notebooks/Methoden.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Methoden\n",
    "\n",
    "### Marcel Lüthi, Departement Mathematik und Informatik, Universität Basel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "// Code um Turtle Bibliothek zu importieren, welche wir im Folgenden nutzen\n",
    "%mavenRepo bintray https://dl.bintray.com/egp/maven\n",
    "%maven ch.unibas.informatik:jturtle:0.5\n",
    "import ch.unibas.informatik.jturtle.Turtle;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Motivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<pre class=\"stretch\"><code data-trim>\n",
    "Turtle turtle = new Turtle();\n",
    "\n",
    "turtle.home();\n",
    "turtle.clear();\n",
    "turtle.penDown();\n",
    "int lengthLegs = 100;\n",
    "turtle.forward(lengthLegs);\n",
    "turtle.turnRight(90);\n",
    "turtle.forward(lengthLegs);\n",
    "turtle.turnRight(135);\n",
    "turtle.forward(Math.sqrt(lengthLegs * lengthLegs + lengthLegs * lengthLegs)) ;\n",
    "turtle.turnRight(90);\n",
    "display(turtle.toImage());\n",
    "</code></pre>\n",
    "\n",
    "* Was macht das Programm?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Intention nicht offensichtlich.\n",
    "* Programm ist schlecht strukturiert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameterlose Methoden\n",
    "\n",
    "* Lassen uns Codeblöcke benennen\n",
    "\n",
    "```java\n",
    "static void doSomething() { // Methodenkopf\n",
    "    statement1;\n",
    "    ...                     // Methodenrumpf\n",
    "    statmentN;\n",
    "}\n",
    "```\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Können beliebig oft aufgerufen werden. \n",
    "* Aufruf führt Anweisungsfolge aus\n",
    "```\n",
    "doSomething()\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Miniübung\n",
    "\n",
    "* Wandeln Sie obiges Programm (Turtle) in eine Methode um. \n",
    "    * Finden Sie einen guten Namen\n",
    "* Rufen Sie das Programm (mehrmals) auf\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kgYHXuDvAylQwAAiyxMDz3BtgdaoYAARZZOA57gywA5UMAIIsM/A49wXYhWoGAEEWGniMuwLsREUDgCBLDXzPPQF2o6oBQJDFBr7mjgA7UtkAIMhyA59zP4BdqW4AEGTBgY+5G8DOVDgACLLkwL/cC2B3qhwABFl04G/uBFCg0gFAkGUHfnMfgArVDgCCLDzwk7sAlKh4ABBk6QH3AOhR9QAgyOJDnTsAFKl8ABBk+aHM+QeqVD8ACLIAUeXsA2UqIAAEWYIocu6BOlUQAIIsQtQ48wACAABIsgxR4rwD/KQaAkCQhYgKZx3gNxURAIIsRRQ45wB/UxUBIMhixO6ccYB/qYwAEGQ5YmfON8DHVEcACLIgsStnG+BzKiQABFmS2JFzDfA1VRIAgixK7MaZBvieSgkAQZYlduI8AzxGtQSAIAsTu3CWAR6nYgJAkKWJHTjHAM9RNQEgyOLE6pxhgOepnAAQZHliZc4vwGtUTwAIskCxKmcX4HUqKAAEWaJYkXMLcIwqCgBBFilW48wCHKeSAkCQZYqVOK8A51BNASDIQsUqnFWA86ioABBkqWIFzinAuVRVAAiyWDE7ZxTgfCorAARZrpiZ8wlwDdUVAIIsWMzK2QS4jgoLAEGWLGbkXAJcS5UFgCCLFrNxJgGup9ICQJBli5k4jwBjqLYAEGThYhbOIsA4Ki4ABFm6mIFzCDCWqgsAQRYv7uYMAoyn8gJAkOWLOzl/APdQfQEgyALGXZw9gPuowAAQZAnjDs4dwL1UYQAIsogxmjMHcD+VGACCLGOM5LwBzEE1BoAgCxmjOGsA81CRASDIUsYIzhnAXFRlAAiymHE1ZwxgPiozAARZzriS8wUwJ9UZAIIsaFzF2QKYlwoNAEGWNK7gXAHMTZUGgCCLGmdzpgDmp1IDQJBljTM5TwBrUK0BIMjCxlmcJYB1qNgAEGRp4wzOEcBaVG0ACLK4cZQzBLAelRsAgixvHOH8AKxJ9QaAIAscr3J2ANalggNAkCWOVzg3AGtTxQEgyCLHs5wZgPWp5AAQZJnjGc4LwB5UcwAIstDxKGcFYB8qOgAEWep4hHMCsBdVHQCCLHZ8xxkB2I/KDgBBlju+4nwA7El1B4AgCx6fcTYA9qXCA0CQJY+POBcAe1PlASDIosd7zgTA/lR6AAiy7PEn5wGgQbUHgCALH784CwAdKj4ABFn6eOMcALSo+gAQZPHDGQDoUfkBIMjy1+b9AzSp/gAQZAHs8u4BunQAAAiyBDZ57wBtugAABFkEe7xzAHQCAAiyDLZ43wC80Q0AIMhC2OFdA/CLjgAAQZbCBu8ZgD/pCgAQZDHcn3cMwHs6AwAEWQ735v0C8BHdAQCCLIj78m4B+IwOAQBBlsQ9ea8AfEWXAIAgi+J+vFMAvqNTAECQZXEv3icAj9AtACDIwrgP7xKAR+kYABBkadyD9wjAM3QNAAiyOK7POwTgWToHAARZHtfm/QHwCt0DAIIskOvy7gB4lQ4CAEGWyDV5bwAcoYsAQJBFcj3eGQBH6SQAEGSZXIv3BcAZdBMACLJQrsO7AuAsOgoABFkq1+A9AXAmXQUAgiyW8/OOADibzgIAQZbLuXk/AFxBdwGAIAvmvLwbAK6iwwBAkCVzTt4LAFfSZQAgyKI5H+8EgKvpNAAQZNmci/cBwAi6DQAEWTjn4V0AMIqOAwBBls45eA8AjKTrAECQxfN+3gEAo+k8ABBk+byX5w/AHXQfAAiygN7HswfgLjoQAARZQu/huQNwJ10IAIIsouN55gDcTScCgCDL6FieNwAz0I0AIMhCOo5nDcAsdCQACLKUjuE5AzATXQkAgiym1/OMAZiNzgQAQZbTa3m+AMxIdwKAIAvqdTxbAGalQwFAkCX1Gp4rADPTpQAgyKJ6Ps8UgNnpVAAQZFk9l+cJwAp0KwAIsrCex7MEYBU6FgAEWVrP4TkCsBJdCwCCLK7HeYYArEbnAoAgy+sxnh8AK9K9ACDIAvs6zw6AVelgABBkiX2N5wbAynQxAAiyyD7PMwNgdToZAARZZp/jeQGwA90MAIIstI/zrADYhY4GAEGW2sd4TgDsRFcDgCCL7fc8IwB2o7MBQJDl9mueDwA70t0AIMiC+znPBoBd6XAAEGTJ/ZjnAsDOdDkACLLo/sszAWB3Oh0ABFl2/+Z5AFCg2wFAkIX3N88CgAodDwCCLL0/eQ4AlOh6ABBk8fUMAOjR+QAgqL781r8/AE26HwAElRfg8ncHoE0HBICg6hJc/d4A8EYXBICg4iJc/M4A8CedEACCastw7fsCwEd0QwAIKi3Epe8KAF/REQEgqLIUV74nADxCVwSAoMJiXPiOAPAMnREAgnZfjnf/fgDwCt0RAIJ2XpB3/m4AcIQOCQBBuy7Ju34vADiDLgkAQTsuyjt+JwA4k04JAEG7Lcu7fR8AuIJuCQBBOy3MO30XALiSjgkAQbsszbt8DwAYQdcEgKAdFucdvgMAjKRzAkDQ6svz6p8fAO6gewJA0MoL9MqfHQDupIMCQNCqS/SqnxsAZqCLAkDQiov0ip8ZAGaikwJA0GrL9GqfFwBmpJsCQNBKC/VKnxUAZqajAkDQKkv1Kp8TAFagqwJA0AqL9QqfEQBWorMCQNDsy/Xsnw8AVqS7AkDQzAv2zJ8NAFamwwJA0KxL9qyfCwB2oMsCQNCMi/aMnwkAdqLTAkDQbMv2bJ8HAHak2wJA0EwL90yfBQB2puMCQNAsS/csnwMACnRdAAiaYfGe4TMAQInOCwBBdy/fd/9+ACjSfQEg6M4F/M7fDQBlOjAABN21hN/1ewEAAQAAJN2xiN/xOwGA33RiAAgavYyP/n0AwL90YwAIGrmQj/xdAMDndGQACBq1lI/6PQDA93RlAAgasZiP+B0AwON0ZgAIuno5v/rnAwDP050BIOjKBf3Knw0AvE6HBoCgq5b0q34uAHCcLg0AQVcs6lf8TADgPDo1AASdvayf/fMAgPPp1gAQdObCfubPAgCuo2MDQNBZS/tZPwcAuJ6uDQBBZyzuZ/wMAGAcnRsAgo4u70f/PQAwnu4NAEFHFvgj/xYAuI8ODgBBry7xr/47AOB+ujgABL2yyL/ybwCAeejkABD07DL/7N8HAOajmwNA0DML/TN/FwCYl44OAEGPLvWP/j0AYH66OgAEPbLYP/J3AIB16OwAEPTdcv/d/w8ArEd3B4Cgrxb8r/4/AGBdOjwABH225H/23wGA9enyABD00aL/0X8DAPah0wNA0Ptl//3/BgD2o9sDQNCfC7/lHwAadHwACPq19Fv+AaBD1weAoLfF3/IPAC06PwAEWf4BoEf3BwAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgAAAAAIEAAAAABAgAAAAAAAAgQAAAAAECAAAAAAgAABAAAAAAQIAAAAACBAAAAAAAABAgA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      "text/plain": [
       "BufferedImage@36118c03: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "BufferedImage@327e2ad: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Turtle turtle = new Turtle();\n",
    "\n",
    "static void drawRightAngledTriangle() {\n",
    "    turtle.home();\n",
    "    turtle.clear();\n",
    "    turtle.penDown();\n",
    "    int lengthLegs = 100;\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(90);\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(135);\n",
    "    turtle.forward(Math.sqrt(lengthLegs * lengthLegs + lengthLegs * lengthLegs)) ;\n",
    "    turtle.turnRight(90);\n",
    "    display(turtle.toImage());\n",
    "}\n",
    "\n",
    "drawRightAngledTriangle();\n",
    "drawRightAngledTriangle();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Methoden im Klassenkontext\n",
    "\n",
    "* In Java Programmen müssen Methoden immer Teil einer Klasse sein\n",
    "\n",
    "```java\n",
    "class MyClass {\n",
    " \n",
    "    static void method1() {\n",
    "        // Implementation \n",
    "    }\n",
    "    \n",
    "    static void method2() {\n",
    "        // Implementation\n",
    "    }\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> Jupyter-Notebooks und die JShell fügen den Klassenkontext implizit dazu."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Wie funktionieren Methodenaufrufe?\n",
    "\n",
    "![methodcalls](images/method-calls.png)\n",
    "\n",
    "* Bei Methodenaufruf verzweigt Programm an erste Stelle von Methode und arbeitet Anweisungen ab\n",
    "* Nach Abarbeitung kehrt Methode zur aufrufenden Stelle zurück"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Namenskonventionen\n",
    "\n",
    "* Namen sollten mit Verb und Kleinbuchstaben beginnen\n",
    "* Methoden beginnen mit Verb\n",
    "\n",
    "##### Beispiele:\n",
    "* ```printHeader```\n",
    "* ```findMaximum```\n",
    "* ```traverseList```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameter (1)\n",
    "\n",
    "\n",
    "> Werte, die vom Rufer an die Methode übergeben werden\n",
    "\n",
    "```\n",
    "static void printMax(int a, int b) {  \n",
    "    if (a > b) { \n",
    "        System.out.println(a);\n",
    "    } else {\n",
    "        System.out.println(b);\n",
    "    }\n",
    "}\n",
    "```\n",
    "\n",
    "* ```a``` und ```b``` (im Methodenkopf) sind *formale Parameter*\n",
    "    * Formale Parameter sind Variablen (benannte Speicherstellen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameter (2)\n",
    "\n",
    "\n",
    "Methode kann mit entsprechenden Werten aufgerufen werden\n",
    "\n",
    "```java\n",
    "int i = 5;\n",
    " \n",
    "...\n",
    "\n",
    "printMax(11, i * 2) \n",
    "```\n",
    "\n",
    "* ```11```und ```i``` sind *aktuelle* Parameter\n",
    "    * Aktuelle Parameter sind *Werte* oder Ausdrücke\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Miniübung\n",
    "\n",
    "* Schreiben Sie eine Methode die die Summer zweier Zahlen berechnet und diese ausgibt\n",
    "* Können Sie die Werte von Variablen innerhalb der Methode verändern?\n",
    "    * Verändert sich dadurch der Wert der Variablen ausserhalb der Methode?\n",
    "* Schreiben Sie das Programm zur Zeichnung von rechtwinkligen Dreicken so um, dass es als Parameter die Seitenlänge der beiden Katheten nimmt (Das Turtle können Sie ausserhalb der Methode erstellen)\n",
    "* Schreiben Sie eine Methode ```setPos``` welches die Turtleposition setzt und nutzen Sie diese im Programm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "BufferedImage@688e9c5d: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Turtle turtle = new Turtle();\n",
    "\n",
    "static void drawRightAngledTriangle(int lengthLegs) {\n",
    "    turtle.home();\n",
    "    turtle.clear();\n",
    "    turtle.penDown();\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(90);\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(135);\n",
    "    turtle.forward(Math.sqrt(lengthLegs * lengthLegs + lengthLegs * lengthLegs)) ;\n",
    "    turtle.turnRight(90);\n",
    "    display(turtle.toImage());\n",
    "};\n",
    "\n",
    "drawRightAngledTriangle(100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Funktionen\n",
    "\n",
    "> Methoden, die Ergebniswerte an den Rufer liefern\n",
    "\n",
    "```java \n",
    "static int max(int a, int b) {\n",
    "    if (a > b) {\n",
    "        return a;\n",
    "    } else { \n",
    "        return b;\n",
    "    }\n",
    "}\n",
    "```\n",
    "\n",
    "* Typ von Rückgabewert statt ```void``` in Methodenkopf\n",
    "* ```return``` Schlüsselwort um Wert zurückzugeben. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Funktionen (Aufruf)\n",
    "\n",
    "Funktionsaufrufe können überall stehen, wo Ausdrücke erlaubt sind\n",
    "\n",
    "Beispiele:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "```java \n",
    "int x = max(5, 3)\n",
    "```    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "```java\n",
    "int y = System.out.println(max(5, 3));\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "```java\n",
    "\n",
    "if (max(a, b) == a) {\n",
    "    System.out.println(\"a > b\");\n",
    "} else { \n",
    "   System.out.println(\"b > a\");\n",
    "}\n",
    "    ```\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Miniübungen\n",
    "\n",
    "* Schreiben Sie eine Funktion, die für eine gegebene Länge der Katheten die Länge der Hypothenuse ausrechnet\n",
    "* Schreiben Sie das Turtle-Programm so um, dass diese Funktion genutzt wird. \n",
    "\n",
    "\n",
    "##### Für schnelle:\n",
    "* Schreiben Sie eine Methode drawCircle, die einen Kreis (mit festem Radius) an einer fixen Position zeichnet.\n",
    "* Schreiben Sie dann eine parameterlose Methode, die die olympischen Ringe zeichnet.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "BufferedImage@768271e0: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Turtle turtle = new Turtle();\n",
    "\n",
    "static double computeHypothenuse(double a, double b) {\n",
    "    return Math.sqrt(a * a + b * b);\n",
    "}\n",
    "\n",
    "\n",
    "static void drawRightAngledTriangle(int lengthLegs) {\n",
    "    turtle.home();\n",
    "    turtle.clear();\n",
    "    turtle.penDown();\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(90);\n",
    "    turtle.forward(lengthLegs);\n",
    "    turtle.turnRight(135);\n",
    "    turtle.forward(computeHypothenuse(lengthLegs, lengthLegs));\n",
    "    turtle.turnRight(90);\n",
    "    display(turtle.toImage());\n",
    "};\n",
    "\n",
    "drawRightAngledTriangle(100);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Lokale und statische Variablen\n",
    "\n",
    "<pre class=\"stretch\"><code class=\"java\" data-trim>\n",
    "class C {\n",
    " static int a;\n",
    "    \n",
    "    static void p() { \n",
    "        int x;\n",
    "    }    \n",
    "    \n",
    "    static void q() { \n",
    "        int y;\n",
    "    }    \n",
    "}\n",
    "</code></pre>\n",
    "\n",
    "* ```a``` ist eine *statische Variable*, welche in jeder Methode der Klasse sichtbar ist. \n",
    "* ```x``` und ```y``` sind *lokale Variablen*.\n",
    "    * Nur in jeweiliger Methode sichtbar\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Experimente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "class C {\n",
    " static int a;\n",
    "    \n",
    "    static void p() { \n",
    "        int x;\n",
    "    }    \n",
    "    \n",
    "    static void q() { \n",
    "        System.out.println(a);\n",
    "        int y;\n",
    "    }    \n",
    "    \n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Sichtbarkeit von Namen\n",
    "\n",
    "![sichtbarkeit](images/scope.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Experimente mit der Sichtbarkeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Sample {\n",
    "\n",
    "    static int x = 0;\n",
    "    \n",
    "    static void P() {\n",
    "        System.out. println( x); \n",
    "    }\n",
    "\n",
    "    static void experiment() {\n",
    "        System.out. println( x); \n",
    "        //int x = 1;\n",
    "        System.out. println( x); \n",
    "        P();        \n",
    "        if (x > 0) {\n",
    "             int x;\n",
    "             int y;\n",
    "        } else {\n",
    "             int y; \n",
    "        }\n",
    "       // for (int i = 0; i < 5; i++) { System.out.println(i); }\n",
    "       // for (int i = 1; i < 5; i++) { System.out.println(i); }\n",
    "    }\n",
    "}\n",
    "Sample.experiment();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Lokalität\n",
    "\n",
    "> Variablen sollen möglichst lokal deklariert werden\n",
    "\n",
    "##### Vorteile\n",
    "\n",
    "* Übersicht - Deklaration und Nutzung nahe beisammen\n",
    "* Sicherheit - Werte von Variablen werden nicht aus anderen Methoden überschrieben\n",
    "* Effizienz - Zugriff auf lokale Variablen ist oft schneller als auf statische Variablen\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Rekursion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Methoden können andere Methoden aufrufen. \n",
    "\n",
    "* Können Methoden sich selbst aufrufen?\n",
    "\n",
    "\n",
    "#### Experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " void f(int i) { \n",
    "    f(i);\n",
    " }\n",
    "f(5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Rekursion (2)\n",
    "\n",
    "Eine Methode ```m()``` heisst rekursiv, wenn sie sich selbst aufruft;\n",
    "\n",
    "Direkt rekursiv:\n",
    "```java\n",
    "    \n",
    "    public void m() { \n",
    "        m (); \n",
    "    } \n",
    "```\n",
    "\n",
    "Indirekt rekursiv:\n",
    "```java\n",
    "    public void m() { \n",
    "        n(); \n",
    "    }\n",
    "    public void n() {\n",
    "       m();\n",
    "    }\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Beispiel 1: Fakultät\n",
    "\n",
    "$n! = (n - 1)! \\cdot n$\n",
    "\n",
    "$1! = 1$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "// Implementation\n",
    "static int factorial(int n) {\n",
    "    System.out.println(n);\n",
    "    if (n == 1) {\n",
    "        return 1;\n",
    "    }\n",
    "    return factorial(n - 1) * n;\n",
    "}\n",
    "factorial(4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Beispiel 2: Fibonacci-Folge\n",
    "\n",
    "$ f_0 = 0 $ \n",
    "\n",
    "$f_1 = 1 $\n",
    "\n",
    "$f_n = f_{n-1} + f_{n - 2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "// Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Beispiel 3: Sierpinski-Dreieck"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "static void drawSierpinskiRec(Turtle turtle, double length, int depth) {\n",
    "    if (depth==0){\n",
    "        for (int i = 0; i < 3; i++) {\n",
    "            turtle.forward(length);\n",
    "            turtle.turnLeft(120);\n",
    "        }\n",
    "    }\n",
    "    else {\n",
    "        drawSierpinskiRec(turtle, length/2.0 , depth-1);\n",
    "        turtle.forward(length/2);\n",
    "        drawSierpinskiRec(turtle, length/2.0, depth-1);\n",
    "        turtle.backward(length/2);\n",
    "        turtle.turnLeft(60);\n",
    "        turtle.forward(length/2);\n",
    "        turtle.turnRight(60);\n",
    "        drawSierpinskiRec(turtle, length/2.0,depth-1);\n",
    "        turtle.turnLeft(60);\n",
    "        turtle.backward(length/2);\n",
    "        turtle.turnRight(60);\n",
    "    }\n",
    "}\n",
    "\n",
    "static void drawSierpinski(double length, int depth) {\n",
    "    Turtle turtle = new Turtle();\n",
    "    turtle.home();\n",
    "    turtle.penDown();\n",
    "    drawSierpinskiRec(turtle, length, depth);\n",
    "    display(turtle.toImage());\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "drawSierpinski(150.0, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Miniübung\n",
    "\n",
    "* Versuchen Sie das Muster zu verstehen indem Sie mit dem Programm experimentieren"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Weitere Übungen\n",
    "\n",
    "* Schreiben Sie die Algorithmen ```binarylog``` und  ```ggt```, die in der Einführungsvorlesung (Slides: Informatik-Grundlagen) besprochen wurden als Methoden hin\n",
    "* Schreiben Sie eine Methode ```static void reduce(int z, int n)```, die mithilfe der Methode ```ggt``` den Bruch $\\frac{z}{n}$ kürzt und den gekürzten Bruch ausgibt. \n",
    "* Schreiben Sie eine Methode ```area```, welche für ein Dreieck mit gegebener Seitenlänge```a```, ```b``` und ```c```, die Fläche berechnet\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "static int binaryLog(int n) {\n",
    "    int i = 0;\n",
    "    while (n > 1) {\n",
    "        i += 1;\n",
    "        n = n / 2;\n",
    "    }\n",
    "    return i;\n",
    "}\n",
    "binaryLog(3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "static int ggt(int a, int b) {\n",
    "\n",
    "    int rest = a % b;\n",
    "    while (rest != 0) {\n",
    "        a = b;\n",
    "        b = rest;\n",
    "        rest = a % b;\n",
    "    }\n",
    "    return b;\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2/1\n"
     ]
    }
   ],
   "source": [
    "static void reduce(int z, int n) {\n",
    "    int ggt = ggt(z, n);\n",
    "    System.out.println((z / ggt) +\"/\" + (n / ggt));\n",
    "}\n",
    "reduce(16,  8);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "static double area(double a, double b, double c) {\n",
    "\n",
    "    // siehe https://en.wikipedia.org/wiki/Heron's_formula\n",
    "    double s = (a + b + c) / 2.0;\n",
    "    return Math.sqrt(s * (s - a) * (s - b) * (s - c));\n",
    "}\n",
    "area(4, 13, 15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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