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       "model_id": "e15757ea0cf743dc9af162093423cb6e",
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       "version_minor": 0
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      "text/plain": [
       "VBox(children=(HBox(children=(Dropdown(description='Regel:', options=('Kombination', 'Permutation', 'Fakultät'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display, Math, clear_output\n",
    "\n",
    "# Interaktives Lern-Tool für Kombinatorik-Regeln\n",
    "# Dies ist ein Jupyter-Notebook-Style Code für interaktive Widgets.\n",
    "# Bitte in einer Umgebung ausführen, die Widgets unterstützt (z.B. JupyterLab/Notebook).\n",
    "\n",
    "# Funktionen zur Berechnung\n",
    "def combination(n, k):\n",
    "    from math import comb\n",
    "    return comb(n, k)\n",
    "\n",
    "def permutation(n, k):\n",
    "    from math import perm\n",
    "    return perm(n, k)\n",
    "\n",
    "def factorial(n):\n",
    "    from math import factorial\n",
    "    return factorial(n)\n",
    "\n",
    "def binomial_coefficient(n, k):\n",
    "    from math import comb\n",
    "    return comb(n, k)\n",
    "\n",
    "def variation(n, k):\n",
    "    from math import perm\n",
    "    return perm(n, k)\n",
    "\n",
    "def multiset_combination(n, k):\n",
    "    from math import comb\n",
    "    return comb(n + k - 1, k)\n",
    "\n",
    "# Funktion, um den Entscheidungsbaum zu zeichnen (nur für Kombinationen und Permutationen)\n",
    "def draw_tree(n, k, is_perm):\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    ax = plt.gca()\n",
    "    ax.clear()\n",
    "    ax.set_title(\"Entscheidungsbaum\", fontsize=14)\n",
    "    ax.axis('off')\n",
    "\n",
    "    if k == 1:\n",
    "        x_start = 0.5\n",
    "        y_start = 0.9\n",
    "        plt.text(x_start, y_start, f\"Start\\n(n={n})\", ha='center', va='center')\n",
    "        for i in range(n):\n",
    "            x = 0.1 + i*(0.8/(n-1)) if n > 1 else 0.5\n",
    "            y = 0.6\n",
    "            plt.plot([x_start, x], [y_start-0.05, y], 'k-')\n",
    "            plt.text(x, y, f\"Wahl {i+1}\", ha='center', va='center')\n",
    "\n",
    "    elif k == 2:\n",
    "        x_start = 0.5\n",
    "        y_start = 0.9\n",
    "        plt.text(x_start, y_start, f\"Start\\n(n={n})\", ha='center', va='center')\n",
    "        child_coords = []\n",
    "        for i in range(n):\n",
    "            x = 0.1 + i*(0.8/(n-1)) if n > 1 else 0.5\n",
    "            y = 0.7\n",
    "            plt.plot([x_start, x], [y_start-0.05, y], 'k-')\n",
    "            plt.text(x, y, f\"W1={i+1}\", ha='center', va='center')\n",
    "            child_coords.append((x, y))\n",
    "        for (ix, iy) in child_coords:\n",
    "            branch_count = (n-1) if is_perm else (n)\n",
    "            for j in range(branch_count):\n",
    "                x2 = ix - 0.08 + j*(0.16/(branch_count-1)) if branch_count > 1 else ix\n",
    "                y2 = 0.45\n",
    "                plt.plot([ix, x2], [iy-0.05, y2], 'k-')\n",
    "                plt.text(x2, y2, f\"W2={j+1}\", ha='center', va='center', fontsize=8)\n",
    "    elif k == 3:\n",
    "        x_start = 0.5\n",
    "        y_start = 0.95\n",
    "        plt.text(x_start, y_start, f\"Start\\n(n={n})\", ha='center', va='center')\n",
    "        layer1 = []\n",
    "        for i in range(n):\n",
    "            x = 0.1 + i*(0.8/(n-1)) if n > 1 else 0.5\n",
    "            y = 0.8\n",
    "            plt.plot([x_start, x], [y_start-0.03, y], 'k-')\n",
    "            plt.text(x, y, f\"W1={i+1}\", ha='center', va='center', fontsize=9)\n",
    "            layer1.append((x, y))\n",
    "        layer2 = []\n",
    "        for (ix, iy) in layer1:\n",
    "            branch_count = (n-1) if is_perm else n\n",
    "            for j in range(branch_count):\n",
    "                x2 = ix - 0.05 + j*(0.1/(branch_count-1)) if branch_count > 1 else ix\n",
    "                y2 = 0.6\n",
    "                plt.plot([ix, x2], [iy-0.03, y2], 'k-')\n",
    "                plt.text(x2, y2, f\"W2={j+1}\", ha='center', va='center', fontsize=7)\n",
    "                layer2.append((x2, y2))\n",
    "        for (ix2, iy2) in layer2:\n",
    "            branch_count = (n-2) if is_perm else n\n",
    "            for j in range(branch_count):\n",
    "                x3 = ix2 - 0.02 + j*(0.04/(branch_count-1)) if branch_count > 1 else ix2\n",
    "                y3 = 0.4\n",
    "                plt.plot([ix2, x3], [iy2-0.03, y3], 'k-')\n",
    "                plt.text(x3, y3, f\"W3={j+1}\", ha='center', va='center', fontsize=6)\n",
    "    else:\n",
    "        plt.text(0.5, 0.5, \"Baumdiagramm für k>3 ist zu groß.\\nBitte k <= 3 für Baum\", ha='center', va='center', fontsize=12)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# Widgets erstellen\n",
    "dropdown_rule = widgets.Dropdown(\n",
    "    options=['Kombination', 'Permutation', 'Fakultät', 'Binomialkoeffizient', 'Variation', 'Mehrfachkombination'],\n",
    "    value='Kombination',\n",
    "    description='Regel:',\n",
    "    style={'description_width': 'initial'}\n",
    ")\n",
    "\n",
    "input_n = widgets.IntText(value=5, description='n:', style={'description_width': 'initial'})\n",
    "input_k = widgets.IntText(value=2, description='k:', style={'description_width': 'initial'})\n",
    "input_k.layout.visibility = 'visible'  # Standardmäßig sichtbar\n",
    "\n",
    "output_area = widgets.Output()\n",
    "\n",
    "# Button zum Berechnen\n",
    "button = widgets.Button(description='Berechnen & Visualisieren')\n",
    "\n",
    "# Callback-Funktion\n",
    "def on_button_click(b):\n",
    "    with output_area:\n",
    "        clear_output()\n",
    "        rule = dropdown_rule.value\n",
    "        n = input_n.value\n",
    "        k = input_k.value if rule in ['Kombination', 'Permutation', 'Binomialkoeffizient', 'Variation', 'Mehrfachkombination'] else None\n",
    "\n",
    "        try:\n",
    "            if rule == 'Kombination':\n",
    "                if k > n:\n",
    "                    print(\"k darf nicht größer als n sein.\")\n",
    "                    return\n",
    "                res = combination(n, k)\n",
    "                display(Math(r\"C(n,k) = \\binom{{{}}}{{{}}} = {}\".format(n, k, res)))\n",
    "                draw_tree(n, k, is_perm=False)\n",
    "            elif rule == 'Permutation':\n",
    "                if k > n:\n",
    "                    print(\"k darf nicht größer als n sein.\")\n",
    "                    return\n",
    "                res = permutation(n, k)\n",
    "                display(Math(r\"P(n,k) = {} = {}\".format(res, res)))\n",
    "                draw_tree(n, k, is_perm=True)\n",
    "            elif rule == 'Fakultät':\n",
    "                res = factorial(n)\n",
    "                display(Math(r\"n! = {} = {}\".format(res, res)))\n",
    "            elif rule == 'Binomialkoeffizient':\n",
    "                if k > n:\n",
    "                    print(\"k darf nicht größer als n sein.\")\n",
    "                    return\n",
    "                res = binomial_coefficient(n, k)\n",
    "                display(Math(r\"\\binom{{{}}}{{{}}} = {}\".format(n, k, res)))\n",
    "            elif rule == 'Variation':\n",
    "                if k > n:\n",
    "                    print(\"k darf nicht größer als n sein.\")\n",
    "                    return\n",
    "                res = variation(n, k)\n",
    "                display(Math(r\"V(n,k) = P(n,k) = {} = {}\".format(res, res)))\n",
    "            elif rule == 'Mehrfachkombination':\n",
    "                res = multiset_combination(n, k)\n",
    "                display(Math(r\"\\binom{{n+k-1}}{{k}} = {} = {}\".format(res, res)))\n",
    "            else:\n",
    "                print(\"Unbekannte Regel.\")\n",
    "        except Exception as e:\n",
    "            print(f\"Fehler: {e}\")\n",
    "\n",
    "# Event verknüpfen\n",
    "button.on_click(on_button_click)\n",
    "\n",
    "# Anpassung der sichtbaren Eingabefelder basierend auf der gewählten Regel\n",
    "def on_rule_change(change):\n",
    "    rule = change['new']\n",
    "    if rule in ['Kombination', 'Permutation', 'Binomialkoeffizient', 'Variation', 'Mehrfachkombination']:\n",
    "        input_k.layout.visibility = 'visible'\n",
    "    else:\n",
    "        input_k.layout.visibility = 'hidden'\n",
    "\n",
    "dropdown_rule.observe(on_rule_change, names='value')\n",
    "\n",
    "# Anzeige\n",
    "controls = widgets.VBox([\n",
    "    widgets.HBox([dropdown_rule]),\n",
    "    widgets.HBox([input_n, input_k]),\n",
    "    button,\n",
    "    output_area\n",
    "])\n",
    "display(controls)\n"
   ]
  }
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