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      "text/plain": [
       "[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 01.07.3 - 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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   "source": [
    "binom(n,k) = binom(n-1,k) + binom(n-1,k-1)"
   ]
  },
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   "source": [
    "## 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": [
    "bei k === 0 -> return 1 (linke Kante)\n",
    "bei k === n -> return 1 (rechte Kante)"
   ]
  },
  {
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   "source": [
    "## Teil 3\n",
    "Programmiere die Funtion `binom`:"
   ]
  },
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   "source": [
    "function binom(n, k) {\n",
    "    if (k === 0) return 1\n",
    "    if (k === n) return 1\n",
    "\n",
    "    return binom(n-1, k) + binom(n-1, k-1)\n",
    "}"
   ]
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  {
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     "text": [
      "01.07.3: function ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: Parameter ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: binom(0,0)=1 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: binom(2,1)=2 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: binom(5,3)=10 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: binom(9,4)=126 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "01.07.3: binom(20,7)=77520 ... \u001b[0m\u001b[32mok\u001b[0m \u001b[0m\u001b[38;5;245m(0ms)\u001b[0m\n",
      "\n",
      "\u001b[0m\u001b[32mok\u001b[0m | 7 passed | 0 failed \u001b[0m\u001b[38;5;245m(2ms)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "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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