inf-abi2027/01 Einführung/07 Rekursion/03M Fibonacci.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 01.07.2 - Fibonacci\n",
    "\n",
    "Die Fibonacci Folge $F$\n",
    "$$0,1,1,2,3,5,8,13,21,34,55,\\dots$$\n",
    "ist folgendermaßen definiert:\n",
    "* $F(0)=0$\n",
    "* $F(1)=1$\n",
    "* $F(2)=F(0)+F(1)$\n",
    "* $F(3)=F(1)+F(2)$\n",
    "* bzw. allgemein: $F(n)=F(n-2)+F(n-1)$\n",
    "\n",
    "Diese soll nun mit einer Funktion `fibo` programmiert werden, die einen Parameter $n$ übergeben bekommt und dann die $n$-te Fibonacci-Zahl berechnet.\n",
    "\n",
    "### Hinweis:\n",
    "$0$ ist die \"nullte\" Zahl, 1 die erste."
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   "source": [
    "## Teil 1\n",
    "Notiere zunächst die rekursiven Funktionsaufrufe für das konkrete Zahlenbeispiel $n=5$:"
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    "fibo(5) = fibo(4) + fibo(3)\n",
    "fibo(4) = fibo(3) + fibo(2)\n",
    "fibo(3) = fibo(2) + fibo(1)\n",
    "fibo(2) = fibo(1) + fibo(0)\n",
    "fibo(1) = 1\n",
    "fibo(0) = 0\n",
    "\n",
    "allgemein: fibo(n) = fibo(n-1) + fibo(n-2)"
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   "source": [
    "## Teil 2\n",
    "Wann bricht die Rekursion ab, d.h. wann wird nicht mehr erneut die Funktion `fibo` aufgerufen?"
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    "bei n === 1 -> return 1\n",
    "bei n === 0 -> return 0"
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   "source": [
    "## Teil 3\n",
    "Programmiere die Funtion `fibo`:"
   ]
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    "function fibo(n) {\n",
    "    if (n === 1) return 1\n",
    "    if (n === 0) return 0\n",
    "\n",
    "    return fibo(n-1) + fibo(n-2)\n",
    "}"
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      "01.07.2: function ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: Parameter ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: fibo(1)=1 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: fibo(3)=2 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: fibo(5)=5 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: fibo(11)=89 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.2: fibo(23)=28657 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(2ms)\u001b[0m\n",
      "\n",
      "\u001b[0m\u001b[32mok\u001b[0m | 7 passed | 0 failed \u001b[0m\u001b[38;5;245m(3ms)\u001b[0m\n"
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    "let _nr = \"01.07.2\"\n",
    "Deno.test(`${_nr}: function`, () => {\n",
    "    assertEquals(typeof fibo, 'function')\n",
    "})\n",
    "Deno.test(`${_nr}: Parameter`, () => {\n",
    "    assertEquals(fibo.length, 1)\n",
    "})\n",
    "Deno.test(`${_nr}: fibo(1)=1`, () => {\n",
    "    assertEquals(fibo(1), 1)\n",
    "})\n",
    "Deno.test(`${_nr}: fibo(3)=2`, () => {\n",
    "    assertEquals(fibo(3), 2)\n",
    "})\n",
    "Deno.test(`${_nr}: fibo(5)=5`, () => {\n",
    "    assertEquals(fibo(5), 5)\n",
    "})\n",
    "Deno.test(`${_nr}: fibo(11)=89`, () => {\n",
    "    assertEquals(fibo(11), 89)\n",
    "})\n",
    "Deno.test(`${_nr}: fibo(23)=28657`, () => {\n",
    "    assertEquals(fibo(23), 28657)\n",
    "})"
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