{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algoritmusok Python nyelven\n",
    "\n",
    "## 7. Előadás: Gráfok és algoritmusok. \n",
    "\n",
    "### 2020. április 9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "█████████████████████\n",
      "█                 █ █\n",
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      "█ █   █ █ █     █   █\n",
      "█ █████ ███ ███ █ ███\n",
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      "█████ █ █ ███ █████ █\n",
      "█     █ █   █   █   █\n",
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      "█████ █ ███ ███████ █\n",
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      "█         █         █\n",
      "█████████████████████\n"
     ]
    }
   ],
   "source": [
    "printmaze(makemaze(10,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random as rn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gráf adatstruktúra\n",
    "\n",
    "Több lehetőség is van, mindnek megvannak az előnyei és hátrányai. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Első lehetőség: élek listája\n",
    "Egy listában tároljuk a gráf éleit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_ellista=[(\"a\",\"b\"),(\"b\",\"c\"),(\"c\",\"d\"),(\"d\",\"b\"),(\"b\",\"e\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def maxfok1(l):\n",
    "    d={}\n",
    "    for el in l:\n",
    "        if el[0] in d:\n",
    "            d[el[0]]=d[el[0]]+1\n",
    "        else:\n",
    "            d[el[0]]=1\n",
    "        if el[1] in d:\n",
    "            d[el[1]]=d[el[1]]+1\n",
    "        else:\n",
    "            d[el[1]]=1\n",
    "    return max(d,key=lambda x:d[x])        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'b'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxfok1(graph_ellista)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Második lehetőség: szomszédsági lista\n",
    "Minden csúcshoz felírjuk a szomszédait. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph = { \"a\" : [\"c\"],\n",
    "          \"b\" : [\"c\", \"e\"],\n",
    "          \"c\" : [\"a\", \"b\", \"d\", \"e\"],\n",
    "          \"d\" : [\"c\"],\n",
    "          \"e\" : [\"c\", \"b\"],\n",
    "          \"f\" : []\n",
    "        } "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def maxfok2(l):\n",
    "    return max(l,key=lambda x: len(l[x]) ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'c'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxfok2(graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "usa={\"AL\" : [ \"FL\", \"GA\", \"TN\", \"MS\" ],\n",
    "\"AK\" : [ ],\n",
    "\"AZ\" : [ \"NM\", \"UT\", \"NV\", \"CA\" ],\n",
    "\"AR\" : [ \"LA\", \"MS\", \"TN\", \"MO\", \"OK\", \"TX\" ],\n",
    "\"CA\" : [ \"AZ\", \"NV\", \"OR\" ],\n",
    "\"CO\" : [ \"NM\", \"OK\", \"KS\", \"NE\", \"WY\", \"UT\" ],\n",
    "\"CT\" : [ \"RI\", \"MA\", \"NY\" ],\n",
    "\"DE\" : [ \"NJ\", \"PA\", \"MD\" ],\n",
    "\"DC\" : [ \"MD\", \"VA\" ],\n",
    "\"FL\" : [ \"GA\", \"AL\" ],\n",
    "\"GA\" : [ \"SC\", \"NC\", \"TN\", \"AL\", \"FL\" ],\n",
    "\"HI\" : [ ],\n",
    "\"ID\" : [ \"WA\", \"OR\", \"NV\", \"UT\", \"WY\", \"MT\" ],\n",
    "\"IL\" : [ \"WI\", \"IA\", \"MO\", \"KY\", \"IN\" ],\n",
    "\"IN\" : [ \"IL\", \"KY\", \"OH\", \"MI\" ],\n",
    "\"IA\" : [ \"MN\", \"SD\", \"NE\", \"MO\", \"IL\", \"WI\" ],\n",
    "\"KS\" : [ \"OK\", \"MO\", \"NE\", \"CO\" ],\n",
    "\"KY\" : [ \"TN\", \"VA\", \"WV\", \"OH\", \"IN\", \"IL\", \"MO\" ],\n",
    "\"LA\" : [ \"MS\", \"AR\", \"TX\" ],\n",
    "\"ME\" : [ \"NH\" ],\n",
    "\"MD\" : [ \"DE\", \"PA\", \"WV\", \"VA\", \"DC\" ],\n",
    "\"MA\" : [ \"NH\", \"VT\", \"NY\", \"CT\", \"RI\" ],\n",
    "\"MI\" : [ \"WI\", \"IN\", \"OH\" ],\n",
    "\"MN\" : [ \"ND\", \"SD\", \"IA\", \"WI\" ],\n",
    "\"MS\" : [ \"AL\", \"TN\", \"AR\", \"LA\" ],\n",
    "\"MO\" : [ \"AR\", \"TN\", \"KY\", \"IL\", \"IA\", \"NE\", \"KS\", \"OK\" ],\n",
    "\"MT\" : [ \"ID\", \"WY\", \"SD\", \"ND\" ],\n",
    "\"NE\" : [ \"KS\", \"MO\", \"IA\", \"SD\", \"WY\", \"CO\" ],\n",
    "\"NV\" : [ \"AZ\", \"UT\", \"ID\", \"OR\", \"CA\" ],\n",
    "\"NH\" : [ \"VT\", \"MA\", \"ME\" ],\n",
    "\"NJ\" : [ \"NY\", \"PA\", \"DE\" ],\n",
    "\"NM\" : [ \"TX\", \"OK\", \"CO\", \"AZ\" ],\n",
    "\"NY\" : [ \"PA\", \"NJ\", \"CT\", \"MA\", \"VT\" ],\n",
    "\"NC\" : [ \"VA\", \"TN\", \"GA\", \"SC\" ],\n",
    "\"ND\" : [ \"MT\", \"SD\", \"MN\" ],\n",
    "\"OH\" : [ \"MI\", \"IN\", \"KY\", \"WV\", \"PA\" ],\n",
    "\"OK\" : [ \"TX\", \"AR\", \"MO\", \"KS\", \"CO\", \"NM\" ],\n",
    "\"OR\" : [ \"CA\", \"NV\", \"ID\", \"WA\" ],\n",
    "\"PA\" : [ \"OH\", \"WV\", \"MD\", \"DE\", \"NJ\", \"NY\" ],\n",
    "\"RI\" : [ \"MA\", \"CT\" ],\n",
    "\"SC\" : [ \"NC\", \"GA\" ],\n",
    "\"SD\" : [ \"NE\", \"IA\", \"MN\", \"ND\", \"MT\", \"WY\" ],\n",
    "\"TN\" : [ \"AL\", \"GA\", \"NC\", \"VA\", \"KY\", \"MO\", \"AR\", \"MS\" ],\n",
    "\"TX\" : [ \"LA\", \"AR\", \"OK\", \"NM\" ],\n",
    "\"UT\" : [ \"AZ\", \"CO\", \"WY\", \"ID\", \"NV\", \"\" ],\n",
    "\"VT\" : [ \"NY\", \"MA\", \"NH\" ],\n",
    "\"VA\" : [ \"MD\", \"DC\", \"WV\", \"KY\", \"TN\", \"NC\" ],\n",
    "\"WA\" : [ \"OR\", \"ID\" ],\n",
    "\"WV\" : [ \"VA\", \"MD\", \"PA\", \"OH\", \"KY\" ],\n",
    "\"WI\" : [ \"MN\", \"IA\", \"IL\", \"MI\" ],\n",
    "\"WY\" : [ \"CO\", \"NE\", \"SD\", \"MT\", \"ID\", \"UT\" ]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'MO'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxfok2(usa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Harmadik lehetőség: szomszédsági mátrix\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "graphszom=np.array([[0,0,1,1],[0,0,0,1],[1,0,0,1],[1,1,1,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1, 1],\n",
       "       [0, 0, 0, 1],\n",
       "       [1, 0, 0, 1],\n",
       "       [1, 1, 1, 0]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphszom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def maxfok3(A):\n",
    "    return A.sum(axis=0).argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxfok3(graphszom)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mikor melyiket válasszuk?\n",
    "Mint mindig a helyzettől függ, mindegyiknek van előnye is és hátránya is.  \n",
    "\n",
    "![interpreted](graf.jpg)\n",
    "\n",
    "**Szomszédsági mátrix**\n",
    " - Lassú hozzáadni és törölni a csúcsokat, mivel át kell méretezni a tömböt.\n",
    " - Nagy a memória igénye. \n",
    " - Gyorsan kérdezhetjük le az éleket.\n",
    " - Algebrai számítások esetén elkerülhetetlen (gráf spektruma, gráf sajátértékei stb..)\n",
    " - Sűrű mátrixok (sok él van, például négyzetesen sok) esetén hasznos.\n",
    "\n",
    "**Szomszédsági lista**\n",
    " - Gyors hozzáadni csúcsokat\n",
    " - Kisebb memória igény\n",
    " - Lassú lekérdezni\n",
    " - Ritka mátrixok (kevés él van, mondjuk lineáris sok) esetén hasznos.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negyedik lehetőség: valami, amit már megírtak, NetworkX\n",
    "\n",
    "Több modul van, ami kifejezetten a gráfok kezelésére készült, ebből nézünk meg most egyet.\n",
    "\n",
    " NetworkX a háttérben szomszédsági listákkal reprezentálja a gráfot: \n",
    "\n",
    "\"The graph internal data structures are based on an adjacency list representation and implemented using Python dictionary datastructures. The graph adjacency structure is implemented as a Python dictionary of dictionaries; the outer dictionary is keyed by nodes to values that are themselves dictionaries keyed by neighboring node to the edge attributes associated with that edge. This “dict-of-dicts” structure allows fast addition, deletion, and lookup of nodes and neighbors in large graphs. The underlying datastructure is accessed directly by methods (the programming interface “API”) in the class definitions. All functions, on the other hand, manipulate graph-like objects solely via those API methods and not by acting directly on the datastructure. This design allows for possible replacement of the ‘dicts-of-dicts’-based datastructure with an alternative datastructure that implements the same methods.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx            # Gráfokhoz\n",
    "import matplotlib.pyplot as plt  # Rajzokhoz\n",
    "import warnings                  # Valami okból a networkx kép rajzoló függvénye olyan kódot használ, ami elavult. Emiatt\n",
    "warnings.simplefilter('ignore')  # folyamatosan figyelmeztetéseket kapunk. Mivel ez minket nem igazán érdekel, \n",
    "                                 # ezért blokkoljuk őket.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Négy gráf adatszerkezet:\n",
    "- `Graph` irányítatlan, nincsenek párhuzamost élek              \n",
    "- `DiGraph` irányított, nincsenek párhuzamost élek\n",
    "- `MultiGraph` irányítatlan, vannak párhuzamost élek\n",
    "- `MultiDiGraph` irányított, vannak párhuzamost élek"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G=nx.Graph()\n",
    "G.add_node(3)                       # Bármilyen hashelhető típus lehet node. \n",
    "G.add_node(\"almafa\")                       # Bármilyen hashelhető típus lehet node. \n",
    "G.add_edge(1,2)\n",
    "G.add_edges_from([(1,4),(1,3)])\n",
    "G.add_edge(1,5)\n",
    "nx.draw(G, with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.remove_edge(1,2)\n",
    "nx.draw(G, with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attribútumok\n",
    "Bármilyen gráfhoz, élhez és csúcshoz tudunk attribútumokat rendelni. Ez sokszor hasznos, például, amikor súlyozott gráfokkal dolgozunk. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'time': '5pm'}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.add_node(\"x\", time='5pm')\n",
    "G.nodes[\"x\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_edge(2, 3, weight=0.9)  # specify edge data\n",
    "G.add_edge(2, 7, color=\"green\") \n",
    "elist = [('a', 'b', 5.0), ('b', 'c', 3.0), ('a', 'c', 1.0), ('c', 'd', 7.3)]\n",
    "G.add_weighted_edges_from(elist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adatok elérése, iterálás"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeView([(3, 1), (3, 2), (1, 4), (1, 5), (2, 7), ('a', 'b'), ('a', 'c'), ('b', 'c'), ('c', 'd')])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.edges()     #Ezzel a függvénnyel elérjük az éleket, de nem tudjuk megváltoztatni őket. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView((3, 'almafa', 1, 2, 4, 5, 'x', 7, 'a', 'b', 'c', 'd'))"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.number_of_nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: {}, 2: {'weight': 0.9}}\n",
      "{'weight': 0.9}\n",
      "0.9\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(G[3])\n",
    "print(G.edges[2,3])\n",
    "print(G.edges[2,3][\"weight\"])\n",
    "\n",
    "G.edges[1, 4]['weight'] = 4\n",
    "print(G.edges[1,4][\"weight\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((3, 1), {})\n",
      "((3, 2), {'weight': 0.9})\n",
      "((1, 4), {'weight': 4})\n",
      "((1, 5), {})\n",
      "((2, 7), {'color': 'green'})\n",
      "(('a', 'b'), {'weight': 5.0})\n",
      "(('a', 'c'), {'weight': 1.0})\n",
      "(('b', 'c'), {'weight': 3.0})\n",
      "(('c', 'd'), {'weight': 7.3})\n"
     ]
    }
   ],
   "source": [
    "for e in G.edges.items():\n",
    "      print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 2\n",
      "1 4\n",
      "a b\n",
      "a c\n",
      "b c\n",
      "c d\n"
     ]
    }
   ],
   "source": [
    "for u, v, weight in G.edges.data('weight'):\n",
    "    if weight is not None:\n",
    "        print(u,v)\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.petersen_graph()\n",
    "plt.subplot(121)\n",
    "nx.draw(G, with_labels=True, font_weight='bold')\n",
    "plt.subplot(122)\n",
    "nx.draw_shell(G, nlist=[range(5, 10), range(5)], with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DegreeView({0: 3, 1: 3, 2: 3, 3: 3, 4: 3, 5: 3, 6: 3, 7: 3, 8: 3, 9: 3})"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.degree()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "degree_sequence = list(G.degree())\n",
    "nb_nodes = len(degree_sequence)\n",
    "nb_arr = len(G.edges())\n",
    "avg_degree = np.mean(np.array(degree_sequence)[:,1])\n",
    "med_degree = np.median(np.array(degree_sequence)[:,1])\n",
    "max_degree = max(np.array(degree_sequence)[:,1])\n",
    "min_degree = np.min(np.array(degree_sequence)[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes : 10\n",
      "Number of edges : 15\n",
      "Maximum degree : 3\n",
      "Minimum degree : 3\n",
      "Average degree : 3.0\n",
      "Median degree : 3.0\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of nodes : \" + str(nb_nodes))\n",
    "print(\"Number of edges : \" + str(nb_arr))\n",
    "print(\"Maximum degree : \" + str(max_degree))\n",
    "print(\"Minimum degree : \" + str(min_degree))\n",
    "print(\"Average degree : \" + str(avg_degree))\n",
    "print(\"Median degree : \" + str(med_degree))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beépített algoritmusok NetworkXben\n",
    "Teljes lista: [Itt](https://networkx.github.io/documentation/stable/reference/algorithms/index.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {0: [0],\n",
       "  1: [0, 1],\n",
       "  4: [0, 4],\n",
       "  5: [0, 5],\n",
       "  2: [0, 1, 2],\n",
       "  6: [0, 1, 6],\n",
       "  3: [0, 4, 3],\n",
       "  9: [0, 4, 9],\n",
       "  7: [0, 5, 7],\n",
       "  8: [0, 5, 8]},\n",
       " 1: {1: [1],\n",
       "  0: [1, 0],\n",
       "  2: [1, 2],\n",
       "  6: [1, 6],\n",
       "  4: [1, 0, 4],\n",
       "  5: [1, 0, 5],\n",
       "  3: [1, 2, 3],\n",
       "  7: [1, 2, 7],\n",
       "  8: [1, 6, 8],\n",
       "  9: [1, 6, 9]},\n",
       " 2: {2: [2],\n",
       "  1: [2, 1],\n",
       "  3: [2, 3],\n",
       "  7: [2, 7],\n",
       "  0: [2, 1, 0],\n",
       "  6: [2, 1, 6],\n",
       "  4: [2, 3, 4],\n",
       "  8: [2, 3, 8],\n",
       "  5: [2, 7, 5],\n",
       "  9: [2, 7, 9]},\n",
       " 3: {3: [3],\n",
       "  2: [3, 2],\n",
       "  4: [3, 4],\n",
       "  8: [3, 8],\n",
       "  1: [3, 2, 1],\n",
       "  7: [3, 2, 7],\n",
       "  0: [3, 4, 0],\n",
       "  9: [3, 4, 9],\n",
       "  5: [3, 8, 5],\n",
       "  6: [3, 8, 6]},\n",
       " 4: {4: [4],\n",
       "  0: [4, 0],\n",
       "  3: [4, 3],\n",
       "  9: [4, 9],\n",
       "  1: [4, 0, 1],\n",
       "  5: [4, 0, 5],\n",
       "  2: [4, 3, 2],\n",
       "  8: [4, 3, 8],\n",
       "  6: [4, 9, 6],\n",
       "  7: [4, 9, 7]},\n",
       " 5: {5: [5],\n",
       "  0: [5, 0],\n",
       "  7: [5, 7],\n",
       "  8: [5, 8],\n",
       "  1: [5, 0, 1],\n",
       "  4: [5, 0, 4],\n",
       "  2: [5, 7, 2],\n",
       "  9: [5, 7, 9],\n",
       "  3: [5, 8, 3],\n",
       "  6: [5, 8, 6]},\n",
       " 6: {6: [6],\n",
       "  1: [6, 1],\n",
       "  8: [6, 8],\n",
       "  9: [6, 9],\n",
       "  0: [6, 1, 0],\n",
       "  2: [6, 1, 2],\n",
       "  3: [6, 8, 3],\n",
       "  5: [6, 8, 5],\n",
       "  4: [6, 9, 4],\n",
       "  7: [6, 9, 7]},\n",
       " 7: {7: [7],\n",
       "  2: [7, 2],\n",
       "  5: [7, 5],\n",
       "  9: [7, 9],\n",
       "  1: [7, 2, 1],\n",
       "  3: [7, 2, 3],\n",
       "  0: [7, 5, 0],\n",
       "  8: [7, 5, 8],\n",
       "  4: [7, 9, 4],\n",
       "  6: [7, 9, 6]},\n",
       " 8: {8: [8],\n",
       "  3: [8, 3],\n",
       "  5: [8, 5],\n",
       "  6: [8, 6],\n",
       "  2: [8, 3, 2],\n",
       "  4: [8, 3, 4],\n",
       "  0: [8, 5, 0],\n",
       "  7: [8, 5, 7],\n",
       "  1: [8, 6, 1],\n",
       "  9: [8, 6, 9]},\n",
       " 9: {9: [9],\n",
       "  4: [9, 4],\n",
       "  6: [9, 6],\n",
       "  7: [9, 7],\n",
       "  0: [9, 4, 0],\n",
       "  3: [9, 4, 3],\n",
       "  1: [9, 6, 1],\n",
       "  8: [9, 6, 8],\n",
       "  2: [9, 7, 2],\n",
       "  5: [9, 7, 5]}}"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0]\n",
      "[1]\n",
      "[2]\n",
      "[3]\n",
      "[4]\n",
      "[5]\n",
      "[6]\n",
      "[7]\n",
      "[8]\n",
      "[9]\n",
      "[0, 1]\n",
      "[0, 4]\n",
      "[0, 5]\n",
      "[1, 2]\n",
      "[1, 6]\n",
      "[2, 3]\n",
      "[2, 7]\n",
      "[3, 4]\n",
      "[3, 8]\n",
      "[4, 9]\n",
      "[5, 7]\n",
      "[5, 8]\n",
      "[6, 8]\n",
      "[6, 9]\n",
      "[7, 9]\n"
     ]
    }
   ],
   "source": [
    "for l in  nx.enumerate_all_cliques(G):\n",
    "    print(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 3, 0, 1, 0, 2, 0, 8]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=10\n",
    "T=nx.Graph()\n",
    "T.add_nodes_from(range(n))\n",
    "for i in range(1,n):\n",
    "    T.add_edge(i,rn.randrange(i))\n",
    "nx.draw_planar(T, with_labels=True, width=1 )\n",
    "nx.to_prufer_sequence(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, None)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.check_planarity(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rajzolás "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `draw(G, keywrds)`\n",
    "- `raw_circular(G, keywrds)`  \n",
    "- `draw_planar(G, keywrds)` \n",
    "- `draw_random(G, keywrds)`  \n",
    "- `draw_spectral(G, keywrds)` \n",
    "- `draw_spring(G, keywrds)` \n",
    "- `draw_shell(G, keywrds)` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = nx.Graph()\n",
    "g.add_nodes_from(usa.keys())\n",
    "\n",
    "for k, v in usa.items():\n",
    "    g.add_edges_from(([(k, t) for t in v]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_planar(g, with_labels=True, width=1 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.erdos_renyi_graph(20, 0.3)\n",
    "color_map = []\n",
    "edge_map = []\n",
    "for edge in G.edges():\n",
    "    if rn.randrange(2)%2==0:\n",
    "        edge_map.append('blue')\n",
    "    else:     \n",
    "        edge_map.append('green')\n",
    "   \n",
    "for node in G:\n",
    "    if rn.randrange(2)%2==0:\n",
    "        color_map.append('blue')\n",
    "    else: \n",
    "        color_map.append('green')      \n",
    "nx.draw(G, node_color=color_map,edge_color=edge_map, with_labels=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ötödik lehetőség: gráf algoritmusok gráfok nélkül\n",
    "\n",
    "Sokszor nem éri meg külön felépíteni egy gráfot, végrehajthatjuk az algoritmust magán az adatokon. Példaképpen most készítünk egy labirintust mélységi bejárás segítségével. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "███\n",
      "█ █\n",
      "███\n"
     ]
    }
   ],
   "source": [
    "# labirintus rajzoló. Egy 0/1/2 numpy tömböt vár. 0-semmi, 1-fal, 2-pozíció \n",
    "def printmaze(a):\n",
    "    def selector(c):\n",
    "        if c==0:\n",
    "            return ' '\n",
    "        if c==1:\n",
    "            return chr(0x2588)\n",
    "        if c==2:\n",
    "            return \"x\"\n",
    "    for row in a:\n",
    "        print(\"\".join([selector(c) for c in row]))\n",
    "    #    print(\"\".join([\"  \" if c==0 else chr(0x2B1B) for c in row]))\n",
    "printmaze(np.array([[1,1,1],[1,0,1],[1,1,1]]))                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Labirintus\n",
    "def makemaze(w=16,h=8):\n",
    "    maze=np.ones((2*w+1,2*h+1))\n",
    "    vis=np.zeros((2*w+1,2*h+1))\n",
    " \n",
    "    def walk(x, y):\n",
    "        vis[x][y] = 1\n",
    "        maze[x,y]=0\n",
    "          \n",
    "        d = [(x - 2, y), (x, y + 2), (x + 2, y), (x, y - 2)]\n",
    "        rn.shuffle(d)\n",
    "        \n",
    "        for (xx, yy) in d:\n",
    "            if (not xx in range(2*w+1)) or (not yy in range(2*h+1)) or vis[xx][yy]: \n",
    "                continue\n",
    "            if xx == x: \n",
    "                maze[x][max(y, yy)-1] = 0\n",
    "            if yy == y: \n",
    "                maze[max(x, xx)-1][y] = 0\n",
    "            walk(xx, yy)\n",
    " \n",
    "    walk(2*rn.randrange(w)+1, 2*rn.randrange(h)+1)\n",
    " \n",
    "    return maze\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "█████████████████████████████████████████████████████████████████████████████████\n",
      "█       █       █         █       █         █                 █       █       █ █\n",
      "█ █ ███ █ █████ █ ███ █████ █ ███ █ ███████ █ ███ ███████████ █████ █ █ █ ███ █ █\n",
      "█ █ █ █   █     █ █ █       █ █ █ █       █     █ █         █     █ █   █ █ █ █ █\n",
      "███ █ ███ ███████ █ █████████ █ █ █ █████ ███████ █ ███ █████████ ███████ █ █ █ █\n",
      "█   █     █     █ █   █     █ █   █ █   █ █       █   █         █       █ █ █   █\n",
      "█ █████████ ███ █ █ █ █ █████ █ █████ █ ███ █████████ ███████ █████████ █ █ ███ █\n",
      "█             █     █   █     █       █     █               █             █     █\n",
      "█████████████████████████████████████████████████████████████████████████████████\n"
     ]
    }
   ],
   "source": [
    "printmaze(makemaze(4,40))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def makemaze2(w=16,h=8,entry=0,inner=0):\n",
    "    maze=np.ones((2*w+1,2*h+1))\n",
    "    vis=np.zeros((2*w+1,2*h+1))\n",
    " \n",
    "    def walk(x, y):\n",
    "        vis[x][y] = 1\n",
    "        maze[x,y]=0\n",
    "          \n",
    "        d = [(x - 2, y), (x, y + 2), (x + 2, y), (x, y - 2)]\n",
    "        rn.shuffle(d)\n",
    "        \n",
    "        for (xx, yy) in d:\n",
    "            if (not xx in range(2*w+1)) or (not yy in range(2*h+1)) or vis[xx][yy]: \n",
    "                continue\n",
    "            if xx == x: \n",
    "                maze[x][max(y, yy)-1] = 0\n",
    "            if yy == y: \n",
    "                maze[max(x, xx)-1][y] = 0\n",
    "            walk(xx, yy)\n",
    " \n",
    "    walk(2*rn.randrange(w)+1, 2*rn.randrange(h)+1)\n",
    "    \n",
    "    ### bejáratok\n",
    "    for i in range(entry):\n",
    "        if rn.randrange(2)==0:\n",
    "            pos=rn.randrange(h)\n",
    "            if rn.randrange(2)==0:\n",
    "                maze[2*pos+1,0]=0\n",
    "            else:\n",
    "                maze[2*pos+1,-1]=0\n",
    "        else:    \n",
    "            pos=rn.randrange(w)\n",
    "            if rn.randrange(2)==0:\n",
    "                maze[0,2*pos+1]=0\n",
    "            else:\n",
    "                maze[-1,2*pos+1]=0\n",
    "    \n",
    "    ### belső körökhöz fal törlés\n",
    "    for i in range(inner):\n",
    "        if rn.randrange(2)==0:\n",
    "            maze[2*rn.randrange(h-1)+2,2*rn.randrange(w)+1]=0\n",
    "        else:\n",
    "            maze[2*rn.randrange(h)+1,2*rn.randrange(w-1)+2]=0\n",
    "    return maze\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "███████████ █████████\n",
      "█ █             █   █\n",
      "█ █ ███ ███████ █ ███\n",
      "█ █   █     █   █   █\n",
      "█ ███ █████ █ █████ █\n",
      "█   █   █ █ █       █\n",
      "█ █████ █ █ █████████\n",
      "█   █   █ █         █\n",
      "███ █ ███ █████████ █\n",
      "█   █     █         █\n",
      "█ █ ███ ███ █████████\n",
      "█   █   █ █   █     █\n",
      "█ ███ ███ █ █ █ ███ █\n",
      "█     █   █ █   █   █\n",
      "█ █████ █████ ███ █ █\n",
      "█ █   █     █ █ █ █  \n",
      "█ █ ███████ █ █ █ ███\n",
      "█ █       █ █   █   █\n",
      "█ ███████ █ ███████ █\n",
      "█         █         █\n",
      "█████████████████████\n"
     ]
    }
   ],
   "source": [
    "printmaze(makemaze2(10,10,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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