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       "[Module: null prototype] {  }"
      ]
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   "source": [
    "import { assertEquals } from \"jsr:@std/assert\"\n",
    "import \"https://git.amgdhg.de/kg/tslib/raw/branch/main/logger.ts\""
   ]
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   "source": [
    "# Aufgabe 01.07.1 - Fakultät\n",
    "\n",
    "Eine wichtige mathematische Funktion ist die Fakultät:\n",
    "$$n! = 1\\cdot2\\cdot3\\cdots(n-2)\\cdot(n-1)\\cdot n$$\n",
    "zum Beispiel:\n",
    "$$5!=1\\cdot2\\cdot3\\cdot4\\cdot5=120$$\n",
    "\n",
    "Ziel soll sein, die Funktion `fakultaet` rekursiv zu programmieren. Dafür gibt es zunächst einige Vorüberlegungen:"
   ]
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   "source": [
    "## Teil 1\n",
    "Notiere zunächst die rekursiven Funktionsaufrufe für das konkrete Zahlenbeispiel $n=5$:"
   ]
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   "source": [
    "fakultaet(5) = fakultaet(4) * 5\n",
    "fakultaet(4) = fakultaet(3) * 5\n",
    "fakultaet(3) = fakultaet(2) * 5\n",
    "fakultaet(2) = fakultaet(1) * 5\n",
    "fakultaet(1) = 1\n",
    "\n",
    "allgemein: fakultaet(n) = fakultaet(n-1) * n"
   ]
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   "source": [
    "## Teil 2\n",
    "Wann bricht die Rekursion ab, d.h. wann wird nicht mehr erneut die Funktion `fakultaet` aufgerufen?"
   ]
  },
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   "source": [
    "bei n === 1"
   ]
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   "source": [
    "## Teil 3\n",
    "Programmiere die Funktion `fakultaet`:"
   ]
  },
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   "outputs": [],
   "source": [
    "function fakultaet(n) {\n",
    "    if (n === 1) return 1\n",
    "    return fakultaet(n-1) * n\n",
    "}"
   ]
  },
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     "text": [
      "01.07.1: function ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.1: Parameter ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.1: fakultaet(1)=1 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.1: fakultaet(3)=6 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.1: fakultaet(5)=120 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.1: fakultaet(11)=39916800 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "\n",
      "\u001b[0m\u001b[32mok\u001b[0m | 6 passed | 0 failed \u001b[0m\u001b[38;5;245m(1ms)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "let _nr = \"01.07.1\"\n",
    "Deno.test(`${_nr}: function`, () => {\n",
    "    assertEquals(typeof fakultaet, 'function')\n",
    "})\n",
    "Deno.test(`${_nr}: Parameter`, () => {\n",
    "    assertEquals(fakultaet.length, 1)\n",
    "})\n",
    "Deno.test(`${_nr}: fakultaet(1)=1`, () => {\n",
    "    assertEquals(fakultaet(1), 1)\n",
    "})\n",
    "Deno.test(`${_nr}: fakultaet(3)=6`, () => {\n",
    "    assertEquals(fakultaet(3), 6)\n",
    "})\n",
    "Deno.test(`${_nr}: fakultaet(5)=120`, () => {\n",
    "    assertEquals(fakultaet(5), 120)\n",
    "})\n",
    "Deno.test(`${_nr}: fakultaet(11)=39916800`, () => {\n",
    "    assertEquals(fakultaet(11), 39916800)\n",
    "})"
   ]
  }
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