inf-abi2027/01 Einführung/07 Rekursion/04 Pascal.ipynb

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    "import { assertEquals } from \"jsr:@std/assert\"\n",
    "import \"https://git.amgdhg.de/kg/tslib/raw/branch/main/logger.ts\""
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    "# Aufgabe 01.07.3 - Pascal'sches Dreieck\n",
    "\n",
    "Das Pascal'sche Dreieck sieht folgendermaßen aus:\n",
    "\n",
    "$$\\begin{matrix}1\\\\1\\quad1\\\\1\\quad2\\quad1\\\\1\\quad3\\quad3\\quad1\\\\1\\quad4\\quad6\\quad4\\quad1\\\\1\\quad5\\quad10\\quad10\\quad5\\quad1\\\\1\\quad6\\quad15\\quad20\\quad15\\quad6\\quad1\\\\\\vdots\\qquad\\qquad\\vdots\\qquad\\qquad\\vdots\\end{matrix}$$\n",
    "\n",
    "Die Zahlen darin sollen mit der Methode `binom(n,k)` berechnet werden, wobei $n$ die Zeile und $k$ die Spalte (innerhalb der Zeile) angibt.\n",
    "\n",
    "### Hinweis:\n",
    "Die Zeilen- und Spaltennummerierung beginnt bei 0!"
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   "source": [
    "## Teil 1\n",
    "Recherchiere im Internet, wie das Pascal'sche Dreieck bzw. dessen Inhalte **rekursiv** berechnet werden können."
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    "## Teil 2\n",
    "Notiere zunächst die rekursiven Funktionsaufrufe für das konkrete Zahlenbeispiel $n=3$ und $k=2$:"
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   "source": [
    "## Teil 3\n",
    "Wann bricht die Rekursion ab, d.h. wann wird nicht mehr erneut die Funktion `binom` aufgerufen?"
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   "source": [
    "## Teil 3\n",
    "Programmiere die Funtion `binom`:"
   ]
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    "let _nr = \"01.07.3\"\n",
    "Deno.test(`${_nr}: function`, () => {\n",
    "    assertEquals(typeof binom, 'function')\n",
    "})\n",
    "Deno.test(`${_nr}: Parameter`, () => {\n",
    "    assertEquals(binom.length, 2)\n",
    "})\n",
    "Deno.test(`${_nr}: binom(0,0)=1`, () => {\n",
    "    assertEquals(binom(0,0), 1)\n",
    "})\n",
    "Deno.test(`${_nr}: binom(2,1)=2`, () => {\n",
    "    assertEquals(binom(2,1), 2)\n",
    "})\n",
    "Deno.test(`${_nr}: binom(5,3)=10`, () => {\n",
    "    console.start()\n",
    "    assertEquals(binom(5,3), 10)\n",
    "    console.end()\n",
    "})\n",
    "Deno.test(`${_nr}: binom(9,4)=126`, () => {\n",
    "    console.start()\n",
    "    assertEquals(binom(9,4), 126)\n",
    "    console.end()\n",
    "})\n",
    "Deno.test(`${_nr}: binom(20,7)=77520`, () => {\n",
    "    console.start()\n",
    "    assertEquals(binom(20,7), 77520)\n",
    "    console.end()\n",
    "})"
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