree (&root, 6); + insert_into_tree (&root, 42); + insert_into_tree (&root, 1); + insert_into_tree (&root, 2); + insert_into_tree (&root, 12); + output_tree (root); + return 0; +} -- GitLab