conditions-recursion-complete.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "126aa47b",
   "metadata": {},
   "source": [
    "# Bedingungen und Rekursion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31316514",
   "metadata": {},
   "source": [
    "### Boolsche Ausdrücke"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01c3551b",
   "metadata": {},
   "source": [
    "Wenn wir Situationen in der Programmierung beschreiben, haben wir es oft mit relativ komplexen Boolschen Ausdrücken zu tun. Wir müssen lernen diese zu lesen, verstehen und, wo möglich, zu vereinfachen. \n",
    "\n",
    "Ein Beispiel, welches zu einem komplexen boolschen Ausdruck führt ist, wenn wir die Punkte in der folgenden farbigen Fläche charakterisieren möchten\n",
    "\n",
    "![shape](images/shape.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7a313c8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "false\r\n"
     ]
    }
   ],
   "source": [
    "class BooleanExpression {\n",
    "    public static boolean isInside(double x, double y) {\n",
    "        boolean inSquare = x > -3 && x < 3 && x > -2 && x < 4;\n",
    "        boolean insideWhiteRect = x > -3 && x < 0 && y >0 && y < 2;\n",
    "        boolean isInside = inSquare && !insideWhiteRect;\n",
    "        return isInside;\n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        System.out.println(isInside(3, 4));\n",
    "    }\n",
    "}\n",
    "BooleanExpression.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6f31416",
   "metadata": {},
   "source": [
    "\n",
    "#### Miniübung\n",
    "\n",
    "* Schreiben Sie einen Ausdruck hin, der `true` ergibt, wenn die durch `x` und `y` gegebene Koordinate, innerhalb der farbigen Fläche liegt\n",
    "    * Testen Sie die Methode `isInside` mit verschiedenen Werten\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35f29149",
   "metadata": {},
   "source": [
    "### Boolsche Algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c46c5215",
   "metadata": {},
   "source": [
    "Um komplexe boolsche Ausdrücke zu verwenden, können wir die Regeln von *De-Morgan* verwenden:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38c98177",
   "metadata": {},
   "source": [
    "    !(A && B) ist gleich !A || !B\n",
    "    !(A || B) ist gleich !A && !B     "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "156b2dce",
   "metadata": {},
   "source": [
    "#### Miniübung\n",
    "\n",
    "* Schreiben Sie ein Programm, welches diese Regeln überprüft. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "80257c94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input false, false:  Gesetz1 true Gesetz2 true\n",
      "Input false, true:  Gesetz1 true Gesetz2 true\n",
      "Input true, false:  Gesetz1 true Gesetz2 true\n",
      "Input true, true:  Gesetz1 true Gesetz2 true\n"
     ]
    }
   ],
   "source": [
    "class BooleanTest {\n",
    "    \n",
    "    public static void testDeMorgan(boolean a, boolean b) {\n",
    "        boolean law1 = (!(a || b) == (!a && !b));\n",
    "        boolean law2 = (!(a && b) == (!a || !b));\n",
    "        System.out.println(\"Input \" + a + \", \" +b + \": \" +\" Gesetz1 \" + law1 + \" Gesetz2 \" + law2);\n",
    "    }\n",
    "\n",
    "    public static void main(String[] args) {\n",
    "       testDeMorgan(false, false);\n",
    "       testDeMorgan(false, true);\n",
    "       testDeMorgan(true, false);\n",
    "       testDeMorgan(true, true);\n",
    "    }\n",
    "    \n",
    "}\n",
    "\n",
    "BooleanTest.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6759389b",
   "metadata": {},
   "source": [
    "#### Miniübung\n",
    "\n",
    "* Wie würde de-Morgan's Gesetz für Relationsoperatoren `==`, `>`, `>=`, etc. aussehen?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76ec5dd2",
   "metadata": {},
   "source": [
    "#### Bindung von Operatoren\n",
    "\n",
    "Bei der Arithmetik kennen wir die Punkt vor Strich-Regel. Gilt so eine Regel auch bei `||`, `&&` und `!`? Experimentieren Sie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f7a2104c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "true && !(true || false)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3527d5cf",
   "metadata": {},
   "source": [
    "### Hochhäuser zeichnen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8b5028a",
   "metadata": {},
   "source": [
    "Wir kommen nun zurück auf unsere Zeichnungsaufgabe vom letzten Mal. Wir wollen Hochhäuser zeichnen. Dazu laden wir zuerst wieder die Turtle Bibliothek"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "775bb506",
   "metadata": {},
   "outputs": [],
   "source": [
    "%mavenRepo shapemodelling-repo https://shapemodelling.cs.unibas.ch/repo/\n",
    "%maven ch.unibas.informatik:jturtle:0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b70caaac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import static ch.unibas.informatik.jturtle.TurtleCommands.*;\n",
    "import java.awt.Color;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c7a9e33",
   "metadata": {},
   "source": [
    "Der Folgende Code zeichent dann ein vier-stöckiges Hochhaus. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "67d6ba48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "BufferedImage@2318056c: 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": [
    "class Building  {\n",
    "    public static void drawRectangle(double xPos, double yPos, double width, double height) {\n",
    "        reset(); // set turtle to origin and make it face upwards\n",
    "        penUp();\n",
    "        goTo(xPos, yPos);\n",
    "        penDown();\n",
    "        \n",
    "        forward(height);\n",
    "        turnRight(90);\n",
    "        forward(width);\n",
    "        turnRight(90);\n",
    "        forward(height);\n",
    "        turnRight(90);\n",
    "        forward(width);    \n",
    "    }\n",
    "    \n",
    "    \n",
    "    public static void drawFourStoreyBuilding(double xPos, double yPos, double width, double height) {\n",
    "        double heightOfStorey = height / 4.0;\n",
    "        drawRectangle(xPos, yPos, width, heightOfStorey);\n",
    "        drawRectangle(xPos, yPos + heightOfStorey, width, heightOfStorey);\n",
    "        drawRectangle(xPos, yPos + 2 * heightOfStorey, width, heightOfStorey);\n",
    "        drawRectangle(xPos, yPos + 3 * heightOfStorey, width, heightOfStorey);        \n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        clear();\n",
    "        drawFourStoreyBuilding(0, 0, 30, 50);\n",
    "        display(drawing());\n",
    "    }\n",
    "    \n",
    "}\n",
    "\n",
    "Building.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56cacdd6",
   "metadata": {},
   "source": [
    "Mit if-Bedingungen können wir nun zwischen verschiednene Hochhäusern unterscheiden, ohne, dass wir jeweils eine komplett neue Methode schreiben müssen. Zum Beispiel können wir Hochhäuser mit und ohne Antenne auf dem Dach schreiben. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "debd8aff",
   "metadata": {},
   "source": [
    "#### Miniübung\n",
    "\n",
    "* Sie wollen nun zwei Arten von 4-stöckigen Häusern zeichnen, nämlich mit oder ohne Antenne. Dies wollen Sie beim Aufruf der Methode angeben können. Ergänzen Sie die Methode um ein Argument `hasAntenna`. \n",
    "* Ergänzen Sie den Code so, dass, alls beim Aufruf gewünscht, eine Antenne gezeichnet wird (zum Beispiel durch einen weiteren Aufruf von drawRectangle)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1083f9b3",
   "metadata": {},
   "source": [
    "#### Wiederholungen durch Rekursion ausdrücken\n",
    "\n",
    "Bisher hatten unsere Methoden eine grosse Einschränkung. Wir konnten immer nur Häuser mit einer fixen Anzahl Stockwerke zeichnen. Dank Rekursion können wir nun auch Methoden schreiben, bei denen man die Anzahl Stockwerke als Parameter angeben kann. \n",
    "\n",
    "Die Strategie ist wie folgt:\n",
    "- mm ein $n$-stöckiges Gebäude zu zeichnen können wir ein Rechteck zeichnen mit einem $n-1$ stöckiges Gebäude oben drauf.\n",
    "- um ein $0$-stöckges Gebäude zu zeichnen müssen wir nichts machen. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7a99f26c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "BufferedImage@2318056c: 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": [
    "class Building {\n",
    "    public static void drawRectangle(double xPos, double yPos, double width, double height) {\n",
    "        reset(); // set turtle to origin and make it face upwards\n",
    "        penUp();\n",
    "        goTo(xPos, yPos);\n",
    "        penDown();\n",
    "        \n",
    "        forward(height);\n",
    "        turnRight(90);\n",
    "        forward(width);\n",
    "        turnRight(90);\n",
    "        forward(height);\n",
    "        turnRight(90);\n",
    "        forward(width);    \n",
    "    }\n",
    "    \n",
    "    \n",
    "    public static void drawNStoreyBuilding(int n, double xPos, double yPos, double width, double heightOfStorey) {\n",
    "        if (n == 0) {\n",
    "            return; // es gibt nichts zu tun\n",
    "        } else {\n",
    "            drawRectangle(xPos, yPos, width, heightOfStorey);\n",
    "            drawNStoreyBuilding(n - 1, xPos, yPos + heightOfStorey, width, heightOfStorey);\n",
    "        }   \n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        clear();\n",
    "        drawNStoreyBuilding(5, 0, 0, 30, 10);\n",
    "        display(drawing());\n",
    "    }\n",
    "    \n",
    "}\n",
    "\n",
    "Building.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd5e33f1",
   "metadata": {},
   "source": [
    "#### Miniübungen\n",
    "\n",
    "* Können Sie mit dieser Strategie ein Programm schreiben, das ein $n$-Eck zeichnet?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c19fb828",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "BufferedImage@2318056c: 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": [
    "class Drawing {\n",
    "    \n",
    "    public static void drawNEck(int n, double length) {\n",
    "       drawSideAndTurn(n, length, 360 / n);\n",
    "    }\n",
    "    \n",
    "    public static void drawSideAndTurn(int n, double length, double angle) {\n",
    "        if (n == 0) {\n",
    "            // do nothing\n",
    "        } else {\n",
    "            forward(length);\n",
    "            turnLeft(angle);\n",
    "            drawSideAndTurn(n -1, length, angle);\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        home();\n",
    "        clear();\n",
    "        penDown();\n",
    "        drawNEck(20, 5);\n",
    "        display(drawing());\n",
    "    }\n",
    "}\n",
    "\n",
    "Drawing.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6043dc15",
   "metadata": {},
   "source": [
    "### Die Schönheit der Rekursion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da39f3cf",
   "metadata": {},
   "source": [
    "Zum Schluss noch etwas Schönes. Wir können mittels Rekursion Fraktale Frafiken zeichnen. Fraktale sind gemoetrische Figuren, die als Teil jeweils wieder dieselbe Figur enthalten. Ein Beispiel dafür ist das Sierpinski Dreick. Diese ist aus drei Dreiecken zusammengesetzt, die selbst wieder aus drei Dreicken bestehen, die selbst wieder aus drei Dreicken bestehen, ...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5b4e3e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Sierpinski {\n",
    "    public static void drawSierpinski(double length, int depth) {\n",
    "        if (depth==0){\n",
    "            for (int i = 0; i < 3; i++) {\n",
    "                forward(length);\n",
    "                turnLeft(120);\n",
    "            }\n",
    "        }\n",
    "        else {\n",
    "            drawSierpinski(length/2.0 , depth-1);\n",
    "            forward(length/2);\n",
    "            drawSierpinski(length/2.0,depth-1);\n",
    "            backward(length/2);\n",
    "            turnLeft(60);\n",
    "            forward(length/2);\n",
    "            turnRight(60);\n",
    "            drawSierpinski(length/2.0,depth-1);\n",
    "            turnLeft(60);\n",
    "            backward(length/2);\n",
    "            turnRight(60);\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        home();\n",
    "        clear();\n",
    "        penUp();\n",
    "        goTo(-30, -75);\n",
    "        turnRight(90);\n",
    "        penDown();\n",
    "        drawSierpinski(130, 1);\n",
    "        display(drawing());\n",
    "    }\n",
    "}\n",
    "\n",
    "Sierpinski.main(new String[0]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b98c806",
   "metadata": {},
   "source": [
    "#### Miniübung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1351c853",
   "metadata": {},
   "source": [
    "* Versuchen Sie den Aufgabe dieser Zeichnung zu verstehen, indem Sie das Dreieck mit unterschiedlichen Rekursionstiefen zeichnen. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Java",
   "language": "java",
   "name": "java"
  },
  "language_info": {
   "codemirror_mode": "java",
   "file_extension": ".jshell",
   "mimetype": "text/x-java-source",
   "name": "Java",
   "pygments_lexer": "java",
   "version": "18.0.1+10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}