{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6d41d2c2-cd8c-438a-9c0f-39b84dd6860a",
   "metadata": {},
   "source": [
    "# Spannbäume"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8db1dad-f52e-4f63-925c-92a0e50b0d6d",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c97cda6-4ca8-4d4f-97bc-69c23768a2c3",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<b>Ziel des Notebooks:</b>\n",
    "\n",
    "- Grundlegende Konzepte der Graphentheorie verstehen\n",
    "    - Zusammenhang\n",
    "    - Bäume, Spannbäume\n",
    "    - gewichtete Graphen\n",
    "- Algorithmen zur Berechnung eines minimalen Spannbaums verstehen und anwenden können\n",
    "\n",
    "<br>\n",
    "    \n",
    "<b>Mathematische Tools:<b>\n",
    "- Graphentheorie\n",
    "    - Teilgraphen\n",
    "    - Zusammenhang\n",
    "    - Bäume, Spannbäume\n",
    "    - gewichtete Graphen\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5070b725-2202-4c69-afcd-7f99bcfba8cb",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bb992b2-8492-4401-8771-b969b5f768c9",
   "metadata": {},
   "source": [
    "Eine Inselgruppe soll erstmals mit einem Fähren-Streckennetz ausgestattet werden.\n",
    "<br>\n",
    "Jede Insel besitzt genau einen Hafen, an dem die Fähren an- und ablegen können. Eine Fähre schippert dabei immer zwischen genau zwei Inseln bzw. Häfen hin- und her. <br> \n",
    "Das Ziel ist es, ein Liniennetz zu erstellen, mit dem man von einer beliebigen Insel zu jeder anderen Insel kommen kann, wobei Umstiege an den Häfen erlaubt sind. Es dürfen aber nur feste, offiziell vorgegebene und bereits bekannte Wasserstraßen genutzt werden.<brr> \n",
    "Um den Aufwand und die Kosten gering zu halten, möchte man möglichst wenige Wasserfahrzeuge einsetzen.\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "204ed6ff-0872-4cc8-b245-b3d79f9a23b5.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "718f5424-6254-454f-8f7b-889788508570",
   "metadata": {},
   "source": [
    "![image.png](attachment:204ed6ff-0872-4cc8-b245-b3d79f9a23b5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ea8c8d-13f0-4630-ad25-d88dd5009c81",
   "metadata": {},
   "source": [
    "Man kann direkt sehen, dass die zugrundeliegende Struktur gut durch einen Graphen $G=(V,E)$ darstellbar ist. Jede Insel entspricht jeweils einem Knoten $v\\in V$ und eine Wasserstraße zwischen Insel $v_1\\in V$ und $v_2\\in V$ wird durch eine Kante $(v_1 v_2)\\in E$ repräsentiert. \n",
    "<br>\n",
    "Um die Notation zu erleichtern, werden wir im Folgenden die Anzahl der Inseln mit $n:=|V|$ bezeichnen.\n",
    "\n",
    "Ein Streckennetz, das alle Inseln (indirekt, also auch mit Umstiegen) miteinander verbindet, entspricht in unserer Konstruktion einem Teilgraphen $S=(V_S,E_S)\\subseteq G$, der alle Knoten von $G$ enthält. Er muss alle Knoten von enthalten, d.h. $V_S=V$, da wir jede Insel anfahren wollen. Es müssen aber nicht notwendigerweise alle Kanten enthalten sein, also $E_S\\subseteq E$. <br>\n",
    "Da wir für jedes beliebige Paar von Inseln eine Verbindung anbieten wollen, muss unser Streckennetz $S$ <b>zusammenhängend</b> sein.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G=(V,E)$ ein Graph. <br>\n",
    " $G$ heißt <b>zusammenhängend</b> genau dann, wenn für alle Knoten $v,w\\in V$ ein Weg von $v$ nach $w$ existiert. Einen solchen Weg nennen wir im Folgenden $(vw)$-Weg.\n",
    "</div>\n",
    "\n",
    "Da wir möglichst wenige Fähren benutzen wollen, muss unser Streckennetz $S$ noch eine weitere Eigenschaft erfüllen: Es soll von allen möglichen Streckennetzen dasjenige mit der kleinsten Kantenkardinalität sein. Mathematisch ausgedrückt:  <br>\n",
    "Für beliebige Streckennetze $S'$, d.h. zusammenhängende Teilgraphen $S'=(V_{S'},E_{S'})\\subseteq G$ soll gelten $|E_{S}| \\leq |E_{S'}|$.\n",
    "\n",
    "\n",
    "\n",
    "<br>\n",
    "Können wir das Minimum an benötigten Fähren direkt bestimmen? Ja, das können wir, es gilt nämlich $$min_{K=(V_K, E_K)\\subseteq G}\\{|E_K| \\mid K \\text{ ist ein zusammenhängender Graph mit } V_K=V \\} = |V|-1 = n-1$$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c915b325-c453-45fc-8350-44318d200e8b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Sei $G=(V,E)$ ein zusammenhängender Graph. Zeigen Sie, dass $$\\min_{K=(V_K, E_K)\\subseteq G}\\{|E_K| \\mid K \\text{ ist ein zusammenhängender Graph mit } V_K=V \\} = n-1$$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5483aa9c-8b4f-442e-8213-acdd238d1d9d",
   "metadata": {},
   "source": [
    "Insgesamt suchen wir also einen zusammenhängenden Teilgraphen $S=(V_S,E_S)$ von $G$ mit $|E_S|=n-1$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99178aea-4cf5-4736-be24-fefdb78bac63",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7481b82e-c60f-4bfa-9421-49bcacf42f50",
   "metadata": {},
   "source": [
    "Eine sehr wichtige Spezialform von Graphen sind sogenannte <b>Bäume</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6195eb7-2a07-4bc4-90b9-2fdf23f51539",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G=(V,E)$ ein Graph. <br>\n",
    "Man nennt $G$ einen <b>Baum</b> genau dann, wenn $G$ kreisfrei und zusammenhängend ist.\n",
    "</div>"
   ]
  },
  {
   "attachments": {
    "fb4f4940-a9a5-45a1-ae34-6daf097adffc.png": {
     "image/png": 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Rihttu0biYxHZeypjTzraL9ueyibU99/X3+9+0tc3dibwjh3u/VFRe9NNN425kOii2bPdudHNN8EWOjoo6MBoJ9rrvhIGHez0Ne8dVX9PluZ7ZmW/r9rP1WO8wkUNVkWOto3O09G2UePNnq9jB9YQC5w0RvhQBNoPFY6tza9atcrt3r3bbb7ha17vl73ukeTeWEvdovF7B1OFjsVvUZyKp6+99/SjCh2LWZaQhBa3tB10RfOyrbaH9ip7kSMhb4M/Hjjgfpe5vk5lClt0DJqWmqp32UknufnHHZc88kOwhU61nVJD/xp21VKIKn50UEwXG0p2TT1FyFToAJyW/r/TWtELmd02lkTYdikbfa7aBnldhBDISrdJW9lHjzffvdkt6zhv/IKgyaoVJlsfbE6njMWz7PcO3f20m9aRaXtJoVPZNh/7H67zb/9qdIRL2+V9Y4sYfZ+KgFbEzKLQdtP0oXvvvbc0y/kiX9rH0m2oWi5VRorLuqnjN8Tt8OALL8QLD6RVu5DoCTNmuCWnnOLVSmbBFjoqarJX+88m9NmDrXbiPAuOdsluGwUyG+Epa6JfSSw52RdtUKtNKrnQ6MVWt71qsVFLPUXHRLKdMWbpxTVi5EQjNI1KCp3Ktnn0oOvd8Uu34opyXkPI2HkSxCo0k2KO8iOLHWpjFo/KXuRYB4PanbaFYnNo22Mgem86X+fPUX5ckUxh+8699465kOg5s2a586us2lZUQRc66RM3xyQOJR/2t22jbaDiTkuXln27KJAxqoN20L6n+JQ9T0ztdPHixW7LjV93Wzu2J89OrOkFR7tEhc76//XPR3qT/88z8ZLS068403Wt6SptvLIRPxYmQLOkj38bNmyIcyW1u5UrV7qNGzcW4pio/X68dFXT8LOvW9GWpt+jkV9rN+rEHi+WWO6o9qZto9+p+yGOqD7X3+9+ljlfp9oqbHLJvHnuzFe9KnlUbEFPXdOHc+GFF7qHHnoofk47tHosyn5gsG2jj17bRA227D02ki2OgTxkCx17rFilA3BlOeWy0Hk5ui189ZFt84W73dZHH3Drb01tlxJ3zDCqg2ZSG1M+YHmA5QgqCLSPWaGTLRJMtYLCVCtA0sYrYOz3jjejZqLXakn/XePlPyoA9Xv0PXZOszqg0tslJDsPHHC/z5yvU20VtmOjr0tPPtm9Ksqbii7YQkfSIxfaUa0nzOtrUaBltG+oOZA8IG/a95TAW5yaO3euu/zyy93tH/jnMPfFZJGBmO5XW7I6YUmX2qa2T/eN3W7Zwre7jqgQKivtIxqJZ7VININypexUf10zRtP8Ncpz//33x/ubipxqhUutaa5SrTDKUrsu6n6c3TZlWGL7p3198ehORY1V2M6YOdNdcuKJhe+GK9ViBKIeAoodVMO+gXZRvHrsscfildZsv1MyK5XllH1jRUu6kJEqxcy4th+IDrTRLa3Bi4WGiBFoNIMd99LTtq1zQSfe62tZ969sh4J1livhD3m7vHj4sLvv+efrmsKmc3VeN2tW8qiYgix0qjXcNHtdRVCZpz/gaCQPaIdqPaq69k3lHJXxih0VDhrdqHWBT5MuNkyjRYeMd02eyfy+ifxkn+vt+/WRc4/0f2ihgpLTMUz7BiPQmCrFn6uuuipezl6U0J911llu586d8WtlZu1MtF2y0/lC9chLL7kdB8Z2MFWbwibLTznFzZ4xI3lUPEEWOrVGc7Ks14KCB4bkAXmrGa9UUERJ/voHv+xGkr61mgXPuVGhE+JUrmQbaAGCge8/OboEdajvtUETdegBjVBBo3NPFIM0bfal5DyNifKoMlCMtm1T5Gl2zdb77LPupSi+VNgqbLt2jbm2zmkzZ7q3F3gKW3CFTr1FTpoOFtp5adAgeUCeFK90bk7NwjpK8uORnXqKnRBHOrYfcOu/ecvoNrILpzJtrYIRaDRDrbxpMvkUwvHMK6+4n+/bN2YKW61RnQvnznVnHX988qhYgsvkNJ+y0Qs6WZJhjRrlZQmDhqjZF9BqilfqZKkpGblQcdN98ejqaxrd2DLyhzEHn1gy+hEMvR+dmxO9UbXLuLjRaA75VoX2HR23gMmyzpZqxYw9R25UTqfOnHlU8XJ9lF/HC1Ls2JE8M+p3+/e7Q+lr8BRIUIWOGuNkex5o0DAkD8iDxatxp81qlOZ9p40m+BEVPGu717rOKztdb+jFTnLOUbza00VLontUOFnaf+iUwVTFHQk1WG6k0UPFKva1cnnj7NljI++558b7wb9t2BCP7JjBaL/QeT1F3DuCmbqmpEHn20x1yhHT2GDT11h9Da2kxOGoBQjGo9XHZMcB1+secSuuiPbR70f7aMd5R5cAIZzH8oO9bv0DX3Zbepm2Nh6mr2GyrGO33nxH36/jo/Y3pnaXx/aXX45vae9fsMAtfsc73A3/8R9jprAV8UKiwRQ6zQz2FDvQPqCmwaIEaIVGE4wxkuWWgy52kve44tYPjcZinZd07mwWIaiCWIXJarizJWKdysq3dLFx9rnwDUfxpefZZ8dOTbOFCe69d8xy07qAaOeppxZqulgQhc6UkoYaKHbKjVEdtEpT4lXoxc4P9rrekdH3Nvj9p0ZXW2M0pypiFSZjKnHIridzb5TkUuyUw+4//9n9ev/+uhYmOG/27HjKW1EEUehMpleiHhQ75abPX82DnlI0U9Pilc7HiQoeXWMmqGInKeJspTlGcyZGrEIjbFRmKlP9KXbKp+eZZ9yfMwsOVJvCNiPaF9556qnu2Cbn5JNVjL9iCtRgW1WI6KChxmw9HygX7Vf6/NVjyuePZmhqvEqWk1527tvipKXmAgVR0RAXD57RIgSVdpcsxoDqiFVohOKQpp5NJQ6pE1g50rve9S72u5I4Z9asozrSvhftR/fdd5978CtfqewDWpjgsczFRtvJ+xGdVo3mpDGyU170lKKZWhavokJG15upXAD5ktGlqMfwZWQnWYRg7bq1o9PWFp7AaE4diFWoh3XcNiufUYGtER2mTpbDlmefdS+nLyIaeeirX42PPbq0y8Uf+UhlH9CozvHRMa/dpkd/3NrkvnfUYFWAtLpxrVq1Kl43XD2Muk9DLo+zzjrL3XPPPW7v3r3xvsZnj8lqabyaf6xbetolruPk4+I4paJm6RnR43Sxo6luur22WCvijKGRp+hv3LrnAbd0WbStznib61g420VHy+QbUItile1jZ599NrEKVXV2dsbTzZrV2WL72jXXXMO+VwKajrb3lVeSR6NOu/hit/dXv3J33nGH++Bf/7XrmD8/ecW5k2fOPGoUKG9ej+jkMZqTpoPIuFcxR3C0j73lLW9xDz30UPxYnz29VpiMXOKVztnZ8cv4nJ2aIzty2YmjU9+KJjk/RxdF7VrT5br/7p9cx6LinNRadJdccom74IIL3DnnnMMMBByl2aM5afrd6jdnZCd8P+/rc3v7+5NHR2hkR/vXW//hHyqf/7JTTnEnzJgR328Xb0d0Wto7WoP+vyeeeIKRnZLQPqa5x08//XQ8NH/nnXe6Xbt2udWrV/PZoyG5xav5x7qz+05wS6/4S3fNP15TfWRHnjw0+jX6/sJIihwtQtC7tdf13PC/3bRFJzCaUyftY9/4xjfcnDlz3B133BE/p32OWAXRFDONujRzNCfN9jX9H+nHCM/xUeHy5MGDyaMjNLJz+iXR8Sb1uWtp6lPbPKrjbaGj+cjtuGiVGq8SXh1IKHbCpgODeidU2KiHVI+Fzx2NyjVevfZV9RU7msYmRSl2kql1lWlr5182Om0NddE+pp76jRs3xvuZOuR0vGIqEUR5i/aHVna2WHETT59NPUZYdK2cweFh98LAQPJMyo4dzp10UvLAuf3R95x1/PHumJxz9bT2/c9ToJ6rdg7L29Q1O/kTYVqyZElc3Chp0OetaYsK3EAj2hKvFr7aLXOL3Oa7N8f//7oHvhQv1XyUoqzIlozmiJKkOK4WcWpdwVl8UuwS65xBuWk/ULu66aabWh6HFOuUIynuqB+dHClMb5g92x2T2Zd0XZ0ro7z4ijPPdA98KTrmJJ/9c1WmueXJy3N08j43pxYVOnbODnNSw6Spa4beKUxG2+KVRkh+sq9yUVElIDXP2Wn3imw/2OtUh2naWmW1tfedwQVCG2DHI6N4pcfELKjoUKqXZ4eLjp1a+EDFlQoe9sPwaAnp3730UtyFZiuvfXfTJvfr+++v3J+2aFHbLyDqXaHTjgY7Huu1iJOI7m4a8zjss5OifH5AK7U9XjVS7CTX5cldajRHhc6W3i1u87/fwyIEk0DHDKqZMWOG6+/vjztd8qSRJBXgFDvh+sW+fW7PK6/EozlLFi92F113Xfw56/HI8LC7/q673JvmzGlroePdOTo2FF+UIG5/B3NSa9PB93Wve50bjnb63bt3u9tvvz3eTswdR+jaHq90Iv/CV485Z6f3T790qy79wNF/z6Gh0YJD5+zkuQDAz/Yld5xb8V8vdytXrRw9P2f+ccmz+VPM0knVWnzEp5iumGo3YitEnS2aytiOWSe2H1qHDzNfwnPSsce6P0WFzv3f+U4cL4/r63PfvPXWOIauXLnSnf62t7mTjzvOnRTd2sW7EZ2iTFvL0oeqxqypAhrZYXTnCPXoKFmwXu3sYyBUhYpXycjJils/dCROtXv56cxoThGmrVkcV1KmDiwliUwBg6/aNZqTxshO2J6NCp3/t2+f+9VXvxrnwiorrld+t3Bh/Hq7p655NaKjA5AS5CL2CqjnQqtxKaFhdGcsXchOK77oq0Z0tH2K+jkCzVK4eJWsrrbq3Pe5aQtPcOvW17iwqBwcyufCoqnRHK22pgUTVq9aHV/4tF2UkO3cuTNeUl7F4LXXXhsXO4ySwDeKQe0azUljZKdxKg41QqK8qejbalZUTKsrb8b557u/+Ju/cZd+4ANjLxra5hEdrwodHYDasaR0I6y4UTKvylY7adkPkHr/KnA0FcSmrWkJVAIdQlbIeJUUO0uPvcB1//0/ufXfvMVd/T8/cXTBo2lsOr+nlcWORnP0fyQq09Y+8F/aGhuUYCheiS4joDh+2223Ffq4A1RTpKn+9jds27YtzgU0lZ2C52j6zLR9lEMqX/KlMFQhs//wYXdgKDp2ZLS70PEmcqsnwJepTvo71YiV6GjVEe2wns0QbAolCNoG6hldvHixG4oagLaDnie4IWSFjldaXS1ZdGDzDV9z69aui//eo5agThYyaInUlDXRtDX932s+eGPbt1n68gE2xY94Bd8oYdaxtqurqzD7r2Ki2pf612+++eb4axlzo/HYKJzyJeWO2k6KQz5sp4UnnOBePWNG8qg4vDlHp6jn5kxEO60asxp4mQ6Y9r7VYPW+6blBmXgRr1KFjJ0fo/a65cavH91Wm738dKbQmX7Fma5rTVdbY6SSQsUtJYbEK/hO+7LSu6J2uKgQs05g/Y20uVHqHFfHsMVCnWP12c9+1ptzm/r6+91P+/rccPJY2n2OjhdVgxpsYXtHJ6C/Wzuo3kMZRnZsFEc9ED09PfFXjegQwFAW3sQrLTbwvtPiImbNxR9xw3f/ya1YvsJNv/JMt2XkD+mxndGiRMVJM2SKHC19XfVipjlJjzyr0CPhgu8Ug5R35HGB0MnSVDaN7qjdKbnX3xt6flQPHTs0iqNOMn12GtnxKf/VFLW/Ov109/pZs9y8Y46Jp63NbONCGFL4c3R0ELr66qvjpNnXOdJq0Lpp3qXejxYtCPFAquCqz2rBggVxgXPOOeeQMKB0lDQX/VzCMZLzdjTCs/T0S1zHwtnxMtTu3Fljz9ux82ns+ydLv8d+V+TOB7/rerf2tiXGp2PW448/TqcMgqDREuUcPhTtdu6O2mL6cRnpc9NNsVCxSLmizmf2LfedFn1+p8yc6c6Kip3XHn+8mxMVPO1U+K2nE9dCmPKlgKPeC70f7cAh9VyoeFND1PuzURySBZSRN6M5WZqWpulpEY3urO1ORqGz5+00Y2Tn0bE/ryIn7xhvozj6f/V5EbMQCrXboo/mZFkb1N+uXEL3yzS6o+JG052VJ2oER3wpVH1Q+EJH0700nSAE2mm1SIEasg6yvjfk9JQPC1T0iKLMFK+KdPJvQ/IodvRzmbC3tXdrrrHQYpZisW5KColZCIkKeN9GAZTYqz0qhpZpESe9V8UjFab2/olHzVXYlqAk2q6mH9pQZnZVH98ac7rA0eej9xPCqBswFd6O5qQ1Uuykpp/VLTOaU1ltLYftZr3FFrMYxUFotI/7NpqTpVig9xDHnYCLHYtHGsHRTBg6XFqnkIWOdgAl0pozbY9D29l1oFWhoGpehYMP769agcMoDjAao3TNA7UR79Vb7DQ6qlNlNEfT1lrdkWUJheKVTa0lZiFUPo7mZIVc7GiamvIovT+N/hOPchDtQIUTNdKRqLGORMn0SLQDaA+vPA5N1IhHoh18JDoIF/b9RQ2x8jlESUmh/1Ygb9aG1T6CilWPvDwycs+e+Lblni3xe4zf2z1/qjw/8n/7km+uw38mP5O6Tes4EuubTXFLfzMxC2Vg+/vQ0FDyjP8stkaFj/ftV5+PvR9iUr4KW+ikG6sea8cIdacoarFDgQOMz9qu4lW64AmmraSKnXVrjxykh+9OFTv6nomkfo/d7Pc1OzFLx61QO8iALO3zy5YtC25/973Y6e3tJY9qs8KOb2rIUtNAop08HrbUifyhsmHaIk1j0/bX8GrUIJmiBowjSqbjdmHtOKg2omlsl50YX3NH09g2352sHHnL3x+JUzpfJ7nwaCMU27XNmrW90lNrtYCNYhfz3hE67feaqqZjtO4XJYdoFoururaMvvr03pRHKR6RR7VZtNMUTrpnVLey9Mqp6m93j4xte/U8REGFngdgHDZ6oHZi90PsVY1pmto940xjG29kJzNtTduq8jumuK1su+tYQY8pysam+ut4bXlTT09PcG0gKuDi9+rDyE46jyIetV8hC50ya1eilE4WylJYAs2Q7pgJ/sA2mWLn+f4jrye3Zk1bo8BBmVmHgbUji0U+FAOTYcWO2nuzp7w2g/4+xaSQPwMf+b00R4A0TKtVOaKAldsQbXolNd2Y7gHUT21W7UbtVdNG1JaCbT+axha9tWVuUfXV2KpdY+f5o5ehVnzTdpvsdtL/q+k62u5MCQHKISpw4vZ+3333FWo1NltJTTFo8eLF8ZLR+vuIR8VAoVMwOhdJDTlOIFrckKslCzRMAOO6NCp2Iumlp3tHHjmycnT2GjuPji18emfreycX11RIKqHo7u5mqWiUnvIF3eyq+moX6kAIubPSip0NGza0/ZyddIGjPGpwcJACp4AodAqo1cUOyQKASTvp2KOus9N5ZWdU7PzhSPmixQlU7GSvnRP9nBYzkEZGdCxmKU7ZQgPELGD0mnzKE9QedCzXcT30dqFiR++znQsUKD+zAsfyKHUco3imRzvJ2uQ+CuTss8+Og5UCmBq1PZ4qNc6rr77aLViwIL4g6znnnEOyAKAx86NiR4XMoSG39PRLXMfC2e6af7zGLf2797izO07W7Dbnnjw0dmRHoiJpxd/+ZVzkqEOnnthjRY5i1saNG93q1auJWUCKcgS1p2blCT7Qe9Z7VU6jzo+83nu6wLntttviQos8qtgoPwvMkgE1rKnS71Bvg3p/rPeBhglg0nS+TmpkJ45Vt0axapze1fXfuKXu3tf0KA4jzwCybJreO9/5zjg+tHJkx6ap6f/btGkT8cgjFDoFp8JEDUkNbDKN2JIFNUqSBQBNpevsaCpbZPMNX3Pbtm5z6x5MLU6QpqIoCTvjTVtjmhqAeuVR7Ngoji00oPhEPPJHR7RTtK4ERlPYgV8NupH5t1Yc2cgQDRNASyTn5PS6R9yKK1a4nu/3uGUd51ldE9MiBBPFMSUUSloajXUAyk0XXLfzZZp1rkx6BVzyKH8xouMBNS4d/JUE1LM4gU1TU2+oRoToDQXQUsnIjpadrjWFrXNFZxyTqhUw6ZFn9Zgq3hGzANTLChzlP1Ptv0+vpkYe5T9GdDyjZSQHBgaq9lgoWbBGTu8DgNwlIzsrbv1QXLRsvnvz6MhOVAT1Hv515QRiQ8wC0CxWoNx7772TKkxsBEdxqauriw6XQFDoeEoNUY1SlDyQLABoO62ypmInsv7BL8fn6mihgo5zZ4+O+iQsfukrMQtAsygXUoGia9o0MoXNfo4CJzwUOp5J94Dqvtxyyy3u+uuvp2ECaL9UsWM0wqMOGTplALSaztfRdDPdJooxNopDTAoXhY5HrMdBc1GtMWoqm3ogOHEXQGFsP+B6d/wyPldHU9jS6kk+AGAqlC/F02ejeFMt1lDglAeLEXhCozc2HGtzT/UcdSqAwln4atd55egqSEo09FVJB4kEgDyoeFEHsKRnwqjA0Xk8Nk1N8YmFBsLGiI4n1FDVONPzTvVYH1+tHgsAaIf09DSLTTYi3ejceQCYDOVN6ZEb0fRZFUCM4JQHRxsPWGN961vfGk9VswaqXlIlEgBQJIpZuhkrctKFDwC0imKOOoNtyXoVO4o9TFMrHwqdglKSoIapnk8Nq6qxXnHFFXGyoMcXXXQRvRIACsXi1oIFCyo9qYpXilU2lYR4BaCVFHuUK+l85uyUWb2GcqHQKRDrBVUvhBU3Sgw0cqPndd9uc+fOTX4KANorG7d2794d96Kqo2b//v3xaDSjOQDyoGJGU9TSHcFW4BCHyodCpwA0xKoEwW52Aq8VOjRKAEWTLm6ycct6UZVUaPn7efPmEccA5GLOnDmVEWWLU4pJmzZt4vzAEuITb4N0gqCDv5ID0VcbvbHXAKAoLHYpNllxo15TK26IWwDaQYWNYpMKGV1XcOXKlZVO5McffzwucohP5UShkwMlBzZXPZ0gqLfTEgSSBABFo9hVrbhJj9xo1JlzBQHkTcWNxSeLTXZezsaNG+PHWm3tiSeeiKeyEaPKieWlW0SNT70JanBiSxqqoTWjwWn1NfVQkGAAaKZqsUsxRh0zk4k39vuUgBCrAEyFTUlT6qr7S5YsmTA+KV86fPhw/BXlQ6HTRHZA1ybVfStuWlGMqMEODAww3xTAlChWSas6Zuz3ahSo2XEQQPiqFTfKqxSb6smvKHTKjSx5ipQkZKd1qGdBX/VaK6aj6fdSnwKYLMUQi12KUVqKVTEle55gKzppAGA86dik+KM4ZLmVTZu1S20QnzARCp1JsEaoBqbG1tXVFTe8VhY3ADAV6eRBt3Rxo/ilW6tilxIVAKhFIzXZTmPFjWxu1Wjni36OjuFyo9CpU7Xihp5PAEWWLm5s6kd6xLmVxY3R/wMAWVbcaAq+jdqw0AmajUKnBh2cLUmoVdy0q/Ft27ZtyvPmAYQpG7fsfBtLINoZuwCUlwobi0/p4kYLlbSy45hiqdwodFKsAVrvpxplq8+3AYCpyhY36Slp9IoCaBflUVqQxHIr6zRWfMojt1LHMFPXyi34QkeNaKKd3JIEFTfWAEkQABRZtrhJjzgzcgOgXRSDLD4pDimnUnwaGhqKn9dz5FbIS9CFjjU0DZFaL2eavZ4ucEgOALSLYlKjHTNFH3FWj66WgwUQLsWgdGyy+JQubsit0A7BFjo2VKqpZ2pcanRqaEoisokCBQ6AdrOYVatjRq/rNT1vV/8mbgFoF1tMQHFI+ZRiU3oJ6KLEJ0aPyi3oER1NPdNNPZ5qcGqUq1evpsABUCgqYpQkKF4pHilGqUNGz+k1xSndV+8oMQtAO1mnTPp8GytsilZUKI6i3Dqig2eQZ2npCrgDAwNxD6ioYapRDg4OVp7zld6LgoqCCwkP4L90vLIRZ033UuKgVdN8XmVR723Tpk30qgIFprij3EKxRmw2TJpe1/cpNun7fGjTiqX6W6u9H5RD0CM61ijVO6oihx0dQNEoTilxsNiUTh4UsygQALRSunPF8qX09FnNhlGHhUaUNW1WrzGyDF8EW+hoCogSCDVGjX7YNDYaJoAisSJHyYYlHJpuqwIHAFpNSzBbjqQiRvFI+ZNyJ4tHmg2jIogcCr4JdupayBR49LExdQ0Ig9q0kgrRNAslHKGM5DB1DSi2WlP91W59H7lRbGXqWrkFPXUtVEoYNJRMjQqEQZ0Was+6aVSHaSEA8qB4k84l9NgWbCIOIQQUOh7SVBcA8IU6ZgAUjzpOddOojooaFTeLFy9mqj+CQaHjMUZ1ABSdpo1Q6ADFpRFljeJo+qzdfF+dNi07aoVyodABAAAoMVvhkXPpEBoKHQAAAADBodDxkPW4MB0EQNEpXjHNFkA7EH9AoeMxzTsFAAAAcDQKHQBAy9gqkfSqAsgb8QcUOgAAAACCQ6EDAAAAIDgUOh5iTXgAvti2bVtyDwDyxeJNoNDxUGdnZ1zoqOHqIl8UPQCKateuXck9AADyRaHjmfXr18cX9hoeHo6LHD1mhAdAESk+3X777XF8WrFiBbEKQK6IOaDQ8Ux6SWlbTQQAikidMdYxs3z58rjwAQAgLxQ6HlKxo5vNOV26dGk8BxUAikaFDvEJQDvYVH91smzZsoXRnRLqiD50PnXPWIMVJRF2sh0AFMn06dNdV1dXHKM0dU3xqru7m3gFoOWUK1mKa9fR6enpcdOm0cdfJhQ6AICWUKKxdu3aOMFQgUORAyAv6mjZtGlT3NGi1R/V2XL48OH4eZQHZS0AoCXs/BwVOip4KHIA5EXT+m15exvRQfkwogMAAICg6FxmjeJYmqtpa1oUhQ6XcqHQAQAAQJBU8LBoU3lR6AAAAAAIDufoAAAAAAgOhQ4AAACA4FDoAAAAAAgOhQ4AAACA4FDoAAAAAAgOhQ4AAACA4FDoAAAAAAgOhQ4AAACA4FDoAAAAAAgOhQ4AAACA4FDoAAAAAAgOhU6OFixY4Pbs2ZM8qm379u3JPQAort7eXjcyMpI8mtj69evdtGnT3JYtWxr6OQAAJoNCJyeDg4Pu6aefdocOHUqeqU5FzvLly93w8HDyDAAUj4qWdevWJY/qY4VRoz8HoDymT5/u1q5dO6lOlO7ubjpRMEZHtEOwR+Tg+eefd6eeeqr7zW9+4970pjclzx7thRdecPPnz3ePPfaYO+uss5JnAaBYlIyoQ2ZoaChOMOqxYsWKeDRHGvk5AOVhsWXz5s1u2bJlrqOjI3mlts7OzspIcU9PT9xhXM/PIXwcZXKyf//++Osrr7wSf61l3rx5btasWW7nzp30SgAAgFJZunRpcq9+a9asqRQ2W7dujb8CQqGTkxdffDH+OtHUNTnvvPPc73//++QRABRLo+fmVKNkhM4cAFlWqDRSsKg4otBBNRQ6OVGho4O6RnQmOrhr0QJNcQMAAAAwORQ6OdG5N1LPiI6Koh07dtDbCQAASkkjx8BUUejkZN++ffHXegud3/72t8kjACiWbdu2JfeYggYAKC4KnZxo1TU5ePCg27t3r/vZz37mvv71r7svfOEL7jOf+Yz7xCc+4a655hr3wQ9+0D3yyCOur6+vsoABAABA6CZ7/h8dLqiFQicnmoomH//4x90ZZ5zhLr30UvehD33IfexjH3P/8i//4j7/+c+7jRs3um9961vuwIED8ffqujsA4AslKbrpOjla3jV903MkIgDqpaWlgami0MnJt7/97fggb0VMPWylNgAoqoceeii+hoVWPLKiRhf7s6LHbnqOmAagURqtUQzRRUF1LS7FGF2DSzHHbp/85CfpSEFVFDo5ecMb3pDcq+7CCy90N9xwg7vrrrsqSyRquhsNF0DR7Nq1K7nn3I033li5COh4tPzr3Llzk0csAQvgaOnz/z73uc/FBY1GdlTcdHd3x7FGRU82N3r44YcrzzGNDWkUOjl54xvfGBcwn/rUp+Jr5OimBQe0jPSzzz4b94recsst7v3vf3+l0HnmmWfirwDgCxU0Skx00yiOEhO7WWwDgGrSRUw9I8AWb1QEEV9QDYVOTvr7++Ov8+bNc4sWLYovCvrmN7/ZnX/++e7kk0+OX5OBgYHknnN79uxJ7gFAcaxcuTK5N5poDA8Px8mJbkpUrLBR8mFFD0kIgEZoBFgxRB0mmzdvHtNpYjHH4o2+R6M/hlEdGAqdnOhCoTI4OBh/rSX9+lNPPZXcm5j9fgAAAB+tWbOm0imiKf0qdHTT1DXrNKHjBI2g0MmJRnTUuzBRoXP48OHk3th58OO57bbb3PHHH++uvfZaejAAtFw60bAThVsVe/S7WbENwEQ0upyOS4BQ6OTERlzSU9OqSRdCf/zjHyc8uN93333uuuuui79PBc/vfve75BUAaB0lFVOhAmY8el1TUWwVN93XdBUA5TCV6WcTxReUB4VOTg4dOhR/nWhEJ10IaURnvMJIFxb98Ic/PObg/9xzzyX3ACAfGnGpR71TTmwZ2WySw7x7ALVMtfMFYaLQyUm9hc7MmTOTe6OefPLJ5N5YGu258sorj3pd1+khEQDQaum59PUWIEuWLEnu1f4Z9cRqBEffq68qjgCUQ7YzpJHOjezUtXp+Tt+nmKMbuVOYKHRyYufeTDT14swzz4xXZTNPPPHEUY3vD3/4g3vPe97jtm/fHj/esGFDpXEPDQ3FXwEgT40kJKbazyjRsRWWFNf0PSadyAAIU3pkJt3+J5KND7Vikp7XiHH6Gj02RZZiJzwUOjmZPn16/HXGjBnx1/G8613vqjTWnTt3xl/THnzwQffoo4/G97/4xS+6Cy64IL4vGtEBgFZTgpAebaln+lq13tpq7PvSixBwnQygfFox0tLZ2Rl3pGR/r6bMch5geCh0cmIH7h/+8IcTNtq3v/3tyT3nHn/88eTeETov54477nAPPPCA++hHP+pe85rXVBIAjfYAQB6y09fUK6rH4yUL6d7a8U4YziY4KnpYfQ0I32SmxZrs9LVq9PsVq7KdJ3o+fS0ehIFPNCcqTkQLCNQ678a8+93vdpdddll8/9JLL42/Zl111VXu4osvju+//vWvj7/K/fffTyIAIBfZUZ1aiUVavUmMfm/2HB0KHaB8Gi12TK2OFMUgTY/VqrVp6diEcFDo5ERDpXfffbf70Y9+5BYsWJA8W938+fPjguWll15yl19++YQNb86cOe7Tn/50/H3nnnsuDRVAbpQwqHfUTDTFzEa3ZaLv1YIE6e9h+hoQvmwHiqaU1VvopEeMx5OevqafURxjNCdMHdGHTPdYIPbs2eNOP/305BEA5Md6T7MnBNei7x/ve5XcpE8O1vfaAgUAwqb4kF5ivqenpzI1djwa/dHP2fRZFTDpzhXJxhajER09T4wJC+VrQChyALSL9cLWmyRM9L3ppahV5Gg0B0A5KD6ki456O1D0ffrZ8dT6XSqAqi1SAL9R6AAACkfJinpllXjoVk9vLoBwaIRFMUCjO41MK0sXMtXOG9TruhSHChq72cq4CA9T1wAAABAMjc5oVLiekaD0+Tq6qDtFT1godAAAAFAaKoQ0UqSbpcGcoxMmpq4BAACgNDSljSKnHBjRAQAAQGmo0LFip6urq6GFVOAXCh0AAAAAwWHqGgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACA6FDgAAAIDgUOgAAAAACIxz/x/qy3pWfjo8BgAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "9a0d92c5-0652-4833-a6a2-e3c547013afd",
   "metadata": {},
   "source": [
    "![image.png](attachment:fb4f4940-a9a5-45a1-ae34-6daf097adffc.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dc6b15c-73a2-43bd-b451-a3d9ac9adf3e",
   "metadata": {},
   "source": [
    "Welche der drei Graphen sind (keine) Bäume und warum (nicht)?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e1eb2db-f6bf-402f-a0ba-604eaa777290",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G=(V,E)$ ein Graph. Dann sind folgende Aussagen äquivalent:\n",
    " \n",
    "1. $G$ ist ein Baum.\n",
    "2. $G$ besitzt $|V|-1$ Kanten und ist zusammenhängend.\n",
    "3. $G$ besitzt $|V|-1$ Kanten und ist kreisfrei.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6fbb020-7b99-4162-8c1b-eb97ec207ab6",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Beweisen Sie die Äquivalenz der obigen drei Aussagen (z.B. durch einen Ringschluss).\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e0d7491-6ff0-48e7-9952-b2f463786020",
   "metadata": {},
   "source": [
    "Wir können unsere Aufgabenstellung also äquivalent umformulieren: Wir suchen nach einem Teilgraphen $S=(V_S,E_S)\\subseteq G$ mit $V_S=V$, der ein Baum ist. Das ist gerade die Definition eines <b>Spannbaums</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4275e3f-2144-46c2-83c2-1c5a0f15e6df",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G=(V,E)$ ein Graph. <br>\n",
    "Ein Baum $T=(V,E_T) \\subseteq G$, der alle Knoten von $G$ enthält und Teilgraph von $G$ ist, heißt <b>Spannbaum</b> von $G$.\n",
    "</div>  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d74f26-a810-4aba-8a0f-fecf8f678b48",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Wieviele mögliche Spannbäume gibt es konkret in unserem Beispiel? Wie sieht es bei allgemeinen Graphen aus?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b799342c-4269-4099-910a-b609a6d4f370",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41341255-407c-4d7f-9f71-b8ea6dfe82d7",
   "metadata": {},
   "source": [
    "Einen Algorithmus zur Berechnung eines Spannbaums kann man leicht angeben."
   ]
  },
  {
   "attachments": {
    "f4c379d1-9d08-448e-a423-9dcf24a61d57.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "83034203-ffa1-47de-93d9-114b980477a9",
   "metadata": {},
   "source": [
    "![image.png](attachment:f4c379d1-9d08-448e-a423-9dcf24a61d57.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72478912-d452-4c93-83ba-64d8f83e6f44",
   "metadata": {},
   "source": [
    "Führen Sie den Algorithmus am obigen Beispiel vom Graphen $G$ aus, um ihn besser zu verstehen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120def8d-fa91-4f6e-a454-849b1e56a0a8",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccd9291e-0118-4e0e-bc6e-9da40693265e",
   "metadata": {},
   "source": [
    "Nach einer Testphase des Liniennetzes wird festgestellt, dass der Kraftstoffverbrauch für die Schiffe sehr hoch ist. Um diesen zu minimieren, soll der Fahrplan nochmal überarbeitet werden. Die Informationen über den Kraftstoffverbrauch pro Strecke können wir in unserem Modell integrieren. Hierfür nutzen wir eine weitere besondere Form von Graphen, die Sie ebenfalls bereits in der Vorlesung kennengelernt haben."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6c66356-99d9-4c09-a06e-64121b90e2f6",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G=(V,E)$ ein Graph und $c:E\\to \\mathbb{R}_{\\geq0}$ eine Gewichtsfunktion, die jeder Kante einen Wert zuschreibt. Dann heißt $G_c=(V,E,c)$ ein <b>gewichteter Graph</b>. \n",
    "    <br>\n",
    "Sei $E'\\subseteq E$ eine Teilmenge der Kanten. Dann schreiben wir auch $c(E'):=\\sum_{e\\in E'} c(e)$.\n",
    "\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff3c93eb-7643-465c-a179-81153800edb0",
   "metadata": {},
   "source": [
    "Wir betrachten also nun unseren Graphen $G_c=(V,E,c)$ mit einer Gewichtsfunktion $c:E\\to\\mathbb{R}_{\\geq0}$, die für jede Wasserstraße den zugehörigen Kraftstoffverbraucht (in Litern) angibt. Unser Graph sieht jetzt so aus:"
   ]
  },
  {
   "attachments": {
    "022a8e46-6189-4dd5-885c-2afed7d4447a.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "29023606-3833-423b-ad6f-53382dc132e8",
   "metadata": {},
   "source": [
    "![image.png](attachment:022a8e46-6189-4dd5-885c-2afed7d4447a.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "024a2e61-62b9-4078-be5b-300e5195811d",
   "metadata": {},
   "source": [
    "Um nun ein besseres Streckennetz zu finden, welches den Kraftstoffverbrauch minimiert, müssen wir zusätzlich noch eine Minimalitätsbedingung an den Spannbaum stellen. Anders formuliert: Wir suchen nach einem (gewichts)minimalen Spannbaum."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb170936-e335-4710-8709-c6f7d518f4b5",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G_c=(V,E,c)$ ein gewichteter Graph. <br>\n",
    "Ein Spannbaum $T=(V,E_T) \\subseteq G$ heißt <b>(gewichts)minimaler Spannbaum</b> von $G_c$ genau dann, wenn für alle Spannbäume $T'$ von $G_c$ gilt: $$c(T) = \\sum_{e\\in E_T} c(e) \\leq \\sum_{e\\in E_{T'}} c(e) = c(T')$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0a2decb-808f-4911-ad67-7ad9de8f7d3d",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Beweisen Sie die folgende Aussage: <br>\n",
    "    <center><i>Jeder gewichtete Graph mit mindestens zwei Knoten und einer Kante besitzt einen minimalen Spannbaum.</i></center>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e04da1f-25b2-435d-bf62-d15ad952b9bb",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Bestimmen Sie ein minimales Streckennetz für die Inselgruppe, die den obigen Anforderungen entspricht. <br>\n",
    "Ist dieses eindeutig oder kann man noch weitere solche Streckennetze finden? Falls ja, welche?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe0bf18d-c8a5-4991-a6b6-dbef84623ae0",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55fd9b8a-2fe0-4e66-8c3d-19b86c7adcef",
   "metadata": {},
   "source": [
    "Es gibt verschiedene Wege, effizient einen minimalen Spannbaum zu berechnen. Einer davon ist durch den <b>Kruskal-Algorithmus</b> gegeben."
   ]
  },
  {
   "attachments": {
    "5ceca576-f6cd-4a09-a1cb-e9005ee723f4.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "51ef4ce3-f999-4248-865c-d60a7bbdc625",
   "metadata": {},
   "source": [
    "![image.png](attachment:5ceca576-f6cd-4a09-a1cb-e9005ee723f4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03843945-750e-46af-b6d2-83deb039ee5f",
   "metadata": {},
   "source": [
    "Wenden Sie diesen Algorithmus auf den Graphen $G_c$ an und vergleichen Sie die Ergebnisse mit der vorherigen Aufgabe."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4110850-b9d3-4cb7-a95f-1bf00361940e",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Verstehen Sie den Algorithmus und beweisen Sie, dass er ein gültiges Ergebnis ausgibt. <br>\n",
    "Ist der Rückgabewert eindeutig, d.h. vom Übergabeparameter unabhängig? Falls nein, nennen Sie Beispiele anhand unseres Graphen $G$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19f97218-44af-46f0-a5bf-8301e9161df7",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ec17db6-d360-4309-9d51-e8bda49cb0f2",
   "metadata": {},
   "source": [
    "Ein weiterer sehr bekannter Algorithmus für minimale Spannbäume ist der <b>Algorithmus von Prim</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0719b921-bdea-46d7-a643-b540ab9a203d",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe\n",
    "***\n",
    "Recherchieren Sie nach dem Prim-Algorithmus für minimale Spannbäume und verstehen Sie seine Funktionsweise. Schreiben Sie für diesen einen Pseudocode im Stil angelehnt an das obige Beispiel. <br>\n",
    "Gehen Sie auch den Prim-Algorithmus wieder am Graphen $G_c$ durch, um die Unterschiede zum Kruskal-Algorithmus zu sehen.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca8cca9f-9935-4f2f-9d43-aefb856662f3",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10575af4-8173-4db8-9c33-8c0f36d82668",
   "metadata": {},
   "source": [
    "Analog zu minimalen Spannbäumen kann man auch <b>maximale</b> Spannbäume definieren."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48d157ee-a228-4e03-bf5f-105ccf5698b9",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Sei $G_c=(V,E,c)$ ein gewichteter Graph. <br>\n",
    "Ein Spannbaum $T=(V,E_T) \\subseteq G_c$ heißt <b>(gewichts)maximaler Spannbaum</b> von $G_c$ genau dann, wenn für alle Spannbäume $T'$ von $G_c$ gilt: $$c(T) = \\sum_{e\\in E_T} c(e) \\geq \\sum_{e\\in E_{T'}} c(e) = c(T')$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7011de7c-c95e-4655-a8f4-e49752e52f32",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Modifizieren Sie einen der beiden obigen Algorithmen, um einen Algorithmus zum Berechnen eines maximalen Spannbaums zu erhalten.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73d07a3b-0c6d-444f-908f-cdeeb27bd6c1",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82fbbfda-64a2-4a9e-90f5-29251b1fb0f4",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "### Rückblick-Aufgabe\n",
    "***\n",
    "Das Ziel dieses Projekts war es, das Konzept von Spannbäumen zu verstehen und einige Algorithmen kennenzulernen, mit denen man konkret in einem endlichen und zusammenhängenden Graphen einen Spannbaum berechnen kann. Für den Spezialfall von gewichteten Graphen haben wir den Algorithmus von Prim und Kruskal analysiert, um einen minimalen Spannbaum zu finden.\n",
    "    \n",
    "Diese beiden Algorithmen sind nur eine der bekanntesten, es gibt noch viele weitere Möglichkeiten, minimale Spannbäume zu berechnen. Finden Sie mindestens einen weiteren Algorithmus zur Berechnung eines minimalen Spannbaums. Stellen Sie diesen vor und vergleichen Sie seine Eigenschaften mit den Algorithmen von Prim und Kruskal. In welchen Situationen ist welcher Algorithmus vorzuziehen?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dca06dc0-fdc1-4bf7-8ef3-ad6a696fd476",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00fbeda-cca0-4bf6-9e9c-3927ffe02299",
   "metadata": {},
   "source": [
    "### Literaturhinweise\n",
    "- Graph theory. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Graph_theory\n",
    "- Quicksort. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Quicksort\n",
    "- Bernhard Korte, Jens Vygen (2018): <i>Combinatorial Optimization.</i> Heidelberg: Springer Berlin."
   ]
  }
 ],
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