Graphs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "728446fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "            Representação de Grafos\n",
    "\n",
    "                Matriz de Adjacência\n",
    "                Lista de Adjacência\n",
    "                Matriz de Incidência\n",
    "\n",
    "            Travessias de Grafos\n",
    "\n",
    "                Busca em Largura (BFS)\n",
    "                Busca em Profundidade (DFS)\n",
    "\n",
    "            Algoritmos Clássicos\n",
    "\n",
    "                Algoritmo de Dijkstra para Caminhos Mais Curtos\n",
    "                Algoritmo de Bellman-Ford\n",
    "                Algoritmo de Kruskal para Árvores Geradoras Mínimas\n",
    "                \n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d647118e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8c506aa8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: networkx in c:\\users\\clevison\\anaconda3\\lib\\site-packages (3.1)\n",
      "Requirement already satisfied: matplotlib in c:\\users\\clevison\\anaconda3\\lib\\site-packages (3.7.1)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (1.0.5)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (0.11.0)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (4.25.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (1.4.4)\n",
      "Requirement already satisfied: numpy>=1.20 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (1.24.3)\n",
      "Requirement already satisfied: packaging>=20.0 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (23.0)\n",
      "Requirement already satisfied: pillow>=6.2.0 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (9.4.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (3.0.9)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from matplotlib) (2.8.2)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install networkx matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b4b1ca7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "af7ce75b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting prettytable\n",
      "  Obtaining dependency information for prettytable from https://files.pythonhosted.org/packages/4d/81/316b6a55a0d1f327d04cc7b0ba9d04058cb62de6c3a4d4b0df280cbe3b0b/prettytable-3.9.0-py3-none-any.whl.metadata\n",
      "  Downloading prettytable-3.9.0-py3-none-any.whl.metadata (26 kB)\n",
      "Requirement already satisfied: wcwidth in c:\\users\\clevison\\anaconda3\\lib\\site-packages (from prettytable) (0.2.5)\n",
      "Downloading prettytable-3.9.0-py3-none-any.whl (27 kB)\n",
      "Installing collected packages: prettytable\n",
      "Successfully installed prettytable-3.9.0\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install prettytable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33471930",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "296acaaa",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "           Matriz de Adjacência\n",
    "           \n",
    "Um grafo pode ser representado de diversas maneiras e uma delas é \n",
    "através de uma matriz de adjacência. Nessa representação, o elemento aij da matriz é 1 (ou \n",
    "algum peso, no caso de um grafo ponderado) se houver uma aresta entre os \n",
    "vértices i e j, e 0 se não houver.\n",
    "\n",
    "Vamos criar um exemplo simples em Python que demonstra como implementar e manipular \n",
    "um grafo utilizando matriz de adjacência:\n",
    "\n",
    "\n",
    "Vamos supor que temos um grafo com 4 vértices (0, 1, 2 e 3).\n",
    "\n",
    "E vamos ter as seguintes arestas:\n",
    "\n",
    "    0 -> 1\n",
    "    0 -> 2\n",
    "    1 -> 2\n",
    "    2 -> 3\n",
    "    3 -> 0\n",
    "   \n",
    "    \n",
    "    \n",
    "Matriz de Adjacência:\n",
    "\n",
    "A matriz é definida da seguinte forma: Se há uma aresta do vértice i para o \n",
    "vértice j, então a posição (i, j) na matriz terá o valor 1, caso contrário, \n",
    "terá o valor 0.\n",
    "\n",
    "\n",
    "   0  1  2  3\n",
    "0 [0, 1, 1, 0]\n",
    "1 [0, 0, 1, 0]\n",
    "2 [0, 0, 0, 1]\n",
    "3 [1, 0, 0, 0]\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca networkx com o alias 'nx'.\n",
    "# A biblioteca networkx é amplamente usada para a criação, \n",
    "# manipulação e estudo da estrutura e funções de grafos complexos.\n",
    "import networkx as nx\n",
    "\n",
    "# Importando a biblioteca matplotlib.pyplot com o alias 'plt'.\n",
    "# A biblioteca matplotlib é uma biblioteca gráfica usada para visualização em Python.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Criando um grafo direcionado (DiGraph).\n",
    "# Um grafo direcionado possui arestas com direção, ou seja, cada aresta \n",
    "# move-se de um vértice de origem para um vértice de destino.\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Adicionando uma aresta ao grafo direcionado G.\n",
    "# Esta aresta vai do vértice 0 para o vértice 1.\n",
    "G.add_edge(0, 1)\n",
    "\n",
    "# Adicionando outra aresta ao grafo G.\n",
    "# Esta aresta começa no vértice 1 e termina no vértice 2.\n",
    "G.add_edge(1, 2)\n",
    "\n",
    "# Adicionando mais uma aresta ao grafo G.\n",
    "# A aresta conecta o vértice 2 ao vértice 3.\n",
    "G.add_edge(2, 3)\n",
    "\n",
    "# Adicionando uma aresta que liga o vértice 3 de volta ao vértice 0.\n",
    "# Isso cria um ciclo entre os vértices 0, 1, 2, e 3.\n",
    "G.add_edge(3, 0)\n",
    "\n",
    "# Adicionando a última aresta ao grafo G.\n",
    "# Esta aresta conecta o vértice 0 diretamente ao vértice 2, formando um atalho entre eles.\n",
    "G.add_edge(0, 2)\n",
    "\n",
    "\n",
    "# Definindo um dicionário para armazenar as posições (coordenadas x, y) de cada vértice no gráfico.\n",
    "# Isso ajudará a posicionar os vértices de forma personalizada quando desenharmos o gráfico.\n",
    "pos = {\n",
    "    0: (-1, 1),   # Atribuindo a posição (-1, 1) ao vértice 0, posicionando-o no topo esquerdo do gráfico.\n",
    "    1: (1, 1),    # Atribuindo a posição (1, 1) ao vértice 1, colocando-o no topo direito do gráfico.\n",
    "    2: (1, -1),   # Definindo a posição (1, -1) para o vértice 2, posicionando-o no canto inferior direito.\n",
    "    3: (-1, -1)   # Estabelecendo a posição (-1, -1) para o vértice 3, fazendo com que ele fique no canto inferior esquerdo.\n",
    "}\n",
    "\n",
    "# Desenhando o grafo utilizando a função 'draw' da biblioteca 'networkx'.\n",
    "# Os argumentos definem diversos aspectos da visualização.\n",
    "nx.draw(\n",
    "    G,               # Especifica o grafo 'G' que será desenhado.\n",
    "    pos=pos,         # Usa o dicionário 'pos' para determinar a posição de cada vértice.\n",
    "    with_labels=True, # Mostra os rótulos/identificadores dos vértices.\n",
    "    font_weight='bold', # Define que o peso da fonte dos rótulos dos vértices será 'bold' (negrito).\n",
    "    node_color='skyblue', # Define a cor dos vértices como 'skyblue' (azul claro).\n",
    "    node_size=1000,      # Define o tamanho dos vértices. \n",
    "    edge_color='gray',   # Define a cor das arestas/linhas entre os vértices como cinza.\n",
    "    arrows=True,         # Especifica que as arestas terão setas (pois é um grafo direcionado).\n",
    "    arrowstyle='-|>'     # Define o estilo da seta.\n",
    ")\n",
    "\n",
    "# Usando a função 'show' da biblioteca 'matplotlib' para exibir o gráfico desenhado.\n",
    "plt.show()\n",
    "\n",
    "\"\"\"\n",
    "    0 -> 1\n",
    "    0 -> 2\n",
    "    1 -> 2\n",
    "    2 -> 3\n",
    "    3 -> 0\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd859887",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b777bd8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c951a4b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Vamos criar um grafo mais complexo, com mais vértices e arestas para demonstração.\n",
    "\n",
    "Imagine um grafo com 7 vértices (0 a 6) e as seguintes arestas:\n",
    "\n",
    "    0 -> 1\n",
    "    0 -> 3\n",
    "    1 -> 2\n",
    "    1 -> 4\n",
    "    2 -> 6\n",
    "    3 -> 5\n",
    "    4 -> 6\n",
    "    5 -> 3\n",
    "    6 -> 5\n",
    "    6 -> 0\n",
    "\n",
    "Matriz de Adjacência:\n",
    "\n",
    "   0  1  2  3  4  5  6\n",
    "0 [0, 1, 0, 1, 0, 0, 0]\n",
    "1 [0, 0, 1, 0, 1, 0, 0]\n",
    "2 [0, 0, 0, 0, 0, 0, 1]\n",
    "3 [0, 0, 0, 0, 0, 1, 0]\n",
    "4 [0, 0, 0, 0, 0, 0, 1]\n",
    "5 [0, 0, 0, 1, 0, 0, 0]\n",
    "6 [1, 0, 0, 0, 0, 1, 0]\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Gráfico:\n",
    "\n",
    "# Vamos usar o código para criar o gráfico deste exemplo:\n",
    "\n",
    "# Importando a biblioteca 'networkx' com o alias 'nx'.\n",
    "# Esta biblioteca é usada para a criação, manipulação e análise de estruturas de grafos.\n",
    "import networkx as nx\n",
    "\n",
    "# Importando a biblioteca 'matplotlib.pyplot' com o alias 'plt'.\n",
    "# Esta biblioteca é usada para criar visualizações gráficas, como gráficos e diagramas.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Criando um novo grafo direcionado usando o método 'DiGraph' da biblioteca 'networkx'.\n",
    "# Um grafo direcionado é um conjunto de vértices e arestas direcionadas (com um sentido definido).\n",
    "G = nx.DiGraph()\n",
    "\n",
    "\n",
    "# Comentário descrevendo a operação que será realizada a seguir: Adição de arestas ao grafo.\n",
    "# Criando uma lista de tuplas chamada 'arestas'. \n",
    "# Cada tupla representa uma aresta direcionada, com o primeiro elemento sendo \n",
    "# o vértice de origem e o segundo elemento o vértice de destino.\n",
    "arestas = [(0, 1), (0, 3), (1, 2), (1, 4), (2, 6), (3, 5), (4, 6), (5, 3), (6, 5), (6, 0)]\n",
    "\n",
    "# Utilizando o método 'add_edges_from' do objeto 'G' (que é nosso grafo direcionado) \n",
    "# para adicionar todas as arestas definidas na lista 'arestas'.\n",
    "# As arestas são adicionadas de acordo com as tuplas, criando uma conexão direcionada \n",
    "# entre os vértices.\n",
    "G.add_edges_from(arestas)\n",
    "\n",
    "\n",
    "# A função spring_layout cria uma disposição que parece \"natural\" para grafos\n",
    "# Isso é útil quando temos um grafo mais complexo e não queremos definir \n",
    "# manualmente cada posição.\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "\n",
    "nx.draw(\n",
    "    G,               # Especifica o grafo 'G' que será desenhado.\n",
    "    pos=pos,         # Usa o dicionário 'pos' para determinar a posição de cada vértice.\n",
    "    with_labels=True, # Mostra os rótulos/identificadores dos vértices.\n",
    "    font_weight='bold', # Define que o peso da fonte dos rótulos dos vértices será 'bold' (negrito).\n",
    "    node_color='skyblue', # Define a cor dos vértices como 'skyblue' (azul claro).\n",
    "    node_size=1000,      # Define o tamanho dos vértices. \n",
    "    edge_color='gray',   # Define a cor das arestas/linhas entre os vértices como cinza.\n",
    "    arrows=True,         # Especifica que as arestas terão setas (pois é um grafo direcionado).\n",
    "    arrowstyle='-|>'     # Define o estilo da seta.\n",
    ")\n",
    "\n",
    "\n",
    "# Utilizando a função 'show' do pacote 'matplotlib.pyplot' para exibir \n",
    "# a visualização do grafo que foi gerada pela função 'draw'.\n",
    "plt.show()\n",
    "\n",
    "\"\"\"\n",
    "    0 -> 1\n",
    "    0 -> 3\n",
    "    1 -> 2\n",
    "    1 -> 4\n",
    "    2 -> 6\n",
    "    3 -> 5\n",
    "    4 -> 6\n",
    "    5 -> 3\n",
    "    6 -> 5\n",
    "    6 -> 0\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0812c73b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b83081a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matriz de Adjacência:\n",
      "+-----+---+---+---+---+---+\n",
      "| V\\V | 0 | 1 | 2 | 3 | 4 |\n",
      "+-----+---+---+---+---+---+\n",
      "|  0  | 0 | 1 | 1 | 0 | 0 |\n",
      "|  1  | 0 | 0 | 0 | 1 | 0 |\n",
      "|  2  | 0 | 0 | 0 | 0 | 1 |\n",
      "|  3  | 0 | 0 | 0 | 0 | 1 |\n",
      "|  4  | 0 | 0 | 0 | 0 | 0 |\n",
      "+-----+---+---+---+---+---+\n",
      "\n",
      "Tabela de Arestas:\n",
      "+--------+---------+\n",
      "| Origem | Destino |\n",
      "+--------+---------+\n",
      "|   0    |    1    |\n",
      "|   0    |    2    |\n",
      "|   1    |    3    |\n",
      "|   2    |    4    |\n",
      "|   3    |    4    |\n",
      "+--------+---------+\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício - Grafo Direcionado e Representações Gráficas\n",
    "\n",
    "Crie um código em Python que crie a Matriz de Adjacência, a \n",
    "Tabela de Arestas e o Gráfico com os dados abaixo:\n",
    "\n",
    "Matriz de Adjacência:\n",
    "+-----+---+---+---+---+---+\n",
    "| V\\V | 0 | 1 | 2 | 3 | 4 |\n",
    "+-----+---+---+---+---+---+\n",
    "|  0  | 0 | 1 | 1 | 0 | 0 |\n",
    "|  1  | 0 | 0 | 0 | 1 | 0 |\n",
    "|  2  | 0 | 0 | 0 | 0 | 1 |\n",
    "|  3  | 0 | 0 | 0 | 0 | 1 |\n",
    "|  4  | 0 | 0 | 0 | 0 | 0 |\n",
    "+-----+---+---+---+---+---+\n",
    "\n",
    "Tabela de Arestas:\n",
    "+--------+---------+\n",
    "| Origem | Destino |\n",
    "+--------+---------+\n",
    "|   0    |    1    |\n",
    "|   0    |    2    |\n",
    "|   1    |    3    |\n",
    "|   2    |    4    |\n",
    "|   3    |    4    |\n",
    "+--------+---------+\n",
    "\"\"\"\n",
    "\n",
    "# Importa a biblioteca PrettyTable, que é usada para criar tabelas \n",
    "# com uma aparência bonita no console.\n",
    "from prettytable import PrettyTable\n",
    "\n",
    "# Importa a biblioteca NetworkX, que é usada para a criação, manipulação \n",
    "# e visualização de estruturas de grafos.\n",
    "import networkx as nx\n",
    "\n",
    "# Importa a biblioteca Matplotlib's pyplot, que é uma coleção de funções e\n",
    "# estilos que fazem com que o Matplotlib funcione como o MATLAB, é usada para plotar o grafo.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# Define uma classe chamada \"GrafoDirecionado\" para representar um grafo direcionado.\n",
    "class GrafoDirecionado:\n",
    "    \n",
    "    # Método construtor da classe.\n",
    "    # Ele é invocado quando criamos uma instância da classe e define as propriedades\n",
    "    # iniciais do objeto.\n",
    "    def __init__(self, numero_vertices):\n",
    "        \n",
    "        # Armazena o número de vértices do grafo.\n",
    "        # Isso é necessário para criar a matriz de adjacência e saber quantas linhas \n",
    "        # e colunas ela terá.\n",
    "        self.numero_vertices = numero_vertices\n",
    "        \n",
    "        # Cria a matriz de adjacência.\n",
    "        # A matriz de adjacência é uma representação de um grafo onde o elemento \n",
    "        # M[i][j] é 1 se há uma aresta do vértice i para o vértice j, e 0 caso contrário.\n",
    "        # Neste caso, estamos inicializando todos os elementos da matriz como 0, \n",
    "        # indicando que não há arestas no grafo inicialmente.\n",
    "        # self.matriz_adjacencia = [[0 for j in range(numero_vertices)] for i in range(numero_vertices)]\n",
    "        \n",
    "        # Criando uma matriz de adjacência para representar um grafo.\n",
    "        self.matriz_adjacencia = [\n",
    "            \n",
    "            # Para cada vértice 'i' em nosso grafo (representado pelo \n",
    "            # número total de vértices)\n",
    "            [0 for j in range(numero_vertices)]\n",
    "            \n",
    "            # Estamos inicializando uma linha inteira com zeros. \n",
    "            # O zero indica que, inicialmente, não há arestas entre os vértices 'i' e 'j'.\n",
    "            for i in range(numero_vertices)\n",
    "            \n",
    "            # Estamos fazendo isso para todos os vértices, criando assim uma matriz quadrada.\n",
    "        ]\n",
    "\n",
    "        \n",
    "        # Lista para armazenar as arestas (ligações) do grafo.\n",
    "        # Será útil para listar todas as arestas posteriormente e para visualizar o grafo.\n",
    "        # Cada elemento da lista é uma tupla (i, j) representando uma aresta do vértice i para o vértice j.\n",
    "        self.arestas = []\n",
    "        \n",
    "    # Método para adicionar uma aresta (ligação) direcionada ao grafo.\n",
    "    # Ele recebe dois parâmetros: i e j, que são os vértices de origem e destino da aresta, respectivamente.\n",
    "    def adiciona_aresta(self, i, j):\n",
    "        \n",
    "        # Verifica se os vértices de origem e destino são os mesmos.\n",
    "        # Em outras palavras, está verificando se a aresta forma um laço, ou seja, começa e termina no mesmo vértice.\n",
    "        if i == j:\n",
    "            \n",
    "            # Imprime uma mensagem de erro informando que laços (arestas que começam e terminam no mesmo vértice) não são permitidos neste grafo.\n",
    "            print(\"Laços não são permitidos!\")\n",
    "            \n",
    "            # Retorna prematuramente, terminando a execução do método sem fazer mais nada.\n",
    "            # Isso é feito para evitar a adição da aresta inválida.\n",
    "            return\n",
    "        \n",
    "        # Se não houver um laço, atualiza a matriz de adjacência.\n",
    "        # O elemento da matriz na posição [i][j] é definido como 1, indicando \n",
    "        # a existência de uma aresta do vértice i para o vértice j.\n",
    "        self.matriz_adjacencia[i][j] = 1\n",
    "        \n",
    "        # Adiciona a aresta à lista de arestas.\n",
    "        # Isso é feito para manter um registro de todas as arestas \n",
    "        # adicionadas e facilitar outras operações, como a visualização do grafo.\n",
    "        self.arestas.append((i, j))\n",
    "        \n",
    "        \n",
    "    # O método especial \"__str__\" determina como o objeto será representado como uma string.\n",
    "    # Isso é útil, por exemplo, quando você tenta imprimir o objeto usando a função print().\n",
    "    def __str__(self):\n",
    "        \n",
    "        # Cria uma instância da classe PrettyTable.\n",
    "        # PrettyTable é uma biblioteca que permite criar tabelas ASCII com uma aparência formatada e organizada.\n",
    "        tabela = PrettyTable()\n",
    "        \n",
    "        # Define os nomes dos campos (colunas) da tabela.\n",
    "        # O primeiro campo é \"V\\V\", e os campos subsequentes são os números dos vértices do grafo.\n",
    "        # A notação [\"V\\\\V\"] + [str(i) for i in range(self.numero_vertices)] cria uma lista que combina [\"V\\V\"] com os números dos vértices convertidos para strings.\n",
    "        # tabela.field_names = [\"V\\\\V\"] + [str(i) for i in range(self.numero_vertices)]\n",
    "        \n",
    "        # Configurando os nomes dos campos (ou cabeçalhos) para uma tabela.\n",
    "        tabela.field_names = [\n",
    "            \n",
    "            # Primeira coluna da tabela terá o nome \"V\\V\".\n",
    "            \"V\\\\V\"\n",
    "            \n",
    "        ] + [\n",
    "            \n",
    "            # Para cada vértice 'i' em nosso grafo (representado pelo número total de vértices)\n",
    "            # Convertendo o índice do vértice para uma string e adicionando-o à lista de nomes de campos.\n",
    "            str(i) for i in range(self.numero_vertices)\n",
    "            \n",
    "            \n",
    "        ]\n",
    "        \n",
    "        # Este loop percorre todos os vértices do grafo.\n",
    "        for i in range(self.numero_vertices):\n",
    "            \n",
    "            # Adiciona uma linha à tabela para representar o vértice atual 'i'.\n",
    "            # A primeira coluna da linha é o número do vértice 'i' (convertido para string).\n",
    "            # As colunas subsequentes são os valores da linha correspondente na matriz de adjacência.\n",
    "            # Juntos, eles representam as conexões do vértice 'i' com todos os outros vértices.\n",
    "            tabela.add_row([str(i)] + self.matriz_adjacencia[i])\n",
    "        \n",
    "        # Retorna a representação da tabela como uma string.\n",
    "        # Isso permite que, quando o objeto GrafoDirecionado for impresso ou convertido em string, seja exibida esta tabela.\n",
    "        return str(tabela)\n",
    "    \n",
    "    \n",
    "    # Método para criar e retornar uma tabela que mostra todas as arestas (ligações) do grafo.\n",
    "    def tabela_arestas(self):\n",
    "        \n",
    "        # Cria uma nova instância da classe PrettyTable.\n",
    "        # Esta biblioteca ajuda a formatar e exibir tabelas em formato ASCII de maneira limpa e organizada.\n",
    "        tabela = PrettyTable()\n",
    "        \n",
    "        # Define os nomes dos campos (colunas) da tabela.\n",
    "        # A tabela terá duas colunas: \"Origem\" para o vértice de origem da aresta e \n",
    "        # \"Destino\" para o vértice de destino da aresta.\n",
    "        tabela.field_names = [\"Origem\", \"Destino\"]\n",
    "        \n",
    "        # Este loop percorre todas as arestas armazenadas na lista 'arestas' do objeto.\n",
    "        for aresta in self.arestas:\n",
    "            \n",
    "            # Adiciona uma nova linha à tabela.\n",
    "            # A linha contém dois elementos: o vértice de origem da aresta (aresta[0]) e o vértice de destino da aresta (aresta[1]).\n",
    "            tabela.add_row([aresta[0], aresta[1]])\n",
    "        \n",
    "        # Retorna a representação da tabela em formato de string.\n",
    "        # Isso permite que a tabela seja impressa ou convertida em uma string quando necessário.\n",
    "        return str(tabela)\n",
    "    \n",
    "    \n",
    "    # Método para visualizar o grafo como um diagrama.\n",
    "    def visualizar(self):\n",
    "        \n",
    "        # Cria um objeto de grafo direcionado usando a biblioteca NetworkX.\n",
    "        # NetworkX é uma biblioteca Python para criação, manipulação e estudo de estruturas de redes complexas.\n",
    "        G = nx.DiGraph()  # Criar um grafo direcionado\n",
    "        \n",
    "        # Este loop percorre todas as arestas armazenadas na lista 'arestas' do objeto.\n",
    "        for i, j in self.arestas:\n",
    "            \n",
    "            # Adiciona uma aresta ao objeto grafo G, de i para j.\n",
    "            # Em outras palavras, estamos transferindo as arestas armazenadas em \n",
    "            # nossa estrutura para o objeto grafo da NetworkX.\n",
    "            G.add_edge(i, j)\n",
    "        \n",
    "        # Define um dicionário para especificar as posições dos vértices (nós) no gráfico.\n",
    "        # Isso é útil para manter uma representação gráfica consistente e clara.\n",
    "        # Cada chave no dicionário representa um vértice, e o valor associado é uma \n",
    "        # tupla (x, y) que define a posição do vértice no gráfico.\n",
    "        pos = {\n",
    "            0: (0.5, 1),   # Vértice 0 está no centro superior\n",
    "            1: (0, 0.5),   # Vértice 1 está no lado esquerdo, ao meio\n",
    "            2: (1, 0.5),   # Vértice 2 está no lado direito, ao meio\n",
    "            3: (0, 0),     # Vértice 3 está no canto inferior esquerdo\n",
    "            4: (1, 0)      # Vértice 4 está no canto inferior direito\n",
    "        }\n",
    "\n",
    "\n",
    "        # Desenha o grafo G usando as posições definidas em 'pos' e várias outras opções de estilo.\n",
    "        nx.draw(\n",
    "            G,                    # Especifica que o grafo 'G' deve ser desenhado.\n",
    "            pos=pos,              # Define as posições dos vértices (nós) conforme especificado anteriormente.\n",
    "            with_labels=True,     # Exibe os rótulos (números) dos vértices.\n",
    "            font_weight='bold',   # Define a espessura da fonte dos rótulos como 'bold' (negrito).\n",
    "            node_color='skyblue', # Define a cor dos vértices como 'skyblue' (azul céu).\n",
    "            node_size=1000,       # Define o tamanho dos vértices.\n",
    "            edge_color='gray',    # Define a cor das arestas como cinza.\n",
    "            arrows=True,          # Indica que as arestas devem ser desenhadas com setas para indicar direção.\n",
    "            arrowstyle='-|>'      # Define o estilo das setas. '-|>' significa uma linha que termina com uma ponta de seta triangular.\n",
    "        )\n",
    "    \n",
    "    # Exibe o gráfico.\n",
    "    # Este é um comando da biblioteca matplotlib.pyplot, e ele renderiza \n",
    "    # e exibe o gráfico preparado.\n",
    "    plt.show()\n",
    "\n",
    "    \n",
    "        \n",
    "# Verifica se este script está sendo executado como um programa principal.\n",
    "# A condição __name__ == \"__main__\" é usada para garantir que o código a seguir\n",
    "# seja executado apenas quando o script for executado diretamente,\n",
    "# e não quando for importado como um módulo em outro script.\n",
    "if __name__ == \"__main__\":\n",
    "    \n",
    "    # Cria uma nova instância da classe GrafoDirecionado com 5 vértices.\n",
    "    grafo = GrafoDirecionado(5)\n",
    "\n",
    "    # Adiciona várias arestas (ligações entre vértices) ao grafo.\n",
    "    grafo.adiciona_aresta(0, 1)\n",
    "    grafo.adiciona_aresta(0, 2)\n",
    "    grafo.adiciona_aresta(1, 3)\n",
    "    grafo.adiciona_aresta(2, 4)\n",
    "    grafo.adiciona_aresta(3, 4)\n",
    "\n",
    "    # Imprime o texto \"Matriz de Adjacência:\" para o console.\n",
    "    print(\"Matriz de Adjacência:\")\n",
    "    \n",
    "    # Imprime a representação da matriz de adjacência do grafo.\n",
    "    # Graças ao método __str__ definido na classe, podemos imprimir\n",
    "    # o objeto diretamente para obter a matriz formatada.\n",
    "    print(grafo)\n",
    "    \n",
    "    # Imprime uma linha em branco para separação visual.\n",
    "    print(\"\\nTabela de Arestas:\")\n",
    "    \n",
    "    # Imprime a tabela que mostra todas as arestas do grafo.\n",
    "    # O método tabela_arestas() retorna a representação da tabela em formato de string.\n",
    "    print(grafo.tabela_arestas())\n",
    "    \n",
    "    # Exibe o grafo visualmente.\n",
    "    # Isso abrirá uma janela (ou aba) mostrando o diagrama do grafo com vértices, arestas e direções.\n",
    "    grafo.visualizar()\n",
    "\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Aqui, temos um grafo com 5 vértices. O vértice 0 está conectado\n",
    "aos vértices 1 e 2, o vértice 1 está conectado ao vértice 3, o vértice\n",
    "2 ao 4 e os vértices 3 e 4 também estão conectados. A matriz de adjacência \n",
    "reflete isso e o gráfico mostrará essas conexões visualmente.\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5edbc769",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2a3095c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in c:\\users\\clevison\\anaconda3\\lib\\site-packages (1.24.3)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6ab4eea3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8abfa16b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matriz de Adjacência:\n",
      "[0 1 1 0 0]\n",
      "[0 0 0 1 0]\n",
      "[0 0 0 0 1]\n",
      "[0 0 0 0 1]\n",
      "[0 0 0 0 0]\n",
      "\n",
      "Lista de Adjacência:\n",
      "0: [1, 2]\n",
      "1: [3]\n",
      "2: [4]\n",
      "3: [4]\n",
      "4: []\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "           Lista de Adjacência\n",
    "           \n",
    "A lista de adjacência é uma das formas mais comuns de representar\n",
    "grafos em memória, especialmente quando o grafo é esparso (tem relativamente \n",
    "poucas arestas). Ela é especialmente útil em termos de economia de espaço\n",
    "em comparação com a matriz de adjacência.\n",
    "\n",
    "Exemplo\n",
    "\"\"\"\n",
    "\n",
    "# Importando os pacotes necessários:\n",
    "# - networkx para manipulação e visualização de grafos;\n",
    "# - numpy para operações de matriz;\n",
    "# - matplotlib.pyplot para visualizações adicionais.\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Inicializando um grafo direcionado (DiGraph) que tem arestas com direção (setas).\n",
    "grafo = nx.DiGraph()\n",
    "\n",
    "# Adicionando vértices ao grafo:\n",
    "# O loop for irá iterar 5 vezes, uma vez para cada número no \n",
    "# intervalo de 0 a 4 (5 não está incluído).\n",
    "\n",
    "for vertice in range(5): # Iniciando um loop for que passará pelos números 0, 1, 2, 3 e 4.\n",
    "    grafo.add_node(vertice) # Para cada iteração do loop, um vértice é adicionado ao grafo. \n",
    "                            # O número da iteração (de 0 a 4) é usado como o nome/identificador do vértice.\n",
    "        \n",
    "\n",
    "# Adicionando arestas ao grafo:\n",
    "# As arestas são adicionadas ao grafo usando uma lista de tuplas, \n",
    "# onde cada tupla representa uma aresta.\n",
    "# Cada tupla contém dois números: o primeiro é o vértice de origem\n",
    "# e o segundo é o vértice de destino da aresta.\n",
    "\n",
    "grafo.add_edges_from([(0, 1),   # Adiciona uma aresta do vértice 0 para o vértice 1.\n",
    "                      (0, 2),   # Adiciona uma aresta do vértice 0 para o vértice 2.\n",
    "                      (1, 3),   # Adiciona uma aresta do vértice 1 para o vértice 3.\n",
    "                      (2, 4),   # Adiciona uma aresta do vértice 2 para o vértice 4.\n",
    "                      (3, 4)    # Adiciona uma aresta do vértice 3 para o vértice 4.\n",
    "                     ])\n",
    "\n",
    "\n",
    "# Criando a matriz de adjacência:\n",
    "# A matriz de adjacência é uma representação do grafo em forma de matriz.\n",
    "# Cada linha e cada coluna da matriz representam um vértice do grafo.\n",
    "# Se houver uma aresta do vértice \"i\" para o vértice \"j\", então o elemento\n",
    "# da matriz na linha \"i\" e coluna \"j\" será 1. Caso contrário, será 0.\n",
    "\n",
    "# Pegando a lista de todos os vértices/nós do grafo.\n",
    "vertices = list(grafo.nodes())\n",
    "\n",
    "# Calculando o número total de vértices no grafo.\n",
    "num_vertices = len(vertices)\n",
    "\n",
    "# Inicializando uma matriz quadrada (número de linhas = número de vértices\n",
    "# e número de colunas = número de vértices) com todos os elementos setados para zero.\n",
    "# A matriz é criada usando o pacote NumPy.\n",
    "# Os elementos da matriz são do tipo inteiro.\n",
    "matriz_adjacencia = np.zeros((num_vertices, num_vertices), dtype=int)\n",
    "\n",
    "\n",
    "# Preenchendo a matriz de adjacência:\n",
    "# Iterando sobre todas as arestas (conexões) presentes no grafo.\n",
    "for origem, destino in grafo.edges():\n",
    "    \n",
    "    # Para cada aresta (origem, destino), encontramos o índice correspondente à origem\n",
    "    # e o índice correspondente ao destino na lista de vértices.\n",
    "    # Em seguida, atualizamos o elemento da matriz de adjacência na\n",
    "    # posição (índice da origem, índice do destino) para 1.\n",
    "    # Isso indica a existência de uma aresta direcionada do vértice de origem \n",
    "    # para o vértice de destino.\n",
    "    matriz_adjacencia[vertices.index(origem), vertices.index(destino)] = 1\n",
    "    \n",
    "    \n",
    "# Exibindo a matriz de adjacência:\n",
    "print(\"Matriz de Adjacência:\")\n",
    "\n",
    "# Iterando sobre cada linha da matriz de adjacência.\n",
    "for linha in matriz_adjacencia:\n",
    "    \n",
    "    # Imprimindo cada linha da matriz.\n",
    "    # Cada linha da matriz representa as conexões do vértice correspondente\n",
    "    # a essa linha com os outros vértices.\n",
    "    print(linha)\n",
    "    \n",
    "\n",
    "# Exibindo a Lista de Adjacência:\n",
    "print(\"\\nLista de Adjacência:\")\n",
    "\n",
    "# Criando um dicionário vazio para armazenar a lista de adjacência.\n",
    "# A chave será o vértice e o valor será uma lista de vértices vizinhos.\n",
    "lista_adjacencia = {}\n",
    "\n",
    "# Iterando sobre todos os vértices do grafo.\n",
    "for vertice in grafo.nodes():\n",
    "    \n",
    "    # Para cada vértice, pegamos seus vértices vizinhos (ou seja, vértices\n",
    "    # diretamente conectados a ele).\n",
    "    # A função 'neighbors' do objeto grafo retorna um iterador\n",
    "    # dos vizinhos do vértice em questão.\n",
    "    # Convertendo esse iterador em uma lista e armazenando no dicionário 'lista_adjacencia'.\n",
    "    lista_adjacencia[vertice] = list(grafo.neighbors(vertice))\n",
    "    \n",
    "    \n",
    "# Iterando sobre os itens do dicionário 'lista_adjacencia' para imprimir.\n",
    "for chave, valor in lista_adjacencia.items():\n",
    "    \n",
    "    # Imprimindo cada chave (vértice) e seus valores (lista de vértices vizinhos).\n",
    "    # A saída mostra o vértice e seus vértices adjacentes no formato \"chave: valor\".\n",
    "    print(f\"{chave}: {valor}\")\n",
    "    \n",
    "    \n",
    "# Desenhando o grafo:\n",
    "\n",
    "# Usando o algoritmo \"spring layout\" do NetworkX para calcular o posicionamento dos vértices.\n",
    "# Este algoritmo tenta posicionar os vértices de tal forma que arestas de comprimentos semelhantes\n",
    "# tenham tamanhos semelhantes e arestas cruzadas sejam minimizadas.\n",
    "posicionamento = nx.spring_layout(grafo)\n",
    "\n",
    "# Desenhando os vértices do grafo. \n",
    "# 'node_color' define a cor dos vértices.\n",
    "# 'node_size' define o tamanho dos vértices.\n",
    "nx.draw_networkx_nodes(grafo, posicionamento, node_color='lightblue', node_size=500)\n",
    "\n",
    "# Desenhando as arestas do grafo.\n",
    "# 'arrows' define se as setas (indicando a direção das\n",
    "# arestas em grafos direcionados) devem ser desenhadas.\n",
    "# 'arrowsize' define o tamanho das setas.\n",
    "nx.draw_networkx_edges(grafo, posicionamento, arrows=True, arrowsize=20)\n",
    "\n",
    "# Desenhando os rótulos dos vértices.\n",
    "# Este método coloca um rótulo (o nome do vértice) em cada vértice.\n",
    "nx.draw_networkx_labels(grafo, posicionamento)\n",
    "\n",
    "# Configurando o título do gráfico que será exibido.\n",
    "plt.title(\"Visualização do Grafo\")\n",
    "\n",
    "# Exibindo o gráfico.\n",
    "# Esta é uma função do Matplotlib que exibe a figura/plot atual.\n",
    "plt.show()\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "A Matriz de Adjacência\n",
    "\n",
    "    0 1 2 3 4\n",
    "0: [0 1 1 0 0]\n",
    "1: [0 0 0 1 0]\n",
    "2: [0 0 0 0 1]\n",
    "3: [0 0 0 0 1]\n",
    "4: [0 0 0 0 0]\n",
    "\n",
    "\n",
    "A Lista de Adjacência é:\n",
    "\n",
    "Lista de Adjacência:\n",
    "0: [1, 2]\n",
    "1: [3]\n",
    "2: [4]\n",
    "3: [4]\n",
    "4: []\n",
    "\n",
    "\n",
    "Vamos descrever o gráfico com base na lista de adjacência:\n",
    "\n",
    "    Temos um grafo direcionado com cinco vértices numerados de 0 a 4.\n",
    "    \n",
    "    O vértice 0 tem setas apontando para os vértices 1 e 2. Isso significa \n",
    "        que há uma aresta do vértice 0 para o vértice 1 e uma aresta do \n",
    "        vértice 0 para o vértice 2.\n",
    "        \n",
    "    O vértice 1 tem uma seta apontando para o vértice 3. Assim, há uma \n",
    "        aresta do vértice 1 para o vértice 3.\n",
    "        \n",
    "    O vértice 2 tem uma seta apontando para o vértice 4. Logo, há uma\n",
    "        aresta do vértice 2 para o vértice 4.\n",
    "        \n",
    "    O vértice 3 também tem uma seta apontando para o vértice 4, indicando \n",
    "        uma aresta do vértice 3 para o vértice 4.\n",
    "        \n",
    "    O vértice 4 não tem arestas saindo dele, indicando que ele não se \n",
    "        conecta a nenhum outro vértice.\n",
    "\n",
    "Em resumo, o grafo contém uma série de conexões unidirecionais entre os vértices, \n",
    "com os vértices 2, 3 e 4 atuando como destinos finais para as arestas entrantes.\n",
    "\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05805f74",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1e31ad6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grau Médio: 2.0\n",
      "Densidade: 0.25\n",
      "\n",
      "Informações dos Vértices:\n",
      "      cor tamanho\n",
      "0    blue     300\n",
      "1   green     400\n",
      "2     red     500\n",
      "3  yellow     600\n",
      "4  orange     700 \n",
      "\n",
      "Informações das Arestas:\n",
      "     peso\n",
      "0 1     5\n",
      "  2     3\n",
      "1 3     2\n",
      "2 4     7\n",
      "3 4     4 \n",
      "\n"
     ]
    },
    {
     "data": {
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v1+iXlfdrWFgYvvnmGyxevFijPSfWsqCcx5EBM9WjRw+kpKRg9uzZiIyMRPv27eHo6Kjz9hKJBP7+/pg3bx7c3Nxw7tw5AEC+fPlgb2+PixcvavT/dBb5p/v4/Ba0iIgIPHnyRI9nBIwfPx6hoaFYvnw5GjRokO7xAKQ55tKlSzX+X6JECfj5+WHFihVaT166xl+/fn1cvXpV/TNKtXr1akgkEtStWzfDY6ROokqdXJdq48aNUCgUaY6TmvB8fhxHR0eN2+w+V6VKFTRq1AjLli0zyGxuiUQCW1tbjRPo8+fP030fpKd+/fp49+5dmpPN6tWr1Y9nV9OmTXHnzh14eHigSpUqab6yujCPk5MTAgICMG7cOCQlJeHKlSvqWPV9XdKj6/tYV0lJSWjVqhXu37+P3bt3pzsiJpFIIJfLNSYXf/jwIc2aE1l5v6b3+3Px4kW9LmeR+DgyYKaqVKmCChUq4Ndff4UgCJleIgBU11gXLVqEli1bomjRohAEAVu3bsXbt2/RsGFDAKpf8E6dOqkXkPH398epU6ewdu3aNPtr2rQpVq5ciVKlSqFChQo4e/YsZs+enenwfHo2bdqEadOmoU2bNihRooR6yBRQ/dGsVKkSatasidy5c6Nv374ICQmBjY0NwsPDceHChTT7W7hwIZo1a4bq1atj2LBhKFiwIB4+fIi///5b/YdO1/iHDRuG1atXIzAwEJMnT0ahQoUQERGBRYsWoV+/fihRokSGz6t06dLo1KkTfv31V9jY2KBBgwa4fPmyeub+p0JCQrBr1y7UrVsXEyZMgLu7O8LDwxEREYGff/453ev9nwoLC8O3336LBg0aoGvXrvj222/h6emJ2NhYXLx4Efv27UtzzIw0bdoUW7duRf/+/dGmTRs8evQIU6ZMgbe3N27dupXp9l26dMHChQsRHByM+/fvo3z58jh69CimT5+OJk2apJvsZdXQoUOxZcsW1K5dG8OGDUOFChWgVCrx8OFD/PPPP/jxxx9RrVo1rfvo1asXHBwc8NVXX8Hb2xvPnz/HjBkz4Orqii+//BJA9l+Xz5UqVQp+fn4YPXo0BEGAu7s7/vrrL41LE1kxbNgwHDhwANOnT8e7d+80fnfy5s0LPz8/BAYGYu7cuejYsSN69+6NqKgo/PLLL2lO5ll5vzZt2hRTpkxBSEgI6tSpgxs3bmDy5MkoUqRImsSBzICIkxcpm+bPny8AEMqUKZPu45/PRL5+/brQoUMHwc/PT3BwcBBcXV2FqlWrCitXrtTYLiYmRujZs6eQL18+wcnJSWjWrJlw//79NHcTvHnzRujRo4fg6ekpODo6CrVq1RKOHDki1KlTR6hTp466ny53E4SEhAgA0v36dOb0sWPHhBo1agiOjo5C3rx5hZ49ewrnzp1L9w6I48ePCwEBAYKzs7N61vyns6R1jV8QBOHBgwdCx44dBQ8PD8HGxkYoWbKkMHv2bCElJUXrayQIgpCYmCj8+OOPgqenp2Bvby9Ur15dOH78uFCoUKE0s7MvXbokNGvWTHB1dRVsbW0Ff3//dO/syEhCQoKwYMECoVatWoKbm5sgl8sFd3d34euvvxZmzZolREVFqfumvi6zZ89Od18zZ84UChcuLNjZ2QmlS5cWli1bpn6dPpXe3QSCIAhRUVFC3759BW9vb0EulwuFChUSxowZIyQkJGT6PFLvJsjMu3fvhPHjxwslS5YUbG1tBVdXV6F8+fLCsGHDhOfPn6v7ARAGDBiQZvtVq1YJdevWFfLlyyfY2toKPj4+Qrt27YSLFy9q9NPldUm9m2DTpk0a7em9/69evSo0bNhQcHZ2FnLnzi20bdtWePjwYZrfMV3uJqhTp06Gvzufvr9WrFghlCxZUrCzsxOKFi0qzJgxQ/jzzz/T7F/X92tiYqIwfPhwwdfXV7C3txcqV64sbN++PdO7Hcg0SQThsxUniCxQ165d0aBBA41Fd4iISIVzBsiinThxAkeOHEFiYiI2b94sdjhERCaJyQBZtB07dqBhw4Y4dOgQRwWIiDLAywRERERWjiMDREREVo7JABERkZXTaZ0BpVKJp0+fwtnZOcNVvIiIiMi0CIKAuLg4+Pj4QCrN+PO/TsnA06dP0xTpICIiIvPw6NEjrQvC6ZQMODs7q3em6wpmREREJK7Y2FgUKFBAfR7PiE7JQOqlARcXFyYDREREZiazS/ycQEhERGTlmAwQERFZOSYDREREVo7JABERkZVjMkBERGTlmAwQERFZOSYDREREVo7JABERkZVjMkBERGTlmAwQERFZOSYDREREVo7JABERkZVjMkBERGTldKpaSEREWXT/PnD6NHD2LHDlChAXB0gkgKsrUK4c8MUXwJdfAlpqzBMZC5MBIiJDSUgANm8GFiwATp1StdnYAAoFIAiq/0skQESEqg0Avv4aGDQIaNlS1ZdIBLxMQERkCFu3AgUKAJ07A2fO/K89Ofl/iQCg+ndqIgAAx44B7doBhQsDf/9ttHCJPsVkgIgoO6KigO+/B777TvVvAFAqdd8+JUX1/flzoHFjoEcPICbG8HESacFkgIhIXw8eqK77b9mi+v+nIwBZlZpArFoF1KypSg6IjITJABGRPp48AWrVAh49+t+ne0NISQFu3ABq1wZevzbcfom0YDJARJRVyclAkyaqT++fXv83lJQU4O5doFWrrF1yINITkwEioqyaORO4dClnEoFUKSnA0aPAokU5dwyij5gMEBFlxaVLwOTJ2ZsfkBUjRqhGCYhyEJMBIqKsmDbNuMdTKIBffjHuMcnqMBkgItLV8+eqOwd0vDxwAEB3AKUAOAHwBdACwNmsHFOhAFauBGJjsxYrURYwGSAi0lVoaJYm9C0GcB/AEACRAOYDeAmgOlSJgs4SEoDw8KxsQZQlTAaIiHS1d2+WkoGFUJ30+wGoA6ANgL0APABMz8pxpVLgQJbSB6IsYW0CIqJPJCcn49mzZ3j8+DGePHmCJ0+eqP79+DGW/9//wSkL+/JMpy0XgDIAHmUlqJQU4MSJrGxBlCVMBojIarx7907zBJ/O9xcvXkBI506BwkCWEoGMxAA4B6BeVjd8/BiIjgbc3Q0QBZEmJgNEZPYEQcDr168zPdHHZGPNf28DxToAQDyAcfps/OIFkwHKEUwGiMikpQ7bazvRP336FImJiTkah60B9vETgHAACwB8oc8OkpIMEAVRWkwGiEg08fHxWj/JP378OMNhe2PLbqoxCcBUANMADNR3J3Z22YyCKH1MBojI4ARBQFRUVKYn+uwM2xvb02xsOwnAxI9fY7MThJdXdrYmyhCTASLKEoVCoR62z+hE/+TJkxwftje2hwDeAnDL4nZToEoCxgMIyU4ABQsCblk9OpFumAwQkVrqsH1ms+2VVlpJ7zSA+tB9gZY5ACYAaAwgEMDnNwdW1/XAMhlQo4auvYmyjMkAkRUQBAHR0dFaP8k/fvwYb9++FTtUk/Y3snZL4F8fv+/5+PU5nWdCpKQADRpk4chEWcNkgMjMKRQKPH/+XOuJ/smTJ0hISBA7VLO3EqqVA2U69j9kqAPnygV06GCovRGlwWSAyIS9f/8+3U/wn35//vy51Q7bG5JcLoePjw/y588PX19f9fdP/+3j4wPbXr2Adet0LlZkgMCAHj0AJ0MseUSUPiYDRCJIHbbP7ET/5s0bsUO1CE5OTsifP3+6J/jU756enpBKdZgNMG4csGFDzgedys4O+PFH4x2PrBKTASIDSx22z2wiHoftDSNv3rwZfpJP/e7i4gKJRGKYA5YsCUybBowYYZj9ZWb+fKBAAeMci6wWkwGiLEgdttd2ouewvWGkDttndILPnz8/fHx8YCfGQjzDhgGbNwNnzqgm9+UEmQyoXx/o3j1n9k/0CSYDRFAN27958ybTRXI4bG8YTk5OGZ7gU7/rPGwvBpkM+OsvoGZN4P59w88fkMmAcuWAjRsBQ41oEGlhucnAhxdA9Fkg5jKQHAcICkBqB9h7Au6VATd/QO4gdpRkBCkpKephe20z7j98+CB2qBYhT548mZ7oDTpsL5a8eYEjR4B69YAbNwADjQalALgkkeD12LFo4OpqkH0SZcZykgFBAKJOArcWA0/3AIkvVe0SGTSWCBEUUN3dKwVcSgKFOgDFegIOhqpJRsb04cOHTK/NP3/+HCk5NZRrRWQymXrYPqMTvY+PD+zt7cUO1Xi8vIATJ4Dhw4FlywCpVO+kIEUigUQQ8CuAnxQKfPj+ezQLC8P06dNRrlw5g4ZN9DmJoEMFkNjYWLi6uiImJgYuLi7GiEt3ghK4txq4NheIuQRI5B9P+LqSqobh8rcGyo4C3PWqJUYGJggC3r59m+kiOdHR0WKHahEcHR21fpJPnW0vk+l6h70V2rdPdQvgw4eqYX5dE1C5HFAo8MzZGW3i4nDss4clEgmCg4MxadIkFCxY0OBhk2XT9fxt3slA3G3geDDw+hhUn/6zMUwnkQNCClBmFFA+BJBZ0acbI0tJScGLFy8yPMGnfuewvWF4eHhkeIJP/berq6v5D9ubgpQUIDISWLgQ+PtvVVtqApU6YiCTqf6tVKpGEgIDgYEDEf7iBTp16ZLhru3s7DBw4ECMGTMGHh4eOfxEyFJYdjIgCMDN34HzI1Qn8CyNBGRGCjj7AV+t4yiBHhISEjK9d/7Zs2cctjcAmUwGb29vrSd6Hx8fODhwbowooqKAs2dVX1evAvHxqlFIJyegfHngiy+ASpWA3LkBANeuXUOZMmUy3a2LiwtGjRqFIUOGwIkLEVEmLDcZEJTA2aHAzQU5dwyJDJDYAHV2At4Ns727pKQk7NmzB69evYKLiwuaNGlidr/EqcP2mV2fj4qKEjtUi+Do6Kj1k7yvry/y5cvHYXsLkpSUBEdHR50TZW9vb4SEhKB79+6wsbHJ4ejIXFlmMiAIwJmBwK1FRjiYFJBIgbp7AK/6eu0hJSUFCxYswPTp0/Hq1St1u4eHB6ZNm4Y+ffoYKthsSUlJwcuXL7XeUvfkyRO8f/9e7FAtgoeHR6Ynejc3Nw7bW6HixYvj9u3bWdqmUqVK+Pvvv5E3b94ciorMma7nb/O6m+DqTCMlAgCgVN10cLgp8O1pwC1rs3kvXryInj174vTp02kei4qKQt++feHk5IROnToZKN70JSQk4OnTp1pP9By2N4zUYXttq+Fx2J60KVmyZJaTgfPnz2Px4sWYMGFCDkVF1sB8koE3/wEXfzLyQZWAMhk41glofBqQZj4Ul5CQgKlTp2LWrFlQZLIQyeDBg/H999/rNcQnCAJiYmIyvXf+9evXWd43peXg4KBxgk89uX96ouewPWVXyZIlERERkeXtTHZxJjIb5pEMpCQBx4LEObaQAry9CFz9GSg3TmvXI0eOoFevXrhx44ZOu37z5g0OHz6MBp/VKU8dttd2S92TJ08QHx+v99Oi/3F3d890kRwO25MxlCxZMsvbVKxYEYMGDcqBaMiamEcycP0XIOYaVOP2YhCASxOBgm0BlxJpHo2JicHo0aOxZMmSLO95/vz5iIiISDNsn9moAmVOKpWmGbZP7zo9h+3JVJQokfbvizbDhg3D9OnTrWuhJ8oRpp8MpCSpFhQSLRH4xM0FQBXNuxh27tyJ/v3748mTJ3rtcteuXYaIzOrY29tnukhOvnz5IJeb/lucKJWuIwO2trbYsWMHGjdunMMRkbUw/b+Uj7cBSSZwu5qgAO6sAPxnADa5cO3aNXTq1Annzp0TOzKLkzt37kxP9Llz5+awPVkcLy8vODs7Iy4uTmu/pKQk/Pfff0wGyGBMPxm4sQCADKryHdmz/CDQazngZAe8W6HHDlI+APfDEXEzP1q0aMEZ+FkklUrh5eWldcje19cXjo6OYodKJAqJRIKSJUvizJkz6T726Z3gP/30Exo1aoTKlSsbM0SyUKadDCTFAK//NciunkQDw9cCPrmBmGzcLp9wZyOaNz/EevWfsbe3z/TeeS8vLw7bE2WiTJkyaZKBGjVqYOjQoejQoYP6b49CoUDHjh1x7tw5JtCUbab9l/mN4Ybg+64AapcC3J2Azaf03YuApGdHrS4RyJ07t9Z75319feHu7s5heyID6NGjB9auXQuFQgGZTIaQkBCMGTMGcrkcFy9exLRp09R9b9y4gREjRmDhwoUiRkyWwLSTgagzqlUAheydfMOOAoevqe4OHL8peyG52CXBJzfw9E329mMKJBKJera9tuvz/NRBZDy1a9fGmTNncOzYMTRo0ADFixdXPxYSEoK///5bY+Rg0aJFaNKkCQIDA8UIlyyEaScDb/4DkL1Pmy9jgKFrgJntgfwGKvRVsZDpJwN2dnaZ3jvPYXsi0+Tv7w9/f/807TY2NggPD0elSpU0lgfv3r07Ll26BE9PT2OGSRbEtM8ESdGqRX+yoX8oUNIb6Ncg8766yi1yjSE3N7dM75338PDgsD2RBSpRogTmzZunUdvk5cuX6NGjB3bu3Mnfe9KLaScDKQnZ2nzLKeCv88D5aarKoYZin0MFwiQSCby8vDKdiGduFQ+JyLB69eqFiIgI7Ny5U922a9cuLF26FH379hUxMjJXpp0MyPRfVetdAjBgJTCokeoOgrcfV+5N+riw39t4wEYGOOlxiMaBLfDnoR16x/a5Ll26YOrUqfDy8mIpUiLKlEQiwfLly1G+fHm8ePFC3f7DDz+gbt26ei1rTNbNtKtb2LpBtcZA1r2OA17EAHMigdy9//e17jgQn6j6d5CeBRDbtO+Ow4cPo1ChQvrt4DOFChVCgQIFmAgQkc7y5s2L0NBQjbYPHz4gKCgISUlJIkVF5sq0kwE3f73nD3q5AgfHpf36toJqmP/gOGBqWz3jyl0RtWvXxv379/Hy5UvMnz8flSpV0nNngLe3t97bEpH1CggIwIABAzTazp49i4kTJ4oTEJktifDpklYZiI2NhaurK2JiYuDi4mKMuFSe7QUONjLoLrsuUa0zoNcKhABg4wa0iU53EsLFixexatUqhIeHawzdaePs7Izbt29zFjAR6eX9+/eoUqUKrl27pm6TSCQ4fPgwvv76axEjI1Og6/nbtEcG3E1tmU0J4PFlhrMRK1SogDlz5uDx48fYtWsX2rRpA1tbW617nD59OhMBItKbo6MjwsPDNS4zCoKAzp07IyYmRsTIyJyYdjJg5wG4fwFDhrmybzZGBQDAt2mmXeRyOQIDA7Fp0yY8e/YMCxcuRNWqVTX65M+fH9u2bcPAgQOzEQwREVCpUiVMnTpVo+3Bgwf8+0I6M+3LBABwdzVwIti4x8yI1B5o/ezjxMasi4mJwY0bN+Dm5obixYvzfmAiMpiUlBTUr18fhw8f1mhft24d2rdvL1JUJDZdz9+mnwykJABbvYBkkYe7JHKgaFeg2jJx4yAiysDDhw9RoUIFjcsDrq6uuHjxIgoWLChiZCQWy5gzAKjWGigxCKKHKqQAJQeLGwMRkRYFCxbEkiVLNNpiYmLQpUsXllwnrUw/GQCAsmOBXIUBiX5rDmSfBCgzCnArL9LxiYh00759ewQFBWm0HT58GHPmzBEpIjIH5pEMyB2AGmuyXb1QLxIZ4FwcKD/R+McmItLDwoUL01wWGD9+PM6fPy9SRGTqzCMZAIC8NVWfzo1KovqqGQbI7Ix8bCIi/bi6umLNmjUak5STk5MRFBSkUe2QKJX5JAMA4D8NKBSE7JY11s3HRODrzaq1BYiIzEjt2rUxevRojbZr165h5MiRIkVEpsy8kgGJFKixEijcOYcPJFVdHvh6E5C/RQ4fi4goZ0ycOBFffPGFRtvChQsRGRkpUkRkqswrGQAAqRyoEQqUn6w6YRt6UqFECjh4AfX2AQVaG3bfRERGZGtri7CwMDg4OGi0d+/eHS9fvhQpKjJF5pcMAKoTdvmfgMZnAJdSMMhlg9Skwq8n0PQ6kK9O9vdJRCSyUqVKYe7cuRptL168QK9evaDDMjNkJcwzGUiVuyLQ+BxQeQ7g+HHmrESetX2kJgGedYF6+4GqSwEbZ4OGSUQkpj59+qBpU82l1Hfu3Illy7iIGqmY/gqEuhKUwLN/gJsLgRf7gZQPAIAkhWY3mVQCmfTjU7b3Agp3BIr1BVyKGzlgIiLjefnyJcqXL69xecDR0RHnz59HiRIlRIyMcpLlLEesh1cvX6BRjSIo4/UB5QoAuewAGzmQkATEJdlh5Mz1sPOuCdizWiARWY+IiIg0IwRVqlTBsWPHNKoekuXQ9fydxTF18zBl6jT8d/cD/rub3qOJ8GrwCr16MREgIusSGBiIfv36YfHixeq2M2fOYNKkSWmqHpJ1sbiRgZs3b6Js2bJQKBQZ9ilVqhSuXLkCqdS8p0wQEWXV+/fvUblyZdy4cUPdJpVKcfjwYdSqVUvEyCgnWE6hoiwaM2aM1kQAAK5fv47du3cbKSIiItPh6OiI8PBwyOX/GxhWKpXo3LmzRrVDsi4WlQwcPXoUW7du1akvi3YQkbX64osvMGXKFI22+/fvY9CgQSJFRGKzmGRAEAQMHz5c5/4HDx7EuXPncjAiIiLTNWLECNSuXVujbc2aNdiwYYNIEZGYLCYZ2LRpE06ePJmlbTg6QETWSiaTYfXq1XB1ddVo79u3Lx49eiRSVCQWi0gGEhMTMWbMmCxvt2HDBr7pichqFSpUCIsWLdJoe/v2LYKDg6FUilAynkRjEcnAokWLcPduuvcRapWSkoLffvstByIiIjIPHTt2RIcOHTTaDh48mGYJY7JsZn9roVKphLe3t95FN1xcXPDo0SOTe15ERMby9u1b+Pv74+HDh+o2GxsbnDp1ChUrVhQvMMo2q7m18NatW9mqvhUbG4t///3XgBEREZkXNzc3rF69GhLJ/4q+JScnIygoCB8+fBAxMjIWs08GChUqBHt7+2ztIzY21kDREBGZpzp16mDkyJEabVevXsWoUaNEioiMyeyTAXt7eyxcuFDv7fPmzYsmTZoYMCIiIvM0efJkVKpUSaNtwYIF2LNnj0gRkbGY/ZyBVA8ePMCBAwfw5s0bxMfHY/HixXj27JlGHxcXF5QpUwbx8fFQKBSoUKECpk2bBj8/P5GiJiIyLdeuXUPlypWRkJCgbvPy8sLFixeRN29eESMjfVh11UIAKFeuHK5cuaLRVr9+fezbt0+kiIiIzMOiRYswYMAAjbYWLVpg27ZtGvMKyPRZzQTCjLx//z5Nm6OjowiREBGZl379+qW5fLpjxw78+eefIkVEOc1ik4H4+Pg0bU5OTiJEQkRkXiQSCVasWJHmssCQIUNw69YtkaKinGSxyQBHBoiI9JcvX740IwHv379Hp06dkJycLFJUlFMsMhkQBIEjA0RE2dSsWTP06dNHo+3UqVNpKh6S+bPIZCAhIQHpzYtkMkBElDVz5sxBiRIlNNqmTZvGxdosjEUmA+ldIgB4mYCIKKucnJwQHh4OuVyublMqlejcuTMXbLMgFpkMpHeJAODIABGRPqpUqYJJkyZptN27dw+DBw8WKSIyNKtKBjgyQESkn1GjRqFWrVoabatWrcKmTZtEiogMySKTgYwuE3BkgIhIPzKZDGvWrEmzcE2fPn3w+PFjkaIiQ7HIZICXCYiIDK9w4cJpasG8efMGXbt2hVKpFCkqMgSLTAY4gZCIKGcEBQWhffv2Gm379+/Hr7/+Kk5AZBAWmQxwZICIKGdIJBIsWrQIBQoU0GgfM2YMLly4IFJUlF1MBoiIKEty586NVatWaRQtSkpKQlBQkEa1QzIfFpkM8DIBEVHOqlu3LoYPH67RduXKFYwePVqkiCg7LDIZ4MgAEVHOmzJlCipWrKjRNn/+fPzzzz/iBER6s8hkgCMDREQ5z87ODuHh4bC3t9doDw4OxuvXr0WKivRhkckARwaIiIyjTJkymD17tkbb8+fP0bt373RrxJBpsppkQCqVws7OToRoiIgs24ABA9C4cWONtm3btiE0NFSkiCirLDIZSO8ygaOjo8bMVyIiMgyJRILQ0FDkyZNHo33w4MG4ffu2SFFRVlhkMpDeyAAvERAR5RwvLy/8+eefGm3x8fHo1KkTkpOTRYqKdMVkgIiIDKJ58+bo3bu3RtvJkycxbdo0kSIiXVlkMpDRZQIiIspZc+fORfHixTXapkyZguPHj4sUEenCIpMBjgwQEYnDyckJ4eHhkMlk6jalUolOnTohLi5OxMhIG4tMBjgyQEQkni+//BITJ07UaLt79y6GDBkiTkCUKYtMBjgyQEQkrjFjxuCrr77SaAsNDcWWLVtEioi0YTJAREQGJ5PJsGbNGjg7O2u09+7dG0+ePBEpKsqIRSYDvExARCS+IkWK4Pfff9doi46ORteuXaFUKkWKitJjccmAIAgcGSAiMhGdO3dGu3btNNr27duH+fPnixQRpcfikoHExMR0M06ODBARGZ9EIsHixYvh6+ur0T569GhcunRJpKjocxaXDGRUsZAjA0RE4nB3d8fq1as12pKSktCxY0ckJCSIFBV9yuKSAVYsJCIyPfXq1cOPP/6o0Xb58mWMHTtWpIjoUxaXDGQ0MsDLBERE4po2bRr8/f012ubNm4e9e/eKFBGlsrhkgCMDRESmyc7ODuHh4WnKyXft2hVRUVEiRUUAkwEiIjKismXL4ueff9Zoe/r0KXr37g1BEESKiiwuGeBlAiIi0zZw4EB8++23Gm1bt27FypUrxQmILC8Z4MgAEZFpk0qlCA0NhYeHh0b74MGDcefOHZGism4WlwxwZICIyPR5e3tj+fLlGm3v3r1D586doVAoRIrKellcMsCRASIi89CyZUv07NlTo+348eOYNm2aSBFZLyYDREQkmnnz5qFYsWIabVOmTMGJEydEisg6WVwywMsERETmI1euXAgLC4NMJlO3paSkoFOnToiLixMxMuticckARwaIiMxLtWrVMGHCBI22O3fuYNiwYSJFZH2sIhmQSCSwt7cXIRoiItLF2LFjUbNmTY22P//8E9u2bRMpIuticclAepcJHB0dIZFIRIiGiIh0IZfLsWbNGuTKlUujvWfPnnj69KlIUVkPi0sG0hsZ4CUCIiLTV7RoUSxYsECjLTo6Gl27dk23ND0ZjsUlAxmNDBARkekLDg5GmzZtNNr27t2bJkkgw7K4ZIAjA0RE5ksikWDJkiXw8fHRaB81ahQuX74sUlSWj8kAERGZFA8PD6xatUqjLTExEUFBQUhMTBQpKstmcckALxMQEZm/Bg0a4IcfftBou3jxIsaOHStSRJbN4pIBjgwQEVmGadOmoXz58hptc+fOxf79+0WKyHJZRTLAkQEiIvNjb2+P8PBw2NnZabQHBwcjOjpapKgsk8UlA+ldJuDIABGReSpfvjxmzpyp0fbkyRP06dMHgiCIFJXlsahkQBAEXiYgIrIwgwcPRsOGDTXaNm/ejNWrV4sUkeWxqGQgOTkZKSkpadp5mYCIyHxJpVKsXLkS7u7uGu0DBw7E3bt3RYrKslhUMsAiRURElsnHxwfLli3TaHv37h06d+4MhUIhUlSWg8kAERGZhdatW6N79+4abceOHcOMGTNEishyWFQykN7kQYCXCYiILMWvv/4KPz8/jbZJkybh1KlTIkVkGSwqGeDIABGRZXN2dkZYWBhkMpm6LSUlBUFBQXj37p2IkZk3i0oGODJARGT5qlevjvHjx2u03b59G8OGDRMpIvNnUckARwaIiKzD+PHjUb16dY225cuXY/v27eIEZOaYDBARkdmRy+UICwtL8/e9Z8+eePbsmUhRmS+LSgZ4mYCIyHr4+fnht99+02iLiopCt27duDphFllUMsCRASIi69KtWze0bt1ao+3vv//G77//LlJE5onJABERmS2JRII//vgD3t7eGu0jRozAlStXRIrK/FhUMsDLBERE1sfDwwOrVq3SaEtMTERQUBASExNFisq8WFQywJEBIiLr1LBhQwwdOlSj7cKFC2luQaT0WVQykNHIgL29vZEjISIiY5sxYwbKlSun0TZnzhwcOHBApIjMh0UlA+mNDDg6OkIqtainSURE6bC3t0d4eDhsbW3VbYIgIDg4GG/evBExMtNnUWfJ9JIBXiIgIrIeFSpUSFO46PHjx+jbty9vN9TCopKB9C4TcPIgEZF1GTp0KBo0aKDRtnHjRoSFhYkUkemzqGSAIwNERCSVSrFy5Urkzp1bo33AgAG4d++eSFGZNotPBjgyQERkfXx9ffHHH39otMXFxaFz585ISUkRKSrTZVHJQHqXCTgyQERkndq0aYOuXbtqtP3777+YOXOmOAGZMItKBniZgIiIPjV//nwUKVJEo23ixIk4ffq0SBGZJotKBjiBkIiIPuXi4oKwsDCNW8wVCgWCgoIyXKjOGllUMsCRASIi+lzNmjXTrER469Yt/PDDDyJFZHqYDBARkcUbP348qlatqtH2xx9/YOfOnSJFZFrkYgeQPYkAzgI4C6XyFI4fVyBXLkAiAeLjgWvXABeXqwD+D0AVALxkQERkjWxsbBAWFoZKlSppfHDs0aMHLl26BC8vLxGjE59E0GFJptjYWLi6uiImJgYuLi7GiCsT9wAs/fj1FoAEgiCDRKLQ6JWcDMhkEkilAoBcAHoA6AegpHHDJSIik7B8+XL06tVLo61x48aIjIyERCIRKaqco+v528wuE7wG0AGAH4BfoEoEAEBIkwgAgI0NPiYCAPAOwO8ASgFoBuBJTgdLREQmpkePHmjZsqVG2549e7Bo0SJxAjIRZpQMbAFQAsAmAAIAfRaNSN1mD1RJwcqP+yIiImsgkUiwbNmyNJcFhg8fjqtXr4oUlfjMIBlQAhgCoA1UIwGGWDlKASAeQDcAnQEkG2CfRERkDvLkyYOVK1dqtCUkJCAoKAhJSUniBCUyE08GlAB6Afjt4/8N+Sk+dV9roUo0mBAQEVmLb7/9FoMHD9Zo+++///DTTz+JFJG4TDwZGA1gRQ4fQwDwF4Ce4CUDIiLrMXPmTJQtW1ajbfbs2Th06JA4AYnIhJOBvQBmG+lYAoDVADYY6XhERCQ2BwcHhIeHw9bWVt0mCAI6d+6MN2/eiBiZ8ZloMhALoCuMG54EqtsOXxjxmEREJCZ/f39MmzZNo+3x48fo378/dLjz3mKYaDLwE1QnZaURjykAiINqsiIREVmLH374AfXq1dNoW79+PdauXavRplAAV68CR44AR48CN28CSmOepnKQCS469BaAN4CEHD5ORiQAHgLIL9LxiYjI2B4/fozy5cvj7du36jYXFxccPXoRR44Uwpo1wPnzQGKi5nYODkCVKkC3bkD79qr/mxIzXnRoNVTLDOvuv/+AwECgYEHVC+HuDtSoAYSF6XN8KYA/9NmQiIjMVP78+bF06dJPWmSIje2LihXzYeBA4OTJtIkAAHz4APz7L9C9O+DlBSxebJ6jBSaYDPye5S3evgUKFACmTwciI4HVq4HChYHOnYGpU7O6txQAi2CY9QyIiMhctGvXDl26dAFQGMAJADOgVNpDEABtY+ipJ//YWKB/f6BePeD585yP15BM7DLBCwCGKxZRvTrw9Cnw8KE+W18GUDbTXkREZDnOnn2HqlUToVS6ALDRax9yOeDrq5pXkF/kK85mepngrEH3lieP6kXRj2FjISIi0xYdDTRvngsSiTv0TQQA1UTDJ0+ABg2A9+8NF19OMsFkQKb31kql6kV49QpYtAj4+29g1Ch99mQDJgNERNZl8GDgxQsgJSX71QsVCuDWLcBcFjQ0sWTgLlSz+fXTv7+qUqGnJzBsGPDbb0CfPvrsKRnAHb3jICIi87J3LxAeDqRonS72DsBQAD4A7AFUBLA+w95KJTBvHnDunOHizCkmlgwkIDtrC4wdC5w+DUREqGZ2DhwI/PKLvnszk7EdIiLKtl9+AWSZDky3BrAKQAiA3QC+BNABqho36ZPJgPnzDRRkDjKxCYRBUC0JbJiZ/P36AcuXqyYR5s2b1a0bQLUkMhERWbJ794CiRTPrFQkgEKoTf4dP2hsBuALV+jTpZxM2Nqq7C9zdsx9rVpnpBEInZOcyweeqVlVdt7l7N6tbSgDkMlgcRERkug4c0KXXNqjOC20/a+8G4CmAkxlumZwMHDumb3TGYWLJQFkYcgnigwcBqVSXjO9zMgDlDBYHERGZrrNnVZ/etbsMoDSAz29Rq/DJ4+mTy4EzZ/QOzyj0vvEuZ3wBfZKB3r0BFxfVSEC+fMDr18CmTcCGDcCIEfpcIlB8jIWIiCzdjRuqT+/aRQFI75Ol+yePp08QVHUMTJmJJQMVoRqiz1qlqBo1gNBQYNUq1WqEuXIB/v7AmjVAp076xsJkgIjIGnz4oGtPbZexM35MqQSSkrISkfGZWDKQC0AdAEeQlUmE3bqpvgxBqQRevfLAggVLIJfbQCaTQSaTQS6Xp/leo0YN+Pv7G+bAREQkCkdHXXp5IP1P/9Efv2c8O1AqBeztsx6XMZlYMgAAgwAcEjWCn36KwrJl0zPtJ5fLcePGDRTN+qQEIiIyEaVLA//3f5ldKigPYB1Ul5E/PXVe+vhd+zyzkiWzE2HOM7EJhADQHEA+0Y7+/j2wNuNbRjUoFArocGcmERGZsC++0GXOQCuoFh3a8ln7KqgWIaqW4ZYpKaoyx6bMBEcG5AAmABhg9CMrlcDPPwPx8br1b9GiBfz8/HI2KCIiylH16gESifbKhEAAgIYA+gGIBVAMqpGCPQDCoG0pfTs7oGZNg4WbI0xwZAAA+gL4GsbMVZRKKa5cAWbO1K2/RCLB5MmTczYoIiLKcQULAk2a6FLYbiuAzlB9YG0M1doC66BaMC99crlqIrurq4GCzSEmmgxIAayEKhkw3CJEWo8olWDPno46DBWpfP/996hQoULmHYmIyOSNGKFapE67XADmA3gGIBHABQDttW6hVAJDhxogwBxmoskAoLqfM9yIx1uMwYNXoFKlSjr1zpUrF6KjozPvSEREJq9SpVh4eGyFaoKgYUgkwJgxQDkzWMPOhJMB4H9FISTI2RGCXwH0gp2dHdavXw8nJ6dMt1i+fDmKFCmCSZMmITY2NgdjIyKinJSUlITvvvsOUVFdATyCqnJt9sjlQIUKLGFsQJ2huk7jCMPOIZADsAUQCmCIurVEiRJYuHBhhltJpVLYfFy3MjY2FhMnTkSRIkXw888/I17XmYdERGQSBEFAz549sW/fPgBxAOoCeI7sJAQyGeDnB/zzj2ryoDkwg2QAAFoCuAbgGwPuswpUa0l3TfNIly5d0LFjx3S36tOnD+7cuYNevXpB9rHeZXR0NEaNGgU/Pz8sWLAAiYmJBoyTiIhyyk8//YQ1a9Z80vIAQHUAqZWFdL99XPJxADsgQFWYyNPTQEEag6CDmJgYAYAQExOjS/ccpBQEIVQQhKKCIEAQBPnH77p8yT5+zy8IwgJBEBRajxQTEyMULVpUgOqdIAAQ7O3thSdPnqj73Lp1S+jUqZMgkUg0+hUoUED4448/hKSkJEM+eSIiMqClS5dq/O3W/JIIQD9BLo8VAEGQSgVBdfNh2i+ZTPXd01MQwsIEQakU+5n9j67nbzMZGUglgeqT/G0A+wA0BeDwyeM2n32lsoPq/tBdAO4DGAht94QCgIuLC9atWwf5J/ea9O/fHz4+Pur/FytWDGvWrMHly5fRpk0bdfujR4/Qu3dvlC5dGmFhYUhJ0X1pZSIiynm7du1Cv379tPQQUKDALty8GYewMKBhQ8DNLW2vPHlUIwFbtgCPHwNBQf8bITAnEkHIfAm92NhYuLq6IiYmBi4uLsaIKwtSANwEcBbAdQDvoUrsHACUgKrgUHplJ3WzYMECDB48GAUKFMDZs2eRV0sJxHPnzmHChAmIiIjQaC9btiwmT56MVq1aQWKO7xIiIgty+vRpfPPNN3j//n2Gfdzc3HD06FGULVtW3SYIwJMnQFSU6oSfNy/g7W2MiPWn6/nbApKBnHf37l24u7vDLb20MB3Hjh3D+PHjcfDgQY32ypUrY8qUKQgICGBSQEQkgrt376JGjRp4+fJlhn1sbW3xzz//oE6dOkaMLGfoev42s8sE4ihatKjOiQAA1KxZEwcOHMD+/ftRvXp1dfu5c+cQGBiIWrVqpUkUiIgoZ71+/RqNGzfWmggAwKpVqywiEcgKJgM5qF69ejh27Bh27dqFihUrqtuPHTuGevXqoUGDBjhx4oR4ARIRWYkPHz6gefPmuHXrltZ+s2fPRvv22lcVtERMBnKYRCJBYGAgzp49i82bN6N06dLqx/bv348aNWqgadOmOH/+vIhREhFZrpSUFAQFBeH48eNa+w0aNAg//vijkaIyLUwGjEQqleK7777DpUuXsGbNGhQtWlT9WEREBCpXroy2bdvi2rVrIkZJRGRZBEHAsGHDsG3bNq39WrVqhXnz5lntfC4mA0Ymk8nQqVMnXL9+HX/88Qfy58+vfmzz5s0oV64cunTpgjt37ogYJRGRZZg7dy4WLFigtU+NGjUQHh6uXkjOGjEZEImNjQ169eqFW7duYf78+ciXLx8AQKlUYs2aNShVqhT69OmDR48eiRwpEZF5Wr9+PYYPH661T/HixbFz5044ODho7WfpmAyIzN7eHoMHD8adO3cwc+ZM5M6dGwCgUCjwxx9/oFixYhg6dChevHghcqRERObj8OHDCA4O1trH09MTe/bsQZ48eYwUleliMmAinJycMGrUKNy7dw8TJ06Es7MzAFU1rfnz56No0aIYPXo0yyYTEWXi6tWraNmyJZKSkjLs4+joiF27dmnM37JmTAZMjKurK0JCQnDv3j2MGjVKPXT1/v17zJo1i2WTiYi0ePr0KQICAvD27dsM+0ilUmzYsAFffvml8QIzcUwGTJSHhwdmzpyJu3fvYvDgwbC1tQWQtmyytuU0iYisSWxsLJo0aYKHDx9q7bdo0SI0bdrUSFGZByYDJs7Lywvz58/HrVu30i2bXLRoUZZNJiKrl5ycjDZt2uDChQta+40bNw59+vQxUlTmg8mAmShYsCD++OMPXL9+HZ06dVLfC/vixQsMHjwYxYsXx/Lly5GcnCxypERExiUIAnr16oW9e/dq7de5c2dMmTLFSFGZFyYDZia1bPKlS5fw3XffqdsfPXqEXr16oUyZMggPD2fZZCKyGhMnTsSqVau09qlfvz6WL19utYsKZYbJgJkqW7YsNm/ejLNnz6JJkybq9tu3b6NTp07w9/fH1q1boUNRSiIis7V8+XJMnjxZa58KFSpgy5Yt6rlXlBaTATNXuXJlRERE4N9//0XdunXV7VeuXMF3332HKlWqIDIykkkBEVmcyMhI9O3bV2uf/PnzIzIyEq6urkaKyjwxGbAQLJtMRNbk7NmzaNeundZLoq6urti9ezd8fX2NGJl5YjJgYVg2mYgs3b179xAYGIj4+PgM+9jY2GDbtm0oV66cESMzX0wGLBDLJhORpYqKikJAQECmS7SvXLlS49IpacdkwIKxbDIRWZIPHz6gefPmuHHjhtZ+s2bNQseOHY0UlWVgMmAFdC2bfPfuXRGjJCLKWEpKCjp37oxjx45p7de/f3+MGDHCSFFZDiYDViSzssklS5ZEnz598PjxY5EjJSLSNHz4cGzZskVrnxYtWuC3337jWgJ6YDJghVg2mYjMybx58/Drr79q7VOtWjWsXbtWvWQ7ZY1E0OEG9NjYWLi6uiImJgYuLi7GiIuMKCYmBvPmzcPcuXMRFxenbnd0dMTgwYMxYsQIuLu7ixghEVmrjRs34vvvv9fap1ixYjh27Bjy5s1rpKjMh67nb44MEFxdXTFx4kTcu3cPI0eO1CibPHPmTBQpUgSTJ09m2WQiMqojR46gc+fOWvvkyZMHu3fvZiKQTUwGSM3DwwOzZs3C3bt3MWjQII2yySEhISybTERGc+3aNbRo0QJJSUkZ9nFwcMCuXbtQrFgxI0ZmmZgMUBpeXl747bffWDaZiETx7NkzBAQE4M2bNxn2kUqlWL9+PapVq2bEyCwXkwHKEMsmE5GxxcXFITAwEA8ePNDab+HChWjevLmRorJ8TAYoUyybTETGkJycjLZt22a6Ouro0aMzLVBEWcNkgHTGsslElFMEQUDfvn3x999/a+0XFBSEadOmGSkq68FkgLJMl7LJu3fvZlJARDqbPHkyVqxYobVPvXr1sGLFCkilPHUZGn+ipDdtZZObNGmCr7/+GocOHRIvQCIyCytWrMDEiRO19ilfvjy2bt2qvsuJDIvJAGVbRmWTU0cOWDaZiDKyZ88e9O7dW2sfX19fREZGwtXV1UhRWR8mA2QQn5ZN3rRpU7plk5s1a4b//vtPvCCJyKScO3cObdu21Tr52MXFBbt379YosEaGx2SADEoqlaJNmza4dOkSVq9erVE2edeuXahUqRLatWvHsslEVu7+/fsIDAzEu3fvMuxjY2ODbdu2oXz58kaMzDoxGaAcIZPJ0LlzZ1y/fh1Lly7VyOo3bdrEsslEViw6OhoBAQF4/vy51n6hoaGoV6+ekaKybkwGKEfZ2Nigd+/e6rLJnp6eAFg2mchaJSQkoEWLFrh+/brWftOnT0dQUJCRoiImA2QUqWWT7969y7LJRFZKqVSiS5cuOHr0qNZ+ffv2xejRo40UFQFMBsjInJycMGrUKNy7dw8hISFwdnYGACQmJmL+/PkoWrQoxowZg+joaJEjJSJDGzFiBDZt2qS1T7NmzbBgwQL18udkHEwGSBQsm0xkXX799VfMnTtXa5+qVati3bp1kMvlRoqKUjEZIFGxbDKR5duyZQt++OEHrX2KFi2Kv/76C05OTkaKij7FZIBMAssmE1mmf//9F0FBQVqXJ/fw8MCePXvUE4zJ+JgMkEnJrGxyiRIl8Oeff7JsMpEZuH79Opo3b641ibe3t8euXbtQvHhxI0ZGn2MyQCYpo7LJDx8+RM+ePVk2mcjEPX/+HAEBAVonA0skEqxbt06jtgmJg8kAmbTUsslnzpxh2WQiM/Hu3TsEBgbi/v37WvstWLAALVu2NEpMpB2TATILX3zxBSIiInD06FF888036naWTSYyLQqFAu3atcO5c+e09hs5ciQGDBhgpKgoM0wGyKx89dVXOHjwIMsmE5kgQRDQr18/7N69W2u/Dh06YMaMGUaKinTBZIDMEssmE5meqVOnYvny5Vr7fPPNNwgNDYVUytOPKeGrQWaLZZOJTMfKlSsxYcIErX3Kli2Lbdu2wc7OzkhRka6YDJDZY9lkInH9888/6NWrl9Y+Pj4+iIyMhJubm3GCoixhMkAWg2WTiYzvv//+w3fffQeFQpFhH2dnZ0RGRqJgwYJGjIyygskAWRyWTSYyjocPH6JJkyZ49+5dhn3kcjm2bNkCf39/I0ZGWcVkgCwWyyYT5Zw3b94gICAAz54909rvzz//RMOGDY0UFemLyQBZPJZNJjKsxMREtGrVClevXtXab+rUqejSpYuRoqLsYDJAVoNlk4myT6lUIjg4GIcPH9bar3fv3hg7dqyRoqLsYjJAVie1bPKdO3fSLZtctGhRzJ49m2WTidIxatQobNiwQWufwMBALFy4UF1ojEwfkwGyWt7e3umWTY6KisLIkSPh5+eH33//nWWTiT5asGABfvnlF619qlSpgvXr10MulxspKjIEJgNk9T4tmxwUFKT+NPP8+XMMGjSIZZOJAGzbtg1DhgzR2qdIkSLYtWsXcuXKZaSoyFCYDBB9VKxYMYSFhbFsMtFnjh07ho4dO2otBObu7o7du3cjX758RoyMDIXJANFnWDaZ6H9u3LiBZs2aISEhIcM+9vb2+Ouvv1CyZEkjRkaGxGSAKAMsm0zW7sWLFwgICNB6261EIkF4eDhq1qxpxMjI0JgMEGWCZZPJGsXHx6Np06a4d++e1n7z589H69atjRQV5RQmA0Q6yqxscsOGDVk2mSyCQqHA999/jzNnzmjtN3z4cAwaNMhIUVFOYjJAlAXayibv27ePZZPJ7AmCgP79+yMiIkJrv++//x6zZs0yUlSU05gMEOmBZZPJUk2fPh3Lli3T2qd27dpYuXIlpFKeQiwFX0mibNClbHJwcDDLJpNZWL16NcaPH6+1T+nSpbF9+3bY29sbKSoyBiYDRAbwadnkX3/9VaNs8urVq1GyZEn07duXZZPJZO3duxc9evTQ2sfb2xu7d+9WVwAly8FkgMiA7O3tMWTIENy9exczZszQKJu8dOlSFCtWDMOGDWPZZDIpFy5cwHfffQeFQpFhn1y5ciEyMhKFChUyYmRkLEwGiHKAk5MTRo8enW7Z5F9//ZVlk8lkPHr0CE2aNEFcXFyGfeRyObZs2aJxFw1ZFiYDRDkotWzy3bt3WTaZTM7bt28REBCAp0+fau23bNkyNGrUyEhRkRiYDBAZQZ48eVg2mUxKYmIiWrVqhStXrmjtN3nyZHTt2tU4QZFomAwQGdGnZZN79uzJsskkCqVSia5du2a6cmbPnj0zvbuALAOTASIRFCxYEMuWLcu0bLK2CV1E+hozZgzWr1+vtU9AQAAWLVqkfm+SZWMyQCSizMomly5dGmvXrmXZZDKYhQsX4ueff9bap3Llyti4cSNsbGyMFBWJjckAkQnQVjY5KCgI/v7+2LZtGyskUrZs374901oChQsXRkREBHLlymWkqMgUMBkgMiHayia3bt0aX375Jcsmk16OHz+ODh06aH3v5M6dG7t374aXl5cRIyNTwGSAyARlVDb57NmzLJtMWXbr1i00a9YMCQkJGfaxs7PDzp07UapUKSNGRqaCyQCRCWPZZMquly9fIiAgAFFRURn2kUgkCA8PR61atYwYGZkSJgNEJu7TsskbN27U+OTGssmkTXx8PJo2bYo7d+5o7Tdv3jyNCaxkfZgMEJkJqVSKtm3b4vLlyxmWTf7+++9x/fp1EaMkU6FQKNC+fXucPn1aa79hw4ZhyJAhRoqKTBWTASIzo61s8saNG1G2bFmWTbZygiBg0KBB2LVrl9Z+bdu2xS+//GKkqMiUMRkgMlMsm0wZmTVrFpYsWaK1T61atbB69WpIpTwNEJMBIrPHssn0qbCwMIwZM0Zrn1KlSmHHjh2wt7c3UlRk6pgMEFkIXcomjx07lmWTLdj+/fvRvXt3rX28vLywe/duuLu7GykqMgdMBogsjLayyTNmzECRIkUwZcoUlk22MBcvXkTr1q2RnJycYR8nJydERESgcOHCxguMzAKTASILpa1s8oQJE1g22YI8fvwYTZo00ZrgyWQybN68GZUrVzZiZGQumAwQWTiWTbZsMTExCAgIwJMnT7T2++OPP9C4cWMjRUXmhskAkZVg2WTLk5SUhFatWuHy5cta+4WEhGQ6l4CsG5MBIivzadnk1q1bq9tTyyaXKVMGa9euhVKpFDFKyoxSqUT37t1x8OBBrf26deuGkJAQI0VF5orJAJGVKlu2LLZs2YIzZ84gICBA3X7r1i2WTTYD48aNQ3h4uNY+3377LZYuXaoeBSLKCJMBIiv3xRdfIDIyMk3Z5MuXL6vLJu/Zs4dJgQlZvHgxZs6cqbVPpUqVsGnTJtjY2BgpKjJnTAaICICqbPKBAwewb98+VKtWTd1+9uxZBAQEoHbt2jh8+LCIERIA7Ny5EwMHDtTap2DBgoiIiFCvNUGUGSYDRKQmkUhQv359HD9+HH/99Rf8/f3Vj6WOHDRs2BAnT54UMUrrdfLkSbRv317rfA43Nzfs2bMH3t7eRoyMzB2TASJKQyKRoGnTpjh37ly6ZZOrV6+O5s2bs2yyEd2+fRtNmzbFhw8fMuxja2uLnTt3onTp0kaMjCwBkwEiypC2ssl//fUXyyYbyatXrxAQEIDXr19r7bdmzRp8/fXXRoqKLAmTASLKlC5lk7t27cqyyTng/fv3aNasGW7fvq2135w5c9CuXTsjRUWWhskAEelMW9nkVatWoWTJkujXrx/LJhtISkoKOnTokOkcjSFDhmDYsGFGioosEZMBIsoybWWTlyxZgmLFiuGHH37Ay5cvRY7UfAmCgMGDB2Pnzp1a+3333XeYM2cO1xKgbGEyQER601Y2ed68eeqyyW/evBE5UtN0/fp1REZGpvvJf/bs2Vi0aJHW7WvWrIk1a9ao600Q6YvJABFl26dlk0eMGKEumxwfH69RNjkuLk7kSE2DUqnE4MGDUaZMGQQGBqJ69eqoX78+Hj58CABYu3YtRo0apXUfJUqUwM6dO9U/a6LskAg6LCsWGxsLV1dXxMTEwMXFxRhxEZEZe/bsGaZPn46lS5ciOTlZ3e7h4YHRo0ejf//+cHR0FDFCcYWFhaFz585p2r29vTFp0iQMGDBA4+f2OU9PT5w4cQJFihTJyTDJAuh6/mYyQEQ55sGDB5g6dSpCQ0ORkpKibvf29sa4cePQs2dP2NnZiRihOMqXL59ppcGMODk54dChQ6hSpYqBoyJLpOv5m5cJiCjHFCpUCMuWLcO1a9c0yiY/e/YMAwcORIkSJbBixQqrKpv87NkzvRMBmUyGjRs3MhEgg2MyQEQ5rnjx4ggLC8PFixfTlE3u0aMHypQpg3Xr1llF2eT9+/frve3ixYvRpEkTA0ZDpMJkgIiMply5chmWTe7YsSP8/f2xfft2i66QuG/fPr22++mnn9CrVy8DR0OkwmSAiIxOW9nkVq1aoWrVqhZZNlkQBL2Sgfz582PkyJE5EBGRCpMBIhJNRmWTU0cOLK1s8s2bN/HkyZMsb/f48WPUrVsXr169yoGoiJgMEJHIdCmb3KhRI4som6zvJQJAlSB169bN4kZLyDQwGSAik6CtbPLevXvVZZMvXLggYpTZk51kAAAiIiIsIiki08NkgIhMSmZlkytWrGiWZZMVCgUOHjyY7f3oc5mBKDNMBojIJH1eNtnX11f9mDmWTT579ixiYmKyvZ+yZcsaIBoiTUwGiMikpZZNvn37tlmXTc6s+qAuunTponH5hMhQmAwQkVlILZt8584dsyybHBYWpve2efLkwZw5cxAaGmrAiIj+h7UJiMgsvX37FvPmzcPcuXPx7t07dbuTkxOGDBmC4cOHqxMGUyCVSrN8J0CdOnXQp08ftG7d2iprOFD2sVAREVmF169f4+eff8bvv/+ODx8+qNtdXV0xfPhwDBkyBM7OzgY5liAIuPf2Hs48PYNzz87hadxTJCuT4SB3QHH34qjiUwVf+HwBdwf3NNum1mXIjJubG4KDg9GnTx+ULl3aIHGT9WIyQERWJbOyyQMGDICDg4Ne+45PisfaS2vx26nfcPmlqsiQjdQGSkEJAQKkEtWn/hQhBVKJFM1LNsfALweiXpF66iSgcOHCePDgQYbHqFGjBvr06YN27drpHSfR55gMEJFVMnTZ5K3XtqLXX70Q/SEaUkihRObFlORSORRKBarnr47VLVejuEdx/Pfff6hWrRqSkpLU/WQyGbp06YIhQ4ZoLLZEZChMBojIqt26dQuTJk3C2rVrNa7VFypUCBMmTECXLl0gl8sz3P5d0jv02NEDG69uhAQSCMj6yn9yqRxSiRRzG83FgKoD8ObNG4SEhODWrVsoV64cJkyYYLBLGETpYTJARARV8aOQkBBs3bpVo7148eKYNGkSvv/+e0ilmjdWvU14iwarG+C/5/8hRUiBIYypNQbT6k3Tee4AkSHoev7mrYVEZNGyWjY5UZGIgPAAgyYCADDj6AzM+neWwfZHZEgcGSAiq/Lvv/9i/PjxOHTokEZ7lSpVMHXqVByWH8bMozP1uiyQGQkkONHzBKr6VjX4vonSw8sEREQZEAQBBw4cwLhx4zQL//gA6AUgh0byZRIZiuYuiov9LsJebp8zByH6BC8TEBFlIMOyyQ0BnQYEEgH8A2A1gJ8BTASgQw2iFCEFt6NvY8X5FfoFTpRDmAwQkdX6tGzyvDXzgCLQ7a/iewBnAaQA0KNUwIJTC7K8GiFRTmIyQERWTyqV4mHeh5BLMr7VUIMbgNEAugGon7VjCRBw/fV1HHt0LGsbEuUgJgNERAD23t0LhaDQrbME2ZpXIJPIcOj+If13QGRgTAaIyOolKhJx/fV1ox1PgIAzT88Y7XhEmWEyQERW70bUDSiUOo4KGIBSUOLcs3NGOx5RZpgMEJHVi0uMM/4xk4x/TKKMMBkgIqsnxhLBUgn//JLp4LuRiKyem72bVRyTKCNMBojI6pXwKAE7me5ljbNLJpHhS58vjXY8oswwGSAiqyeXylE+X/msbXQLwBUANz/+/9XH/18BkKR9UwECvvD5IqthEuUYHVfYICKybIHFA3H+2XndKxXuAhDzyf+vfvwCgCEAbDPeVCko0civkV5xEuUEJgNERAB6Vu6JKf83RfcNhul3HKlEiqo+VVEhXwX9dkCUA3iZgIgIQH6X/GhRsoXuSxLrSSkoMajaoBw9BlFWMRkgIvrol0a/QC7LuWRALpGjZv6aaF+ufY4dg0gfTAaIiD4qmrsoZjecnWP7l0llWNVqFdcYIJPDdyQR0Sf6f9kfbcu0NfgJWwIJQluEoph7MYPul8gQmAwQEX1CKpEirHUYWpRsAUl2ShN+sj8JJFjefDk6lO9ggAiJDI/JABHRZ2xlttjUdhPG1x4PqUQKmUSm135kEhnyOOZBZFAkulfqbuAoiQyHyQARUTpkUhkm152M071Oo0zeMgBUixPptK1EBgkk6FShE64PuI7GxRrnZKhE2cZ1BoiItKjsXRkX+l7A/z34Pyw8vRDbr29HsjIZgCo5kEACAYK6BLKHgwd6Ve6FPlX6oLBbYREjJ9IdkwEiokxIJBLUKVwHdQrXQXJKMq68uoKzT8/i2btnSE5Jhr3cHiU8SqCKTxUUdC0oShVEouxgMkBElAU2MhtU9KqIil4VxQ6FyGA4Z4CIiMjKMRkgIiKyckwGiIiIrByTASIiIivHZICIiMjKMRkgIiKyckwGiIiIrByTASIiIivHZICIiMjKMRkgIiKyckwGiIiIrByTASIiIivHZICIiMjKMRkgIiKyckwGiIiIrJxcl06CIAAAYmNjczQYIiIiMpzU83bqeTwjOiUDcXFxAIACBQpkMywiIiIytri4OLi6umb4uETILF0AoFQq8fTpUzg7O0MikRg0QCIiIsoZgiAgLi4OPj4+kEoznhmgUzJARERElosTCImIiKwckwEiIiIrx2SAiIjIyjEZICIisnJMBoiIiKwckwEiIiIrx2SAiIjIyv0/8A6i+Oi5EX8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício Grafo Lista de Adjacência\n",
    "\n",
    "Modifique o exemplo anterior para criar um exemplo mais \n",
    "completo, considerando algumas adições:\n",
    "\n",
    "    - Atributos de Vértices e Arestas: Adicione informações adicionais \n",
    "        a alguns vértices e arestas, como peso, cor, etc.\n",
    "    \n",
    "    - Cálculo de Alguns Parâmetros do Grafo: Calcule algumas \n",
    "        propriedades do grafo, como grau médio, densidade, entre outras.\n",
    "        \n",
    "    - Exibição em Formato Tabular de Informações: Use o pandas para exibir \n",
    "        as informações de vértices e arestas em formatos de tabela.\n",
    "        \n",
    "    - Personalização da Visualização: Personalizaremos ainda mais a visualização\n",
    "        do grafo.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "import networkx as nx  # Importando a biblioteca NetworkX para manipulação de grafos.\n",
    "import numpy as np     # Importando a biblioteca Numpy para cálculos numéricos.\n",
    "import matplotlib.pyplot as plt  # Importando a biblioteca Matplotlib para visualização gráfica.\n",
    "import pandas as pd    # Importando a biblioteca Pandas para manipulação de dados em formatos tabulares.\n",
    "\n",
    "# Criando um grafo direcionado (com setas para indicar a direção das arestas).\n",
    "grafo = nx.DiGraph()\n",
    "\n",
    "\n",
    "# Definindo um dicionário para armazenar os atributos de cada vértice.\n",
    "# A chave do dicionário representa o ID do vértice (um número inteiro neste caso).\n",
    "# O valor associado a cada chave é outro dicionário contendo os atributos do vértice,\n",
    "# especificamente a \"cor\" (um string representando a cor em inglês) e \"tamanho\" (um número inteiro).\n",
    "\n",
    "vertices_atributos = {\n",
    "    0: {\"cor\": \"blue\", \"tamanho\": 300},   # Vértice 0 terá cor azul e tamanho 300\n",
    "    1: {\"cor\": \"green\", \"tamanho\": 400},  # Vértice 1 terá cor verde e tamanho 400\n",
    "    2: {\"cor\": \"red\", \"tamanho\": 500},    # Vértice 2 terá cor vermelha e tamanho 500\n",
    "    3: {\"cor\": \"yellow\", \"tamanho\": 600}, # Vértice 3 terá cor amarela e tamanho 600\n",
    "    4: {\"cor\": \"orange\", \"tamanho\": 700}  # Vértice 4 terá cor laranja e tamanho 700\n",
    "}\n",
    "\n",
    "# Iterando sobre o dicionário 'vertices_atributos' para adicionar cada vértice ao grafo.\n",
    "# Para cada iteração, 'vertice' recebe o ID do vértice (chave do dicionário) e 'atributos'\n",
    "# recebe o dicionário associado contendo os atributos \"cor\" e \"tamanho\".\n",
    "for vertice, atributos in vertices_atributos.items():\n",
    "    \n",
    "    # Adicionando o vértice ao grafo com os atributos definidos.\n",
    "    # O operador '**' é utilizado para desempacotar o dicionário 'atributos' como argumentos nomeados.\n",
    "    grafo.add_node(vertice, **atributos)\n",
    "    \n",
    "\n",
    "# Definindo um dicionário para armazenar os atributos de cada aresta.\n",
    "# A chave do dicionário representa a tupla (origem, destino) de cada aresta.\n",
    "# O valor associado a cada chave é outro dicionário contendo o atributo \"peso\" da aresta.\n",
    "\n",
    "arestas_atributos = {\n",
    "    (0, 1): {\"peso\": 5},  # A aresta de 0 para 1 possui peso 5\n",
    "    (0, 2): {\"peso\": 3},  # A aresta de 0 para 2 possui peso 3\n",
    "    (1, 3): {\"peso\": 2},  # A aresta de 1 para 3 possui peso 2\n",
    "    (2, 4): {\"peso\": 7},  # A aresta de 2 para 4 possui peso 7\n",
    "    (3, 4): {\"peso\": 4}   # A aresta de 3 para 4 possui peso 4\n",
    "}\n",
    "\n",
    "# Adicionando as arestas (sem os atributos) ao grafo.\n",
    "# Utilizamos o método 'keys()' para obter apenas as tuplas (origem, destino) das arestas \n",
    "# e adicioná-las ao grafo.\n",
    "grafo.add_edges_from(arestas_atributos.keys())\n",
    "\n",
    "\n",
    "# Iterando sobre o dicionário 'arestas_atributos' para atualizar os atributos de cada aresta no grafo.\n",
    "# Para cada iteração, 'aresta' recebe a tupla (origem, destino) da aresta e 'atributos' \n",
    "# recebe o dicionário associado contendo o atributo \"peso\".\n",
    "for aresta, atributos in arestas_atributos.items():\n",
    "    \n",
    "    # Atualizando os atributos da aresta específica no grafo.\n",
    "    # Utilizamos o método 'update()' para modificar/adicional o atributo \"peso\" à aresta no grafo.\n",
    "    grafo[aresta[0]][aresta[1]].update(atributos)\n",
    "\n",
    "\n",
    "# Calculando e imprimindo algumas propriedades do grafo.\n",
    "\n",
    "# Calculando o grau médio do grafo. \n",
    "# O método 'degree()' retorna um objeto DegreeView com os graus de cada vértice.\n",
    "# Convertendo isso para um dicionário e, em seguida, obtendo seus valores (graos).\n",
    "# Finalmente, usando a função 'mean()' do numpy para calcular a média desses graus.\n",
    "\n",
    "# Obtendo os graus (número de arestas) de todos os vértices do grafo.\n",
    "graus = dict(grafo.degree())\n",
    "\n",
    "# Extraindo apenas os valores (quantidades de arestas) do dicionário.\n",
    "valores_graus = list(graus.values())\n",
    "\n",
    "# Calculando a média dos graus dos vértices.\n",
    "media_graus = np.mean(valores_graus)\n",
    "\n",
    "# Imprimindo o grau médio.\n",
    "print(f\"Grau Médio: {media_graus}\")\n",
    "\n",
    "\n",
    "# Calculando a densidade do grafo.\n",
    "# A densidade é uma medida que indica quão conectado é o grafo.\n",
    "# Um valor de 1 significa que o grafo é completamente conectado, enquanto um valor de 0 indica que não há conexões.\n",
    "densidade_do_grafo = nx.density(grafo)\n",
    "\n",
    "# Imprimindo o valor da densidade.\n",
    "print(f\"Densidade: {densidade_do_grafo}\\n\")\n",
    "\n",
    "\n",
    "# Imprimindo informações dos vértices e arestas em formato\n",
    "# tabular usando a biblioteca pandas.\n",
    "\n",
    "# Mostrando os atributos dos vértices em formato de tabela.\n",
    "# Convertendo o dicionário 'vertices_atributos' em um DataFrame do pandas.\n",
    "# A transposição (.T) torna os vértices como índices e os atributos como colunas.\n",
    "print(\"Informações dos Vértices:\")\n",
    "vertices_df = pd.DataFrame(vertices_atributos).T\n",
    "print(vertices_df, \"\\n\")\n",
    "\n",
    "# Mostrando os atributos das arestas em formato de tabela.\n",
    "# Convertendo o dicionário 'arestas_atributos' em um DataFrame do pandas.\n",
    "# Novamente, a transposição (.T) torna as arestas como índices e os atributos como colunas.\n",
    "print(\"Informações das Arestas:\")\n",
    "arestas_df = pd.DataFrame(arestas_atributos).T\n",
    "print(arestas_df, \"\\n\")\n",
    "\n",
    "# Desenhando o grafo\n",
    "# Preparando os atributos visuais para a representação gráfica do grafo.\n",
    "\n",
    "# Inicializando a lista para armazenar as cores dos vértices.\n",
    "cores = []\n",
    "\n",
    "# Iterando por todos os vértices e seus atributos no grafo.\n",
    "for vertice, atributos in grafo.nodes(data=True):\n",
    "    \n",
    "    # Obtendo a cor do vértice atual a partir de seus atributos.\n",
    "    cor_do_vertice = atributos[\"cor\"]\n",
    "    \n",
    "    # Adicionando a cor à lista de cores.\n",
    "    cores.append(cor_do_vertice)\n",
    "    \n",
    "    \n",
    "# Inicializando a lista para armazenar os tamanhos dos vértices.\n",
    "tamanhos = []\n",
    "\n",
    "\"\"\"\n",
    "    grafo.nodes(data=True):\n",
    "    \n",
    "        Este é um método da biblioteca networkx que retorna todos\n",
    "        os vértices (nós) de um grafo.\n",
    "        \n",
    "        O argumento data=True indica que, além do vértice em si, \n",
    "        queremos também os atributos associados a esse vértice. Se esse \n",
    "        argumento fosse False ou não estivesse presente, obteríamos apenas \n",
    "        os vértices sem seus atributos.\n",
    "        \n",
    "        Portanto, grafo.nodes(data=True) retorna uma sequência de pares, onde\n",
    "        cada par contém um vértice e seus atributos.\n",
    "\n",
    "    for vertice, atributos in ...:\n",
    "    \n",
    "        Este é um loop for que itera sobre cada par (vértice, atributos) retornado\n",
    "        por grafo.nodes(data=True).\n",
    "        \n",
    "        vertice é uma variável que armazena o vértice atual da iteração.\n",
    "        \n",
    "        atributos é uma variável que armazena os atributos do vértice atual\n",
    "        da iteração (geralmente na forma de um dicionário).\n",
    "\"\"\"\n",
    "# Iterando por todos os vértices e seus atributos no grafo.\n",
    "for vertice, atributos in grafo.nodes(data=True):\n",
    "    \n",
    "    # Obtendo o tamanho do vértice atual a partir de seus atributos.\n",
    "    tamanho_do_vertice = atributos[\"tamanho\"]\n",
    "    \n",
    "    # Adicionando o tamanho à lista de tamanhos.\n",
    "    tamanhos.append(tamanho_do_vertice)\n",
    "    \n",
    "    \n",
    "# Inicializar uma lista vazia para armazenar os pesos das arestas.\n",
    "# Os pesos representam os valores associados a cada aresta. Por exemplo, \n",
    "# em um grafo de estradas, o peso pode representar a distância entre as cidades.\n",
    "pesos = []\n",
    "\n",
    "# Iterar sobre todas as arestas do grafo.\n",
    "# A função 'edges' do grafo, quando chamada com o \n",
    "# argumento 'data=True', retorna uma lista de tuplas.\n",
    "# Cada tupla contém o nó de origem, o nó de destino e um \n",
    "# dicionário de atributos associados à aresta.\n",
    "for origem, destino, atributos in grafo.edges(data=True):\n",
    "    \n",
    "    # Obter o peso da aresta atual do dicionário de atributos.\n",
    "    # Aqui, assumimos que cada aresta tem um atributo chamado \"peso\". \n",
    "    # Se não houver tal atributo, ocorrerá um erro.\n",
    "    peso_atual = atributos[\"peso\"]\n",
    "    \n",
    "    # Adicionar o peso atual à lista de pesos.\n",
    "    # Isso constrói nossa lista de pesos à medida que iteramos sobre todas as arestas.\n",
    "    pesos.append(peso_atual)\n",
    "    \n",
    "    \n",
    "    \n",
    "# Desenhando o grafo:\n",
    "\n",
    "# Gerando um posicionamento dos vértices do grafo usando o \n",
    "# layout spring (também chamado de \"Fruchterman-Reingold\").\n",
    "# Isso distribui os vértices de maneira que arestas de tamanhos\n",
    "# semelhantes fiquem próximas uma da outra, imitando uma simulação de molas.\n",
    "posicionamento = nx.spring_layout(grafo)\n",
    "\n",
    "# Desenhando os vértices (nós) do grafo:\n",
    "# - 'grafo': é o grafo que queremos desenhar.\n",
    "# - 'posicionamento': especifica as coordenadas (x, y) para cada \n",
    "# vértice, determinando onde eles serão colocados no espaço de desenho.\n",
    "# - 'node_color=cores': define a cor de cada vértice com base na \n",
    "# lista 'cores' que construímos anteriormente.\n",
    "# - 'node_size=tamanhos': determina o tamanho de cada vértice usando a\n",
    "# lista 'tamanhos' que também construímos anteriormente. \n",
    "# Este tamanho pode ser útil para destacar certos vértices ou \n",
    "# representar algum tipo de valor ou magnitude.\n",
    "nx.draw_networkx_nodes(grafo, posicionamento, node_color=cores, node_size=tamanhos)\n",
    "\n",
    "# Desenhando as arestas (conexões) entre os vértices do grafo:\n",
    "# - 'arrows=True': como estamos trabalhando com um grafo direcionado, \n",
    "# queremos mostrar a direção de uma aresta \n",
    "# para outra usando setas.\n",
    "# - 'arrowsize=20': determina o tamanho das setas. Um valor maior \n",
    "# resulta em setas mais largas.\n",
    "# - 'width=pesos': controla a espessura ou largura de cada aresta usando\n",
    "# a lista 'pesos'. Arestas com maior peso \n",
    "# serão mais grossas, o que pode ser útil para visualizar a importância \n",
    "# ou capacidade da conexão, por exemplo, em um grafo de tráfego rodoviário.\n",
    "nx.draw_networkx_edges(grafo, posicionamento, arrows=True, arrowsize=20, width=pesos)\n",
    "\n",
    "# Adicionando rótulos aos vértices, que são, por padrão, os\n",
    "# próprios identificadores dos vértices.\n",
    "nx.draw_networkx_labels(grafo, posicionamento)\n",
    "\n",
    "# Adicionando um título ao gráfico.\n",
    "plt.title(\"Visualização do Grafo Personalizada\")\n",
    "\n",
    "# Exibindo o gráfico.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c7582f3e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6a7470de",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "            Matriz de Incidência\n",
    "            \n",
    "\n",
    "A Matriz de Incidência é outra maneira de representar grafos além \n",
    "da Matriz de Adjacência e da Lista de Adjacência. Em grafos direcionados, a \n",
    "Matriz de Incidência define a relação entre vértices e arestas, de tal forma que:\n",
    "\n",
    "    Cada linha da matriz representa um vértice.\n",
    "    Cada coluna da matriz representa uma aresta.\n",
    "    Se o vértice v é a origem da aresta e, então a matriz terá -1 na posição correspondente.\n",
    "    Se o vértice v é o destino da aresta e, então a matriz terá 1 na posição correspondente.\n",
    "    Caso contrário, a matriz terá 0.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca 'networkx' e dando a ela o alias \"rede\".\n",
    "# Esta biblioteca é usada para criar, manipular e estudar a \n",
    "# estrutura e a dinâmica de redes complexas.\n",
    "import networkx as rede\n",
    "\n",
    "# Importando o módulo 'pyplot' da biblioteca 'matplotlib' e \n",
    "# dando a ele o alias \"grafico\".\n",
    "# 'matplotlib' é uma biblioteca usada para criar\n",
    "# visualizações gráficas em Python. \n",
    "# O módulo 'pyplot' fornece uma interface que permite criar\n",
    "# figuras e gráficos de forma semelhante ao MATLAB.\n",
    "import matplotlib.pyplot as grafico\n",
    "\n",
    "# Criando um novo grafo direcionado e armazenando-o na variável \"grafo\".\n",
    "# Um grafo direcionado é um conjunto de vértices (ou nós) conectados\n",
    "# por arestas direcionadas (ou setas),\n",
    "# onde cada aresta tem uma direção, do ponto inicial ao ponto final.\n",
    "grafo = rede.DiGraph()\n",
    "\n",
    "# Adicionando arestas (ou conexões) ao grafo direcionado \"grafo\" \n",
    "# a partir de uma lista de tuplas.\n",
    "# Cada tupla representa uma aresta, onde o primeiro elemento é o \n",
    "# nó de origem e o segundo é o nó de destino.\n",
    "# Por exemplo, a tupla (0, 1) adiciona uma aresta do nó 0 ao nó 1.\n",
    "# Se os nós não existirem no grafo, 'networkx' os criará automaticamente.\n",
    "grafo.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 4), (3, 4)])\n",
    "\n",
    "# Configurando a disposição dos nós do grafo usando o layout \"spring\".\n",
    "# O layout \"spring\" (ou \"Fruchterman-Reingold\") é uma técnica que posiciona os nós\n",
    "# de modo que arestas de comprimentos semelhantes fiquem igualmente espaçadas, tentando minimizar\n",
    "# a quantidade de sobreposições entre as arestas.\n",
    "# O resultado é um dicionário, armazenado na variável \"posicao_nos\", onde as chaves são os nós\n",
    "# e os valores são as coordenadas (x, y) de cada nó.\n",
    "posicao_nos = rede.spring_layout(grafo)\n",
    "\n",
    "# Desenhando os nós do grafo na tela. \n",
    "# 'grafo' é o grafo que queremos visualizar.\n",
    "# 'posicao_nos' determina a posição de cada nó.\n",
    "# 'node_color' define a cor dos nós, neste caso, azul claro.\n",
    "# 'node_size' especifica o tamanho dos nós, neste caso, 700.\n",
    "rede.draw_networkx_nodes(grafo, posicao_nos, node_color='lightblue', node_size=700)\n",
    "\n",
    "# Desenhando as arestas (ou conexões) do grafo na tela.\n",
    "# 'grafo' é o grafo que queremos visualizar.\n",
    "# 'posicao_nos' determina a posição inicial e final de cada aresta.\n",
    "# 'arrows=True' indica que as arestas são direcionadas, ou seja, possuem uma seta indicando a direção.\n",
    "# 'arrowsize' define o tamanho da seta, neste caso, 20.\n",
    "rede.draw_networkx_edges(grafo, posicao_nos, arrows=True, arrowsize=20)\n",
    "\n",
    "\n",
    "# Desenhando os rótulos dos nós na tela.\n",
    "# Cada nó receberá um rótulo que corresponde ao seu identificador no grafo.\n",
    "# 'grafo' é o grafo que queremos visualizar.\n",
    "# 'posicao_nos' determina a posição onde o rótulo de cada nó será colocado.\n",
    "rede.draw_networkx_labels(grafo, posicao_nos)\n",
    "\n",
    "\n",
    "# Criando rótulos para as arestas (conexões) do grafo.\n",
    "# Estamos usando uma compreensão de dicionário para criar um dicionário chamado \"rotulos_conexoes\".\n",
    "# Cada chave deste dicionário é uma tupla representando uma aresta (início, fim).\n",
    "# O valor associado a cada chave é uma string no formato \"início->fim\".\n",
    "# Por exemplo, para a aresta que vai do nó 0 ao nó 1, teríamos a chave (0, 1) e o valor \"0->1\".\n",
    "# rotulos_conexoes = {(inicio, fim): f\"{inicio}->{fim}\" for inicio, fim in grafo.edges()}\n",
    "\n",
    "# Inicializando um dicionário vazio para armazenar os rótulos das conexões.\n",
    "rotulos_conexoes = {}\n",
    "\n",
    "# Iterando sobre cada aresta (conexão) do grafo.\n",
    "# 'grafo.edges()' retorna uma lista de tuplas, onde cada tupla \n",
    "# representa uma conexão (início, fim).\n",
    "for inicio, fim in grafo.edges():\n",
    "    \n",
    "    # Criando o rótulo da conexão no formato \"início->fim\".\n",
    "    rotulo = f\"{inicio}->{fim}\"\n",
    "    \n",
    "    # Adicionando o rótulo ao dicionário, usando a tupla (início, fim) como chave.\n",
    "    rotulos_conexoes[(inicio, fim)] = rotulo\n",
    "    \n",
    "# Desenhando os rótulos das arestas na tela.\n",
    "# 'grafo' é o grafo que queremos visualizar.\n",
    "# 'posicao_nos' determina a posição onde o rótulo de cada aresta será colocado.\n",
    "# 'edge_labels' é o dicionário que contém os rótulos que queremos mostrar para cada aresta.\n",
    "rede.draw_networkx_edge_labels(grafo, posicao_nos, edge_labels=rotulos_conexoes)\n",
    "\n",
    "# Definindo o título da visualização gráfica. \n",
    "# Neste caso, o título será \"Visualização do Grafo\".\n",
    "grafico.title(\"Visualização do Grafo\")\n",
    "\n",
    "# Exibindo a visualização gráfica na tela.\n",
    "# Esta função irá mostrar uma janela com o grafo desenhado, incluindo nós, arestas e rótulos.\n",
    "grafico.show()\n",
    "\n",
    "\"\"\"\n",
    "    O valor −1 indica que o vértice correspondente àquela linha é a origem \n",
    "        da aresta correspondente àquela coluna.\n",
    "\n",
    "    O valor 1 indica que o vértice correspondente àquela linha é o destino da \n",
    "        aresta correspondente àquela coluna.\n",
    "\n",
    "    O valor 0 indica que o vértice não está conectado à aresta em questão.\n",
    "\n",
    "Assim, esses valores ajudam a representar e entender a direção de cada aresta no grafo.\n",
    "    \n",
    "temos as seguintes arestas:\n",
    "\n",
    "    0 -> 1\n",
    "    0 -> 2\n",
    "    1 -> 3\n",
    "    2 -> 4\n",
    "    3 -> 4\n",
    "    \n",
    "+-----+----+-----+----+----+----+\n",
    "| V\\V | 0  | 1   | 2  | 3  | 4  |\n",
    "+-----+----+-----+----+----+----+\n",
    "|  0  | -1 | -1  |  0 |  0 |  0 |  <- Vértice 0: É a origem das arestas 0 e 1.\n",
    "|  1  |  1 |  0  | -1 |  0 |  0 |  <- Vértice 1: É o destino da aresta 0 e a origem da aresta 2.\n",
    "|  2  |  0 |  1  |  0 | -1 |  0 |  <- Vértice 2: É o destino da aresta 1 e a origem da aresta 3.\n",
    "|  3  |  0 |  0  |  1 |  0 | -1 |  <- Vértice 3: É o destino da aresta 2 e a origem da aresta 4.\n",
    "|  4  |  0 |  0  |  0 |  1 |  1 |  <- Vértice 4: É o destino das arestas 3 e 4.\n",
    "+-----+----+-----+----+----+----+\n",
    "\n",
    "\n",
    "    Aresta 0: vai do vértice 0 ao vértice 1\n",
    "    Aresta 1: vai do vértice 0 ao vértice 2\n",
    "    Aresta 2: vai do vértice 1 ao vértice 3\n",
    "    Aresta 3: vai do vértice 2 ao vértice 4\n",
    "    Aresta 4: vai do vértice 3 ao vértice 4\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "922774a5",
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  },
  {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ordem de visita usando busca em largura:\n",
      "A -> B -> C -> D -> E -> \n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "            \n",
    "        Travessias de Grafos\n",
    "\n",
    "            Busca em Largura (BFS)\n",
    "            \n",
    "\n",
    "Travessias de grafos são técnicas que permitem visitar todos os \n",
    "vértices de um grafo de maneira sistemática. Estas travessias são \n",
    "fundamentais em muitos problemas de grafos, pois fornecem um meio\n",
    "para inspecionar cada vértice e cada aresta.\n",
    "\n",
    "Busca em Largura (BFS - Breadth-First Search) é uma das técnicas mais \n",
    "conhecidas para travessia de grafos.\n",
    "\n",
    "Aqui está uma breve descrição da BFS:\n",
    "\n",
    "Conceito:\n",
    "A BFS explora o grafo em \"camadas\". Ela começa no vértice inicial e explora\n",
    "todos os vértices vizinhos no mesmo nível de profundidade antes de se mover \n",
    "para os vértices no próximo nível de profundidade.\n",
    "\n",
    "Mecanismo:\n",
    "\n",
    "    - Comece com um nó inicial e marque-o como visitado.\n",
    "    - Coloque este nó em uma fila.\n",
    "    - Enquanto a fila não estiver vazia:\n",
    "        - Remova um nó da fila.\n",
    "        - Para cada vizinho desse nó:\n",
    "            Se o vizinho não foi visitado:\n",
    "                Marque-o como visitado.\n",
    "                Coloque-o na fila.\n",
    "\n",
    "Utilidades e Aplicações da BFS:\n",
    "\n",
    "    - Descoberta do caminho mais curto: Em um grafo não ponderado, a BFS pode \n",
    "        ser usada para encontrar o caminho mais curto entre dois nós.\n",
    "    \n",
    "    - Análise de redes sociais: Por exemplo, pode ser usada para encontrar \n",
    "        amigos em um certo nível de separação.\n",
    "        \n",
    "    - Algoritmos de roteamento de rede: Como o algoritmo de roteamento OSPF.\n",
    "    - Verificar a conectividade: Para verificar se um grafo é conectado ou não.\n",
    "    - Resolução de quebra-cabeças: Como o quebra-cabeça do tipo \"Deslizar\", onde há \n",
    "        movimentos legais que podem ser interpretados como arestas e configurações \n",
    "        do tabuleiro como vértices.\n",
    "\n",
    "Características da BFS:\n",
    "\n",
    "    A BFS não é recursiva.\n",
    "    Utiliza uma estrutura de dados de fila para manter o registro dos vértices \n",
    "        que precisam ser explorados.\n",
    "    É garantido que a BFS visite os vértices mais próximos do nó inicial antes \n",
    "        de visitar vértices mais distantes.\n",
    "\n",
    "Em resumo, a BFS é uma abordagem sistemática para explorar todos os vértices de um grafo, \n",
    "começando pelo vértice inicial e movendo-se em ondas através dos vértices, de acordo com \n",
    "sua proximidade ao ponto de partida.\n",
    "\n",
    "\n",
    "                \n",
    "Vamos dar um exemplo prático da Busca em Largura (BFS - Breadth First \n",
    "Search) utilizando a biblioteca NetworkX em Python.\n",
    "\n",
    "Exemplo Prático:\n",
    "\n",
    "Suponha que temos um grafo representando uma rede de amigos, e queremos \n",
    "saber a ordem em que os amigos seriam visitados se começarmos com uma pessoa \n",
    "específica e visitarmos seus amigos, depois os amigos de seus amigos e assim por diante.\n",
    "\n",
    "Grafo:\n",
    "\n",
    "  A\n",
    " / \\\n",
    "B   C\n",
    "|   |\n",
    "D   E\n",
    "\n",
    "Aqui, \"A\" tem dois amigos \"B\" e \"C\". \n",
    "      \"B\" tem um amigo \"D\" e \n",
    "      \"C\" tem um amigo \"E\".\n",
    "\n",
    "Vamos fazer a BFS começando pelo vértice \"A\".\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Importa a biblioteca 'networkx', que é usada para a criação, \n",
    "# manipulação e estudo de estruturas\n",
    "# de redes complexas (grafos). O \"nx\" é um apelido comum para\n",
    "# simplificar chamadas subsequentes.\n",
    "import networkx as nx\n",
    "\n",
    "# Inicializa um novo grafo vazio. Neste caso, estamos criando \n",
    "# um grafo não-direcionado.\n",
    "grafo = nx.Graph()\n",
    "\n",
    "# Adiciona arestas ao grafo. Uma aresta é uma ligação entre dois nós.\n",
    "# A função 'add_edges_from' permite adicionar múltiplas arestas de uma vez.\n",
    "# Aqui, estamos adicionando arestas que ligam os \n",
    "# nós 'A' e 'B', 'A' e 'C', 'B' e 'D' e 'C' e 'E'.\n",
    "grafo.add_edges_from([('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'E')])\n",
    "\n",
    "\n",
    "# Definição da função de Busca em Largura (BFS - Breadth-First Search).\n",
    "# A função recebe um grafo e um nó inicial como parâmetros.\n",
    "def busca_em_largura(grafo, no_inicial):\n",
    "\n",
    "    # Lista que vai conter os nós que já foram visitados.\n",
    "    nos_visitados = []\n",
    "\n",
    "    # Lista que ajuda a controlar os próximos nós a serem visitados.\n",
    "    # Funciona como uma fila, onde o primeiro nó inserido é o primeiro a ser retirado.\n",
    "    fila = []\n",
    "\n",
    "    # Adiciona o nó inicial à lista de nós visitados e à fila.\n",
    "    nos_visitados.append(no_inicial)\n",
    "    fila.append(no_inicial)\n",
    "\n",
    "    # Continua o processo enquanto houver nós na fila para serem visitados.\n",
    "    while fila:\n",
    "\n",
    "        # Retira o primeiro nó da fila para ser o nó atualmente visitado.\n",
    "        no_atual = fila.pop(0)\n",
    "\n",
    "        # Imprime o nome do nó que está sendo visitado.\n",
    "        print(no_atual, end=\" -> \")\n",
    "        \n",
    "        # Loop para visitar cada vizinho (nó adjacente) do nó atual.\n",
    "        for vizinho in grafo[no_atual]:\n",
    "\n",
    "            # Verifica se o vizinho ainda não foi visitado.\n",
    "            if vizinho not in nos_visitados:\n",
    "\n",
    "                # Se o vizinho não foi visitado, ele é adicionado à lista de visitados.\n",
    "                nos_visitados.append(vizinho)\n",
    "\n",
    "                # E também é adicionado à fila para ser visitado em seguida.\n",
    "                fila.append(vizinho)\n",
    "                \n",
    "                \n",
    "# Imprime uma mensagem para indicar que a ordem de visita dos nós do grafo será mostrada\n",
    "# usando o algoritmo de busca em largura (BFS).\n",
    "print(\"Ordem de visita usando busca em largura:\")\n",
    "\n",
    "# Chama a função 'busca_em_largura' passando o grafo criado\n",
    "# anteriormente e o nó 'A' como nó inicial.\n",
    "# A função vai imprimir a ordem em que os nós são \n",
    "# visitados, começando pelo nó 'A'.\n",
    "busca_em_largura(grafo, 'A')\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Por que o caminho mais curto é: A B C D E ?\n",
    "\n",
    "Quando falamos de \"caminho mais curto\" em um grafo não ponderado \n",
    "usando a Busca em Largura (BFS), estamos nos referindo ao número\n",
    "mínimo de arestas que precisamos atravessar para ir de um vértice a outro.\n",
    "\n",
    "No grafo:\n",
    "\n",
    "  A\n",
    " / \\\n",
    "B   C\n",
    "|   |\n",
    "D   E\n",
    "\n",
    "Vamos descrever a ordem em que a BFS visita os vértices, \n",
    "começando pelo vértice A:\n",
    "\n",
    "    - A é o ponto de partida.\n",
    "    - A partir de A, os vizinhos mais próximos são B e C. A ordem \n",
    "        exata entre B e C pode variar dependendo de como os vizinhos \n",
    "        são armazenados e recuperados, mas suponhamos que B venha antes \n",
    "        de C. Portanto, B é visitado e depois C.\n",
    "    \n",
    "    - Após B e C, os próximos vértices na fila são D e E. D é o vizinho \n",
    "        de B e E é o vizinho de C. Novamente, a ordem entre D e E pode \n",
    "        variar, mas suponhamos que D venha antes de E. Portanto, D é visitado \n",
    "        e depois E.\n",
    "\n",
    "Então, a ordem de visita é: A → B → C → D → E.\n",
    "\n",
    "Essa ordem representa a menor quantidade de arestas que precisamos atravessar \n",
    "para chegar a cada vértice a partir de A. Por exemplo, para ir de A para D, precisamos \n",
    "passar por B, fazendo um total de 2 arestas. Mesmo conceito para E: de A para E \n",
    "passamos por C, totalizando 2 arestas.\n",
    "\n",
    "Essa é a essência da BFS em grafos não ponderados: ela garante que visitamos todos\n",
    "os vértices à mesma distância do ponto de partida antes de visitarmos os vértices \n",
    "que estão a uma maior distância.\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
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   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ordem de visita usando busca em largura: ['A', 'B', 'C', 'D', 'E']\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importa a biblioteca 'networkx' com o apelido \"rede\".\n",
    "# Esta biblioteca é utilizada para a criação, manipulação e estudo da estrutura de redes e grafos.\n",
    "import networkx as rede\n",
    "\n",
    "# Importa a biblioteca 'matplotlib.pyplot' com o apelido \"grafico\".\n",
    "# Esta biblioteca é utilizada para plotar gráficos e visualizações em Python.\n",
    "import matplotlib.pyplot as grafico\n",
    "\n",
    "# Inicializa um grafo vazio do tipo simples (ou seja, sem direção nas conexões).\n",
    "# Um grafo é uma estrutura que consiste de nós (também chamados de vértices) e conexões (arestas) entre estes nós.\n",
    "grafo = rede.Graph()\n",
    "\n",
    "# Adiciona conexões (arestas) ao grafo entre os nós indicados.\n",
    "# A chamada 'add_edges_from' recebe uma lista de tuplas, onde cada tupla representa uma conexão.\n",
    "# Por exemplo, ('A', 'B') indica uma conexão entre o nó 'A' e o nó 'B'.\n",
    "# Neste código, nós 'A', 'B', 'C', 'D' e 'E' são adicionados ao grafo, e as conexões definidas são: \n",
    "# 'A' com 'B', 'A' com 'C', 'B' com 'D' e 'C' com 'E'.\n",
    "grafo.add_edges_from([('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'E')])\n",
    "\n",
    "\n",
    "# Definição da função de Busca em Largura (BFS - Breadth-First Search).\n",
    "# Esta função realiza uma busca em largura em um grafo, começando a partir\n",
    "# de um nó inicial especificado.\n",
    "def busca_em_largura(grafo, no_inicio):\n",
    "    \n",
    "    # Cria uma lista vazia para armazenar os nós que já foram visitados.\n",
    "    nos_visitados = []\n",
    "    \n",
    "    # Cria uma lista vazia que funcionará como uma fila.\n",
    "    # Esta fila será utilizada para controlar a ordem de visita dos nós.\n",
    "    fila = []\n",
    "    \n",
    "    # Adiciona o nó inicial às listas de nós visitados e à fila.\n",
    "    nos_visitados.append(no_inicio)\n",
    "    fila.append(no_inicio)\n",
    "\n",
    "    # Cria uma lista vazia para armazenar a ordem de visita dos nós.\n",
    "    ordem_visita = []\n",
    "\n",
    "    # Enquanto houver elementos na fila, o loop continuará executando.\n",
    "    while fila:\n",
    "        \n",
    "        # Remove e retorna o primeiro nó da fila, designando-o como o nó atual.\n",
    "        no_atual = fila.pop(0)\n",
    "        \n",
    "        # Adiciona o nó atual à lista de ordem de visita.\n",
    "        ordem_visita.append(no_atual)\n",
    "\n",
    "        # Para cada vizinho do nó atual no grafo:\n",
    "        for vizinho in grafo[no_atual]:\n",
    "            \n",
    "            # Se o vizinho ainda não foi visitado:\n",
    "            if vizinho not in nos_visitados:\n",
    "                \n",
    "                # Adiciona o vizinho à lista de nós visitados.\n",
    "                nos_visitados.append(vizinho)\n",
    "                \n",
    "                # Adiciona o vizinho ao final da fila.\n",
    "                fila.append(vizinho)\n",
    "\n",
    "    # Retorna a lista com a ordem de visita dos nós.\n",
    "    return ordem_visita\n",
    "\n",
    "\n",
    "# Chama a função busca_em_largura, passando o grafo e o nó 'A' como ponto de partida.\n",
    "# O resultado (ordem de visita dos nós) é armazenado na variável \"ordem\".\n",
    "ordem = busca_em_largura(grafo, 'A')\n",
    "\n",
    "# Imprime a ordem de visita dos nós, obtida pela busca em largura.\n",
    "print(\"Ordem de visita usando busca em largura:\", ordem)\n",
    "\n",
    "\n",
    "# Define as posições dos nós no desenho do grafo.\n",
    "# Estas posições são coordenadas (x, y) para cada nó, permitindo\n",
    "# que sejam desenhados em locais específicos.\n",
    "posicoes = {'A': (0.5, 1), 'B': (0, 0.5), 'C': (1, 0.5), 'D': (0, 0), 'E': (1, 0)}\n",
    "\n",
    "# Desenha os nós do grafo nas posições especificadas.\n",
    "# Define a cor dos nós como azul claro ('lightblue') e o tamanho como 1000.\n",
    "rede.draw_networkx_nodes(grafo, posicoes, node_color='lightblue', node_size=1000)\n",
    "\n",
    "# Desenha as arestas (conexões) do grafo.\n",
    "# A largura das arestas é definida como 1.0 e a transparência (alpha) como 0.5 (50% opaco).\n",
    "rede.draw_networkx_edges(grafo, posicoes, width=1.0, alpha=0.5)\n",
    "\n",
    "# Desenha os rótulos (nomes) dos nós nas posições especificadas.\n",
    "# O tamanho da fonte dos rótulos é definido como 12.\n",
    "rede.draw_networkx_labels(grafo, posicoes, font_size=12)\n",
    "\n",
    "# Define o título da visualização do grafo.\n",
    "grafico.title(\"Visualização do Grafo com Busca em Largura\")\n",
    "\n",
    "# Desativa os eixos x e y da visualização, para que o gráfico \n",
    "# fique mais limpo e focado apenas no grafo.\n",
    "grafico.axis('off')\n",
    "\n",
    "# Exibe o gráfico do grafo.\n",
    "grafico.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b68dcec0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2ceb35e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício Busca em Largura (BFS)\n",
    "\n",
    "Objetivo: Utilizar a biblioteca networkx para criar e visualizar grafos.\n",
    "\n",
    "Descrição:\n",
    "\n",
    "Você recebeu uma lista de conexões entre vários pontos. Sua tarefa é usar \n",
    "a biblioteca networkx para criar um grafo com essas conexões e, em seguida, \n",
    "visualizá-lo usando matplotlib.\n",
    "\n",
    "Dados fornecidos:\n",
    "\n",
    "    Lista de conexões (arestas):\n",
    "        F-A\n",
    "        F-B\n",
    "        A-B\n",
    "        A-D\n",
    "        A-E\n",
    "        B-C\n",
    "        B-D\n",
    "\n",
    "    Posições sugeridas para cada nó no gráfico:\n",
    "        F: (0, 2)\n",
    "        A: (-1, 1)\n",
    "        B: (1, 1)\n",
    "        D: (0, 0)\n",
    "        E: (-2, 0)\n",
    "        C: (2, 0)\n",
    "        \n",
    "Grafo\n",
    "\n",
    "   F\n",
    "  / \\\n",
    " A   B\n",
    " |\\  |\\\n",
    " E   D C  \n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca \"networkx\" com o apelido \"nx\".\n",
    "# Essa biblioteca é especializada em criação, manipulação e \n",
    "# estudo de estruturas e dinâmicas complexas de redes.\n",
    "import networkx as nx\n",
    "\n",
    "# Importando a biblioteca \"matplotlib.pyplot\" com o apelido \"plt\".\n",
    "# Essa biblioteca é utilizada para criar visualizações gráficas.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Criando um novo grafo não direcionado e armazenando-o na variável \"grafo\".\n",
    "grafo = nx.Graph()\n",
    "\n",
    "# Definindo a lista de arestas que será adicionada ao grafo.\n",
    "# Cada aresta é representada por um par de nós, indicando uma conexão entre eles.\n",
    "arestas = [('F', 'A'), ('F', 'B'), ('A', 'B'), ('A', 'D'), ('A', 'E'), ('B', 'C'), ('B', 'D')]\n",
    "\n",
    "# Adicionando todas as arestas definidas anteriormente ao grafo.\n",
    "grafo.add_edges_from(arestas)\n",
    "\n",
    "# Definindo um dicionário com as posições que cada nó deve ocupar na visualização do grafo.\n",
    "# As posições são coordenadas (x, y) que indicam onde cada nó será posicionado no desenho.\n",
    "# Por exemplo, o nó 'F' será posicionado na coordenada (0, 2).\n",
    "posicoes = {\n",
    "    'F': (0, 2),\n",
    "    'A': (-1, 1),\n",
    "    'B': (1, 1),\n",
    "    'D': (0, 0),\n",
    "    'E': (-2, 0),\n",
    "    'C': (2, 0)\n",
    "}\n",
    "\n",
    "# Define o tamanho da figura que será gerada para a visualização do grafo.\n",
    "# O tamanho é definido em polegadas, sendo 8 polegadas de largura e 6 de altura.\n",
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "\n",
    "# Desenha o grafo na figura definida anteriormente usando as seguintes opções:\n",
    "# - \"grafo\": O objeto grafo que foi criado anteriormente.\n",
    "# - \"posicoes\": Posições pré-definidas para os nós do grafo.\n",
    "# - \"with_labels=True\": Indica que os rótulos (nomes) dos nós serão mostrados.\n",
    "# - \"node_size=1500\": Define o tamanho dos nós no desenho.\n",
    "# - \"node_color='lightblue'\": Define a cor dos nós como azul claro.\n",
    "# - \"font_size=15\": Define o tamanho da fonte dos rótulos dos nós.\n",
    "# - \"width=2\": Define a largura das arestas.\n",
    "# - \"edge_color='gray'\": Define a cor das arestas como cinza.\n",
    "nx.draw(grafo, \n",
    "        posicoes, \n",
    "        with_labels=True, \n",
    "        node_size=1500, \n",
    "        node_color='lightblue', \n",
    "        font_size=15, \n",
    "        width=2, \n",
    "        edge_color='gray')\n",
    "\n",
    "\n",
    "# Define o título da figura. O título aparecerá acima da visualização do grafo.\n",
    "plt.title(\"Visualização do Grafo\")\n",
    "\n",
    "# Exibe a figura criada. Esta linha é necessária para que a figura apareça.\n",
    "plt.show()\n",
    "\n",
    "\"\"\"\n",
    "Lista de conexões (arestas):\n",
    "        F-A\n",
    "        F-B\n",
    "        A-B\n",
    "        A-D\n",
    "        A-E\n",
    "        B-C\n",
    "        B-D\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "540f5dc1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "01edfebc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ordem de visitação: ['A', 'B', 'D', 'C', 'E']\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "        Travessias de Grafos\n",
    "\n",
    "            Busca em Profundidade (DFS)\n",
    "            \n",
    "A Busca em Profundidade (DFS - Depth First Search) é um algoritmo \n",
    "de travessia de grafo que visita todos os vértices de um grafo ou \n",
    "árvore em profundidade, seguindo tão longe quanto possível ao longo \n",
    "de cada ramo antes de retroceder. Aqui está um exemplo prático de \n",
    "como a DFS funciona:\n",
    "\n",
    "Grafo Exemplificado:\n",
    "\n",
    "Vamos considerar o seguinte grafo:\n",
    "\n",
    "  A\n",
    " / \\\n",
    "B   C\n",
    "|   |\n",
    "D   E\n",
    "\n",
    "A representação do grafo acima em uma lista de adjacências seria:\n",
    "\n",
    "A -> [B, C]\n",
    "B -> [D]\n",
    "C -> [E]\n",
    "D -> []\n",
    "E -> []\n",
    "\n",
    "Algoritmo de Busca em Profundidade (DFS):\n",
    "\n",
    "Vamos começar a busca no vértice A.\n",
    "\n",
    "    - Visite o vértice A.\n",
    "    - Mova-se para um vértice adjacente de A. Digamos, B.\n",
    "    - Visite o vértice B.\n",
    "    - Mova-se para um vértice adjacente de B. No caso, D.\n",
    "    - Visite o vértice D. Como D não tem adjacentes não visitados, retornamos.\n",
    "    - Volte para A e visite o próximo vértice adjacente, C.\n",
    "    - Visite o vértice C.\n",
    "    - Mova-se para um vértice adjacente de C. No caso, E.\n",
    "    - Visite o vértice E.\n",
    "\n",
    "Ordem de visitação: A, B, D, C, E.\n",
    "Código Python para DFS:\n",
    "\"\"\"\n",
    "\n",
    "# Função que implementa o algoritmo de Busca em \n",
    "# Profundidade (DFS - Depth-First Search).\n",
    "# Ela percorre o grafo começando por um vértice \n",
    "# específico e explorando o mais profundamente possível\n",
    "# antes de retroceder.\n",
    "def busca_em_profundidade(grafo, vertice_atual, vertices_visitados=[]):\n",
    "    \n",
    "    # Verifica se o vértice atual ainda não foi visitado.\n",
    "    if vertice_atual not in vertices_visitados:\n",
    "        \n",
    "        # Adiciona o vértice atual à lista de vértices visitados.\n",
    "        vertices_visitados.append(vertice_atual)\n",
    "        \n",
    "        # Itera sobre os vértices vizinhos do vértice atual.\n",
    "        for vizinho in grafo[vertice_atual]:\n",
    "            \n",
    "            # Realiza uma chamada recursiva da função para explorar \n",
    "            # os vizinhos do vértice atual.\n",
    "            busca_em_profundidade(grafo, vizinho, vertices_visitados)\n",
    "    \n",
    "    # Retorna a lista de vértices visitados ao final da execução.\n",
    "    return vertices_visitados\n",
    "    \n",
    "    \n",
    "# Representação do grafo em forma de lista de adjacências.\n",
    "# Chave é o vértice e o valor é uma lista dos vértices vizinhos.\n",
    "grafo_representacao = {\n",
    "    'A': ['B', 'C'],\n",
    "    'B': ['D'],\n",
    "    'C': ['E'],\n",
    "    'D': [],\n",
    "    'E': []\n",
    "}\n",
    "\n",
    "# Realiza uma chamada da função de busca em profundidade começando pelo vértice 'A'.\n",
    "sequencia_visita = busca_em_profundidade(grafo_representacao, 'A')\n",
    "\n",
    "# Imprime a sequência de vértices visitados pelo algoritmo de busca em profundidade.\n",
    "print(\"Ordem de visitação:\", sequencia_visita)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea66e5d2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ac9cc2c3",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importando as bibliotecas necessárias:\n",
    "# 'networkx' é uma biblioteca que fornece estruturas de dados \n",
    "# para representar grafos e muitos algoritmos para analisá-los.\n",
    "# 'matplotlib.pyplot' é uma biblioteca para criar visualizações gráficas.\n",
    "import networkx as rede\n",
    "import matplotlib.pyplot as grafico\n",
    "\n",
    "# Inicializando um grafo vazio. Aqui, estamos criando um grafo não direcionado.\n",
    "grafo = rede.Graph()\n",
    "\n",
    "# Definindo uma lista de arestas para serem adicionadas ao grafo.\n",
    "# Cada tupla representa uma aresta entre dois vértices.\n",
    "arestas = [('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'E')]\n",
    "grafo.add_edges_from(arestas)  # Adicionando todas as arestas ao grafo de uma única vez.\n",
    "\n",
    "\n",
    "# Definindo as posições dos vértices para desenhar o grafo. \n",
    "# As posições são representadas como coordenadas (x, y) em um plano.\n",
    "posicoes_vertices = {\n",
    "    'A': (0, 2),   # Vértice 'A' está na posição x=0 e y=2.\n",
    "    'B': (-1, 1),  # Vértice 'B' está na posição x=-1 e y=1.\n",
    "    'C': (1, 1),   # Vértice 'C' está na posição x=1 e y=1.\n",
    "    'D': (-1, 0),  # Vértice 'D' está na posição x=-1 e y=0.\n",
    "    'E': (1, 0)    # Vértice 'E' está na posição x=1 e y=0.\n",
    "}\n",
    "\n",
    "# Configurando o tamanho da figura onde o grafo será desenhado.\n",
    "grafico.figure(figsize=(8,6))\n",
    "\n",
    "\n",
    "# Desenhando o grafo com as configurações especificadas.\n",
    "# 'pos=posicoes_vertices': determina a posição de cada vértice no desenho.\n",
    "# 'with_labels=True': mostra o rótulo de cada vértice.\n",
    "# 'node_size=1500': determina o tamanho dos vértices.\n",
    "# 'node_color='lightblue'': determina a cor dos vértices.\n",
    "# 'font_size=15': tamanho da fonte dos rótulos dos vértices.\n",
    "# 'width=2': largura das arestas.\n",
    "# 'edge_color='gray'': cor das arestas.\n",
    "rede.draw(grafo, \n",
    "          pos=posicoes_vertices, \n",
    "          with_labels=True, \n",
    "          node_size=1500, \n",
    "          node_color='lightblue', \n",
    "          font_size=15, \n",
    "          width=2, \n",
    "          edge_color='gray')\n",
    "\n",
    "# Definindo o título da visualização.\n",
    "grafico.title(\"Visualização do Grafo\")\n",
    "\n",
    "# Exibindo o grafo desenhado.\n",
    "grafico.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6b3d669",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "83d6ebd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício Busca em Profundidade (DFS)\n",
    "\n",
    "Dada uma lista de cidades do estado de São Paulo e suas respectivas\n",
    "conexões, o objetivo deste exercício é criar um programa que visualize\n",
    "essas cidades e as conexões entre elas em um gráfico.\n",
    "\n",
    "Requisitos:\n",
    "\n",
    "    - As cidades e suas conexões são as seguintes:\n",
    "        São Paulo (SP) está conectada com Guarulhos (GRU), Osasco (OSC) e São Caetano (SC).\n",
    "        Guarulhos (GRU) está conectada com São Paulo (SP) e Arujá (ARU).\n",
    "        Osasco (OSC) está conectada com São Paulo (SP) e Barueri (BAR).\n",
    "\n",
    "    - Para representar visualmente o grafo, defina as posições das cidades \n",
    "     da seguinte forma:\n",
    "        'SP': (0, 3),  # Colocando SP no topo\n",
    "        'GRU': (-1, 2),\n",
    "        'ARU': (-1, 1),\n",
    "        'OSC': (0, 2),\n",
    "        'BAR': (0, 1),\n",
    "        'SC': (1, 2)\n",
    "\n",
    "    - A figura resultante deve ter tamanho 10x8 (figsize).\n",
    "\n",
    "    - As cidades devem ser representadas com um tamanho de nó de 1500, cor \n",
    "        'lightblue' e tamanho de fonte 15.\n",
    "\n",
    "    - As conexões (arestas) entre as cidades devem ter largura 2 e cor 'gray'.\n",
    "\n",
    "    - O gráfico deve conter um título: \"Visualização do Grafo - Cidades de SP\".\n",
    "\n",
    "Observação:\n",
    "\n",
    "Não é necessário criar funções adicionais ou tratar exceções. O foco deste exercício \n",
    "é a representação gráfica e manipulação de um grafo simples.\n",
    "\n",
    "   SP\n",
    "  / | \\\n",
    "GRU OSC SC\n",
    " |   |\n",
    "ARU BAR\n",
    "\"\"\"\n",
    "\n",
    "# Importando as bibliotecas necessárias:\n",
    "# 'networkx' é uma biblioteca que fornece estruturas de dados \n",
    "# Importando as bibliotecas necessárias:\n",
    "# 'networkx' é uma biblioteca que fornece estruturas de dados para representar grafos e muitos algoritmos para analisá-los.\n",
    "# 'matplotlib.pyplot' é uma biblioteca para criar visualizações gráficas.\n",
    "import networkx as rede\n",
    "import matplotlib.pyplot as grafico\n",
    "\n",
    "# Inicializando um grafo vazio. Aqui, estamos criando um grafo não direcionado.\n",
    "grafo_cidades = rede.Graph()\n",
    "\n",
    "# Definindo uma lista de arestas que representam ligações entre cidades.\n",
    "# Cada tupla representa uma ligação entre duas cidades.\n",
    "ligacoes_cidades = [\n",
    "    ('SP', 'GRU'),\n",
    "    ('SP', 'OSC'),\n",
    "    ('SP', 'SC'),\n",
    "    ('GRU', 'ARU'),\n",
    "    ('OSC', 'BAR')\n",
    "]\n",
    "\n",
    "# Adicionando todas as ligações ao grafo de uma só vez.\n",
    "grafo_cidades.add_edges_from(ligacoes_cidades) \n",
    "\n",
    "# Definindo as posições dos vértices (cidades) para desenhar o grafo. \n",
    "# As posições são especificadas como coordenadas cartesianas (x, y) para \n",
    "# representar a posição de cada vértice no gráfico.\n",
    "\n",
    "# Criando um dicionário para armazenar as coordenadas de cada cidade.\n",
    "# As chaves do dicionário são os nomes das cidades (vértices) e os valores\n",
    "# são tuplas representando as coordenadas (x, y).\n",
    "coordenadas_cidades = {\n",
    "    'SP': (0, 3),      # A cidade de São Paulo (SP) é posicionada na coordenada (0, 3).\n",
    "    'GRU': (-1, 2),    # Guarulhos (GRU) é posicionada em (-1, 2).\n",
    "    'ARU': (-1, 1),    # Arujá (ARU) é posicionada em (-1, 1).\n",
    "    'OSC': (0, 2),     # Osasco (OSC) é posicionada em (0, 2).\n",
    "    'BAR': (0, 1),     # Barueri (BAR) é posicionada em (0, 1).\n",
    "    'SC': (1, 2)       # Outra cidade (SC) é posicionada em (1, 2).\n",
    "}\n",
    "\n",
    "\n",
    "# Configurando o tamanho da figura onde o grafo será desenhado.\n",
    "grafico.figure(figsize=(10,8))\n",
    "\n",
    "# Desenhando o grafo com as configurações especificadas.\n",
    "# 'pos=coordenadas_cidades': determina a posição de cada cidade no desenho.\n",
    "# 'with_labels=True': mostra o rótulo de cada cidade.\n",
    "# 'node_size=1500': determina o tamanho dos vértices (cidades).\n",
    "# 'node_color='lightblue'': determina a cor dos vértices (cidades).\n",
    "# 'font_size=15': tamanho da fonte dos rótulos das cidades.\n",
    "# 'width=2': largura das arestas (ligações entre cidades).\n",
    "# 'edge_color='gray'': cor das arestas.\n",
    "rede.draw(grafo_cidades, \n",
    "          pos=coordenadas_cidades, \n",
    "          with_labels=True, \n",
    "          node_size=1500, \n",
    "          node_color='lightblue', \n",
    "          font_size=15, width=2, \n",
    "          edge_color='gray')\n",
    "\n",
    "# Definindo o título da visualização.\n",
    "grafico.title(\"Visualização do Grafo - Cidades de SP\")\n",
    "\n",
    "# Exibindo o grafo desenhado.\n",
    "grafico.show()\n",
    "\n",
    "\"\"\"\n",
    "   SP\n",
    "  / | \\\n",
    "GRU OSC SC\n",
    " |   |\n",
    "ARU BAR\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6508cca5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aaf58d00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Caminho mais curto de A para F: ['A', 'B', 'D', 'F']\n",
      "Distância total: 9\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "            Algoritmos Clássicos\n",
    "\n",
    "                Algoritmo de Dijkstra para Caminhos Mais Curtos\n",
    "                \n",
    "\n",
    "    O algoritmo de Dijkstra é usado para encontrar o caminho mais curto de \n",
    "um nó (vértice) de origem para todos os outros nós em um grafo ponderado e \n",
    "direcionado, onde todas as arestas têm peso não negativo. É amplamente \n",
    "utilizado em aplicações como sistemas de roteamento de redes de \n",
    "computadores, sistemas de navegação por GPS, entre outros.\n",
    "\n",
    "Vamos considerar um exemplo prático:\n",
    "\n",
    "Imagine que temos uma cidade com várias interseções (nós) e ruas que as \n",
    "conectam (arestas). Cada rua tem uma distância associada a ela (peso da \n",
    "aresta). Suponha que queremos encontrar a rota mais curta do ponto A para o \n",
    "ponto B na cidade.\n",
    "\n",
    "Aqui está uma representação simplificada:\n",
    "\n",
    "A - 4 - B - 2 - D\n",
    "|       |       |\n",
    "2       1       3\n",
    "|       |       |\n",
    "C - 5 - E       F\n",
    "\n",
    "No grafo acima:\n",
    "\n",
    "    A, B, C, D, E, F são interseções (nós).\n",
    "    \n",
    "    Os números representam a distância entre as interseções (peso das arestas).\n",
    "\n",
    "    Se quisermos encontrar a rota mais curta de A para F, podemos \n",
    "usar o algoritmo de Dijkstra.\n",
    "\n",
    "Aqui está uma implementação simples usando a biblioteca networkx:\n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca networkx para manipulação e análise de grafos.\n",
    "import networkx as nx\n",
    "\n",
    "# Criando um grafo direcionado (DiGraph). Grafos direcionados \n",
    "# são aqueles onde as arestas têm uma direção específica, de um vértice \n",
    "# origem para um vértice destino.\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Adicionando arestas ao grafo junto com seus pesos.\n",
    "# A função add_edge adiciona uma aresta direcionada do \n",
    "# primeiro vértice para o segundo com um atributo de peso especificado.\n",
    "G.add_edge('A', 'B', weight=4)   # Aresta de A para B com peso 4\n",
    "G.add_edge('A', 'C', weight=2)   # Aresta de A para C com peso 2\n",
    "G.add_edge('B', 'E', weight=1)   # Aresta de B para E com peso 1\n",
    "G.add_edge('B', 'D', weight=2)   # Aresta de B para D com peso 2\n",
    "G.add_edge('C', 'E', weight=5)   # Aresta de C para E com peso 5\n",
    "G.add_edge('D', 'F', weight=3)   # Aresta de D para F com peso 3\n",
    "G.add_edge('E', 'B', weight=1)   # Aresta de E para B com peso 1\n",
    "\n",
    "# Utilizando o algoritmo de Dijkstra para determinar o caminho mais curto entr\n",
    "# e os vértices A e F.\n",
    "# A função single_source_dijkstra retorna a distância mínima e o \n",
    "# caminho mais curto de um vértice de origem para um destino.\n",
    "distancia, caminho = nx.single_source_dijkstra(G, 'A', 'F')\n",
    "\n",
    "# Imprimindo o caminho mais curto determinado pelo algoritmo de Dijkstra de A para F.\n",
    "print(f\"Caminho mais curto de A para F: {caminho}\")\n",
    "\n",
    "# Imprimindo a distância total (soma dos pesos) do caminho mais curto de A para F.\n",
    "print(f\"Distância total: {distancia}\")\n",
    "\n",
    "\"\"\"\n",
    "A - 4 - B - 2 - D\n",
    "|       |       |\n",
    "2       1       3\n",
    "|       |       |\n",
    "C - 5 - E       F\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9689097",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d5f2a05e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rota mais barata do Rio para Brasília: ['Rio', 'Salvador', 'Brasília']\n",
      "Custo total: R$300\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Vamos considerar um exemplo relacionado ao transporte aéreo.\n",
    "\n",
    "Imagine que temos várias cidades e voos entre elas. Cada voo tem um custo \n",
    "associado. Queremos descobrir a maneira mais barata de voar de uma \n",
    "cidade (origem) para outra (destino), mesmo que isso signifique fazer escalas em outras cidades.\n",
    "\n",
    "Aqui está uma representação simplificada:\n",
    "\n",
    "Rio - 300 - SP - 150 - BH\n",
    "  |          |         |\n",
    "  200       250        80\n",
    "  |          |         |\n",
    "      Salvador - 100 - Brasília\n",
    "\n",
    "\n",
    "No grafo acima:\n",
    "\n",
    "    Rio, SP, BH, Salvador, Brasília são cidades (nós).\n",
    "    Os números representam o custo dos voos entre as cidades (peso das arestas).\n",
    "\n",
    "Se quisermos encontrar a maneira mais barata de voar do Rio para \n",
    "Brasília, podemos usar o algoritmo de Dijkstra.\n",
    "\n",
    "Aqui está a implementação usando a biblioteca networkx:\n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca networkx para manipulação e análise de grafos.\n",
    "import networkx as nx\n",
    "\n",
    "# Criando um grafo direcionado (DiGraph). Grafos direcionados são \n",
    "# aqueles onde as arestas têm uma direção específica, de um vértice \n",
    "# origem para um vértice destino.\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Adicionando arestas ao grafo junto com seus custos.\n",
    "# A função add_edge adiciona uma aresta direcionada do primeiro \n",
    "# vértice para o segundo com um atributo de peso especificado. Neste \n",
    "# contexto, os pesos representam os custos de viajar entre cidades.\n",
    "G.add_edge('Rio', 'SP', weight=300)         # Rota do Rio para SP com custo de R$300\n",
    "G.add_edge('Rio', 'Salvador', weight=200)   # Rota do Rio para Salvador com custo de R$200\n",
    "G.add_edge('SP', 'Salvador', weight=250)    # Rota de SP para Salvador com custo de R$250\n",
    "G.add_edge('SP', 'BH', weight=150)          # Rota de SP para BH com custo de R$150\n",
    "G.add_edge('BH', 'Brasília', weight=80)     # Rota de BH para Brasília com custo de R$80\n",
    "G.add_edge('Salvador', 'Brasília', weight=100) # Rota de Salvador para Brasília com custo de R$100\n",
    "\n",
    "# Utilizando o algoritmo de Dijkstra para determinar a rota mais barata entre o Rio e Brasília.\n",
    "# A função single_source_dijkstra retorna o custo mínimo e a rota mais \n",
    "# barata de um ponto de origem para um destino.\n",
    "custo, rota = nx.single_source_dijkstra(G, 'Rio', 'Brasília')\n",
    "\n",
    "# Imprimindo a rota mais barata determinada pelo algoritmo de Dijkstra do Rio para Brasília.\n",
    "print(f\"Rota mais barata do Rio para Brasília: {rota}\")\n",
    "\n",
    "# Imprimindo o custo total (soma dos pesos, ou custos) da rota mais barata do Rio para Brasília.\n",
    "print(f\"Custo total: R${custo}\")\n",
    "\n",
    "\"\"\"\n",
    "Rio - 300 - SP - 150 - BH\n",
    "  |          |         |\n",
    "  200       250        80\n",
    "  |          |         |\n",
    "      Salvador - 100 - Brasília\n",
    "      \n",
    "Quando executamos o código acima, obtemos:\n",
    "\n",
    "Rota mais barata do Rio para Brasília: ['Rio', 'Salvador', 'Brasília']\n",
    "Custo total: R$300\n",
    "\n",
    "O algoritmo mostra que a maneira mais barata de voar do Rio para Brasília \n",
    "é fazendo escala em Salvador, com um custo total de R$300.\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd2c34b6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "696be381",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Caminho mais curto de A para E: ['A', 'C', 'E']\n",
      "Distância total: 90\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício Caminho mais curto usando o Algoritmo de Dijkstra\n",
    "\n",
    "Contexto:\n",
    "\n",
    "Você recebeu um mapa de uma cidade que mostra diferentes pontos\n",
    "de interesse conectados por estradas. Cada estrada tem uma distância\n",
    "associada, que representa a distância em quilômetros entre dois pontos de interesse.\n",
    "\n",
    "Mapa da Cidade:\n",
    "\n",
    "    Pontos de interesse: A, B, C, D, E.\n",
    "    Estradas e suas distâncias:\n",
    "        A - B: 50 km\n",
    "        A - C: 30 km\n",
    "        B - D: 40 km\n",
    "        C - D: 20 km\n",
    "        C - E: 60 km\n",
    "        D - E: 70 km\n",
    "\n",
    "Tarefa:\n",
    "Utilize o algoritmo de Dijkstra para determinar o caminho mais \n",
    "curto entre o ponto A e o ponto E. Após determinar o caminho, visualize\n",
    "o mapa da cidade e destaque o caminho encontrado.\n",
    "\n",
    "Requisitos:\n",
    "\n",
    "    - Crie um grafo ponderado que represente o mapa da cidade.\n",
    "    \n",
    "    - Adicione vértices e arestas ao grafo com os respectivos pesos (distâncias).\n",
    "    \n",
    "    - Aplique o algoritmo de Dijkstra para determinar o caminho mais curto de A para E.\n",
    "    \n",
    "    - Imprima o caminho mais curto e sua distância total.\n",
    "    \n",
    "    - Visualize o mapa da cidade em forma de um gráfico, mostrando os pontos\n",
    "        de interesse, as estradas e suas distâncias.\n",
    "    \n",
    "    - No gráfico, destaque o caminho mais curto encontrado entre A e E.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "# Importando a biblioteca networkx para manipulação e análise de grafos.\n",
    "# Importando a biblioteca matplotlib.pyplot para visualização dos grafos.\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Criando um grafo ponderado, onde as arestas têm pesos associados.\n",
    "grafo_ponderado = nx.Graph()\n",
    "\n",
    "# O grafo_ponderado é uma estrutura de dados que representa um conjunto de \n",
    "# vértices (ou nós) e arestas (ou conexões) entre esses vértices.\n",
    "# Em um grafo ponderado, cada aresta tem um valor associado a ela, chamado de \"peso\".\n",
    "# O método add_edge é usado para adicionar uma aresta ao grafo.\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'A' e o vértice 'B' com um peso de 50 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('A', 'B', weight=50)\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'A' e o vértice 'C' com um peso de 30 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('A', 'C', weight=30)\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'B' e o vértice 'D' com um peso de 40 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('B', 'D', weight=40)\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'C' e o vértice 'D' com um peso de 20 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('C', 'D', weight=20)\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'C' e o vértice 'E' com um peso de 60 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('C', 'E', weight=60)\n",
    "\n",
    "# Adiciona uma aresta entre o vértice 'D' e o vértice 'E' com um peso de 70 ao grafo_ponderado.\n",
    "grafo_ponderado.add_edge('D', 'E', weight=70)\n",
    "\n",
    "# O algoritmo de Dijkstra é utilizado para encontrar o caminho mais curto em\n",
    "# grafos ponderados, considerando os pesos das arestas.\n",
    "# NetworkX, uma biblioteca Python, fornece uma implementação deste\n",
    "# algoritmo através da função \"shortest_path\".\n",
    "\n",
    "# Usando a função shortest_path para determinar a sequência de vértices \n",
    "# no caminho mais curto de 'A' a 'E' no grafo_ponderado.\n",
    "# O argumento \"weight\" especifica que o atributo 'weight' \n",
    "# das arestas deve ser usado como peso para calcular o caminho.\n",
    "caminho_mais_curto = nx.shortest_path(grafo_ponderado, 'A', 'E', weight='weight')\n",
    "\n",
    "# Utilizando a função shortest_path_length para determinar a soma \n",
    "# dos pesos das arestas no caminho mais curto de 'A' a 'E'.\n",
    "# Assim como anteriormente, o argumento \"weight\" indica que o \n",
    "# atributo 'weight' das arestas deve ser considerado.\n",
    "distancia_mais_curta = nx.shortest_path_length(grafo_ponderado, 'A', 'E', weight='weight')\n",
    "\n",
    "# Imprimindo o resultado do caminho mais curto e sua distância (soma dos pesos das arestas) total.\n",
    "print(f\"Caminho mais curto de A para E: {caminho_mais_curto}\")\n",
    "print(f\"Distância total: {distancia_mais_curta}\")\n",
    "\n",
    "# A função \"spring_layout\" de NetworkX utiliza o algoritmo \n",
    "# Fruchterman-Reingold para gerar uma disposição espacial dos vértices.\n",
    "# Esse algoritmo simula uma série de molas entre os vértices, fazendo \n",
    "# com que vértices conectados se atraiam e os não conectados se repelem.\n",
    "# O resultado é uma disposição que tende a destacar a estrutura do grafo.\n",
    "posicoes = nx.spring_layout(grafo_ponderado)\n",
    "\n",
    "# A função \"draw\" de NetworkX é utilizada para visualizar o grafo.\n",
    "# - \"posicoes\" determina onde cada vértice será posicionado no gráfico.\n",
    "# - \"with_labels=True\" indica que queremos que os nomes dos vértices sejam exibidos.\n",
    "# - \"node_size=500\" define o tamanho de cada vértice.\n",
    "# - \"node_color='lightblue'\" especifica a cor dos vértices.\n",
    "nx.draw(grafo_ponderado, posicoes, with_labels=True, node_size=500, node_color='lightblue')\n",
    "\n",
    "\n",
    "# Desenhando os rótulos (pesos) nas arestas do grafo.\n",
    "# nx.draw_networkx_edge_labels(grafo_ponderado, posicoes, edge_labels={(u, v): grafo_ponderado[u][v]['weight'] for u, v in grafo_ponderado.edges()})\n",
    "\n",
    "\n",
    "# Inicializando um dicionário vazio chamado 'rotulos_arestas'. \n",
    "# Esse dicionário irá armazenar os pares de vértices das arestas \n",
    "# como chaves e os respectivos pesos como valores.\n",
    "rotulos_arestas = {}\n",
    "\n",
    "# Começando a iteração por todas as arestas do grafo ponderado. \n",
    "# Cada aresta é representada por um par de vértices (u, v).\n",
    "for u, v in grafo_ponderado.edges():\n",
    "    \n",
    "    # Para cada aresta, obtemos o peso associado a ela no grafo ponderado.\n",
    "    # O peso é obtido acessando o atributo 'weight' da aresta entre os vértices 'u' e 'v'.\n",
    "    # Esse peso é então armazenado no dicionário 'rotulos_arestas', \n",
    "    # usando o par de vértices (u, v) como chave e o peso como valor.\n",
    "    rotulos_arestas[(u, v)] = grafo_ponderado[u][v]['weight']\n",
    "\n",
    "# Após coletar todos os rótulos das arestas, usamos a \n",
    "# função 'draw_networkx_edge_labels' para desenhar os rótulos.\n",
    "# Passamos o grafo ponderado, as posições previamente definidas\n",
    "# dos vértices ('posicoes') e o dicionário de rótulos das arestas.\n",
    "# Dessa forma, a visualização do grafo mostrará os pesos das arestas\n",
    "# ao lado de cada aresta correspondente.\n",
    "nx.draw_networkx_edge_labels(grafo_ponderado, posicoes, edge_labels=rotulos_arestas)\n",
    "\n",
    "\n",
    "# Destacando no gráfico o caminho mais curto encontrado, \n",
    "# desenhando-o com cor vermelha e espessura maior.\n",
    "# A função 'zip' é usada para combinar dois ou mais \n",
    "# iteráveis. Aqui, estamos combinando o 'caminho_mais_curto' com uma versão\n",
    "# deslocada de si mesmo (caminho_mais_curto[1:]). O objetivo é \n",
    "# criar pares consecutivos de vértices que representam as arestas \n",
    "# no caminho mais curto.\n",
    "# Por exemplo, se caminho_mais_curto = ['A', 'B', 'C'], o resultado \n",
    "# do 'zip' será [('A', 'B'), ('B', 'C')], que representa as arestas\n",
    "# do caminho mais curto.\n",
    "arestas_caminho = list(zip(caminho_mais_curto, caminho_mais_curto[1:]))\n",
    "\n",
    "# Agora, usando a função 'draw_networkx_edges', desenhamos apenas \n",
    "# as arestas que fazem parte do caminho mais curto no grafo.\n",
    "# 'grafo_ponderado' é o grafo onde queremos visualizar o caminho, \n",
    "# 'posicoes' determina a posição de cada vértice no gráfico.\n",
    "# 'edgelist=arestas_caminho' indica que queremos desenhar apenas as \n",
    "# arestas listadas em 'arestas_caminho'.\n",
    "# 'edge_color='r'' dá a cor vermelha para essas arestas, destacando-as no grafo.\n",
    "# 'width=2' define a largura dessas arestas para ser um pouco mais espessa, \n",
    "# tornando-as mais proeminentes.\n",
    "nx.draw_networkx_edges(grafo_ponderado, posicoes, edgelist=arestas_caminho, edge_color='r', width=2)\n",
    "\n",
    "# Exibindo o gráfico.\n",
    "plt.show()\n",
    "\n",
    "\"\"\"\n",
    "Pontos de interesse: A, B, C, D, E.\n",
    "    Estradas e suas distâncias:\n",
    "        A - B: 50 km\n",
    "        A - C: 30 km\n",
    "        B - D: 40 km\n",
    "        C - D: 20 km\n",
    "        C - E: 60 km\n",
    "        D - E: 70 km\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74642450",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "779b1bb7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "66e826f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grafos\n",
    "            \n",
    "            Algoritmos Clássicos\n",
    "\n",
    "                Algoritmo de Bellman-Ford\n",
    "                \n",
    "                \n",
    "O Algoritmo de Bellman-Ford é usado para encontrar o caminho mais \n",
    "curto de um vértice de origem a todos os outros vértices em um grafo \n",
    "ponderado. Diferentemente do algoritmo de Dijkstra, o Bellman-Ford \n",
    "pode trabalhar com pesos negativos de arestas e pode detectar \n",
    "ciclos negativos.\n",
    "\n",
    "\n",
    "Vamos imaginar que temos cidades interligadas por estradas que, devido\n",
    "a certos fenômenos misteriosos, podem fazer você viajar no tempo!\n",
    "\n",
    "Descrição do gráfico:\n",
    "\n",
    "    Cidade A para Cidade B leva 2 horas.\n",
    "    Cidade B para Cidade C leva 3 horas.\n",
    "    Cidade A para Cidade C tem um fenômeno que reduz o tempo da \n",
    "        viagem em 4 horas (peso negativo).\n",
    "\n",
    "A questão é: Qual é o caminho mais rápido da Cidade A para a Cidade C?\n",
    "\n",
    "Codificação e resposta:\n",
    "\"\"\"\n",
    "\n",
    "# Importando as bibliotecas necessárias para a tarefa.\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Criando um grafo direcionado (DiGraph) para \n",
    "# representar as conexões entre as estações.\n",
    "grafo = nx.DiGraph()\n",
    "\n",
    "# Estamos criando conexões (também conhecidas como arestas ou rotas) entre as estações no grafo. \n",
    "# Em um contexto de transporte ou viagem, as arestas podem representar rotas diretas entre duas estações.\n",
    "# O parâmetro 'weight' em cada conexão especifica o tempo (ou custo) necessário para viajar entre essas duas estações.\n",
    "\n",
    "# Adiciona uma rota direta da 'Estação Alfa' para a 'Estação Beta' que leva 4 unidades de tempo.\n",
    "grafo.add_edge('Estação Alfa', 'Estação Beta', weight=4)\n",
    "\n",
    "# Adiciona uma rota direta da 'Estação Alfa' para a 'Estação Gama' que leva 2 unidades de tempo.\n",
    "grafo.add_edge('Estação Alfa', 'Estação Gama', weight=2)\n",
    "\n",
    "# Adiciona uma rota direta da 'Estação Beta' para a 'Estação Delta'. \n",
    "# Aqui, temos um valor de duração negativo (-2), o que é raro em cenários reais. \n",
    "# No entanto, o algoritmo Bellman-Ford é capaz de lidar com pesos \n",
    "# negativos, o que é uma de suas características distintivas. \n",
    "# Em um contexto real, ter um peso negativo poderia representar um benefício, \n",
    "# recompensa ou algum tipo de incentivo.\n",
    "grafo.add_edge('Estação Beta', 'Estação Delta', weight=-2)\n",
    "\n",
    "# Adiciona uma rota direta da 'Estação Gama' para a 'Estação Delta' que \n",
    "# leva 3 unidades de tempo.\n",
    "grafo.add_edge('Estação Gama', 'Estação Delta', weight=3)\n",
    "\n",
    "\n",
    "# Aplicando o algoritmo de Bellman-Ford para calcular os caminhos mais curtos da 'Estação Alfa' para todas as outras estações.\n",
    "# 'predecessores' é um dicionário que mapeia cada estação ao seu predecessor no caminho mais curto.\n",
    "# 'distancias' é um dicionário que mapeia cada estação à sua distância mínima da 'Estação Alfa'.\n",
    "predecessores, distancias = nx.bellman_ford_predecessor_and_distance(grafo, 'Estação Alfa')\n",
    "\n",
    "\n",
    "# Inicializamos a reconstrução do caminho mais curto a partir da \n",
    "# 'Estação Delta', pois queremos determinar o caminho da 'Estação Alfa' \n",
    "# para a 'Estação Delta'.\n",
    "# Começamos pelo destino e trabalhamos retroativamente até a origem.\n",
    "caminho = ['Estação Delta']\n",
    "\n",
    "# Iniciamos com o destino ('Estação Delta') como o nó atual.\n",
    "no_atual = 'Estação Delta'\n",
    "\n",
    "# Continuamos a encontrar o predecessor (estação anterior) de cada nó\n",
    "# até chegarmos à origem ('Estação Alfa').\n",
    "# A ideia é retroceder passo a passo, de estação em estação, \n",
    "# usando o dicionário de predecessores até que alcancemos a estação inicial.\n",
    "while no_atual != 'Estação Alfa':\n",
    "    \n",
    "    # Obtemos o nó predecessor (estação anterior) do nó atual.\n",
    "    # O dicionário \"predecessores\" fornece a próxima estação na \n",
    "    # rota mais curta de volta à estação de origem.\n",
    "    no_atual = predecessores[no_atual][0]\n",
    "    \n",
    "    # Adicionamos esse nó predecessor ao nosso caminho.\n",
    "    caminho.append(no_atual)\n",
    "\n",
    "# Como construímos o caminho do destino para a origem, o caminho está ao contrário.\n",
    "# Por isso, invertemos a lista para que ela comece na 'Estação Alfa' e \n",
    "# termine na 'Estação Delta'.\n",
    "caminho.reverse()\n",
    "\n",
    "# Definindo uma disposição (layout) espacial para os \n",
    "# vértices (neste caso, estações) do grafo.\n",
    "# O layout \"spring\" (mola) posiciona os vértices de tal \n",
    "# forma que todas as arestas tenham mais ou menos o mesmo comprimento\n",
    "# e tenta minimizar o número de arestas que se cruzam no gráfico.\n",
    "pos = nx.spring_layout(grafo)\n",
    "\n",
    "# Desenhando o grafo:\n",
    "# - `pos` especifica as posições dos vértices.\n",
    "# - `with_labels=True` garante que os rótulos dos vértices sejam exibidos.\n",
    "# - `node_color='lightblue'` dá uma cor azul clara aos vértices.\n",
    "# - `edge_color='gray'` dá uma cor cinza às arestas.\n",
    "nx.draw(grafo, pos, with_labels=True, node_color='lightblue', edge_color='gray')\n",
    "\n",
    "\n",
    "# Extraindo os pesos (neste contexto, durações das rotas \n",
    "# entre estações) das arestas do grafo.\n",
    "# O resultado é um dicionário onde a chave é uma tupla \n",
    "# representando a aresta e o valor é o peso dessa aresta.\n",
    "etiquetas_arestas = nx.get_edge_attributes(grafo, 'weight')\n",
    "\n",
    "\n",
    "# Desenhando as etiquetas (pesos/durações) nas arestas do grafo.\n",
    "# - `edge_labels=etiquetas_arestas` especifica o que será exibido nas arestas.\n",
    "nx.draw_networkx_edge_labels(grafo, pos, edge_labels=etiquetas_arestas)\n",
    "\n",
    "\n",
    "# Destacando o caminho mais curto entre 'Estação Alfa' e 'Estação Delta' no gráfico:\n",
    "\n",
    "# Iterando sobre cada par de estações consecutivas no caminho mais curto.\n",
    "# Por exemplo, se o caminho for ['Estação Alfa', 'Estação Beta', 'Estação Delta'],\n",
    "# as combinações de estações serão [('Estação Alfa', 'Estação Beta'), ('Estação Beta', 'Estação Delta')].\n",
    "for i in range(len(caminho) - 1):\n",
    "    \n",
    "    # Obtendo as coordenadas x e y da primeira estação do par no layout definido.\n",
    "    x0, y0 = pos[caminho[i]]\n",
    "    \n",
    "    # Obtendo as coordenadas x e y da segunda estação do par no layout definido.\n",
    "    x1, y1 = pos[caminho[i+1]]\n",
    "    \n",
    "    # Usando a função `plot` do Matplotlib para desenhar uma linha entre as duas estações.\n",
    "    # A linha é desenhada em vermelho ('color='r'`) e tem largura 2 (`lw=2`), \n",
    "    # tornando-a mais espessa.\n",
    "    plt.plot([x0, x1], [y0, y1], color='r', lw=2)\n",
    "\n",
    "# Mostrando o gráfico final.\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Explicação:\n",
    "\n",
    "\n",
    "há quatro estações: Alfa, Beta, Gama e Delta. Temos as seguintes \n",
    "rotas entre as estações:\n",
    "\n",
    "    Estação Alfa -> Estação Beta: Duração de 4 horas.\n",
    "    Estação Alfa -> Estação Gama: Duração de 2 horas.\n",
    "    Estação Beta -> Estação Delta: Duração de -2 horas.\n",
    "    Estação Gama -> Estação Delta: Duração de 3 horas.\n",
    "\n",
    "Aqui, é crucial observar que a rota da Estação Beta para a Estação\n",
    "Delta tem uma duração de -2 horas, o que significa que é uma rota\n",
    "\"rápida\", onde, em vez de adicionar tempo à jornada, na verdade, você \n",
    "\"ganha\" 2 horas. Isto é para mostrar a capacidade do Bellman-Ford de \n",
    "lidar com pesos negativos.\n",
    "\n",
    "Ao aplicar o algoritmo de Bellman-Ford, buscamos o caminho mais \n",
    "rápido (ou seja, de menor duração) da Estação Alfa para a Estação Delta:\n",
    "\n",
    "    Caminho Direto através da Estação Gama: Alfa -> Gama -> Delta = 2 horas + 3 horas = 5 horas.\n",
    "    Caminho através da Estação Beta: Alfa -> Beta -> Delta = 4 horas - 2 horas = 2 horas.\n",
    "\n",
    "O caminho mais rápido é através da Estação Beta com um tempo total de 2 horas, \n",
    "graças à rota \"rápida\" da Estação Beta para a Estação Delta.\n",
    "\n",
    "Na visualização, o caminho mais rápido é destacado em vermelho, mostrando \n",
    "claramente a rota ótima de Alfa -> Beta -> Delta.\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eef65e55",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1bde0c24",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distâncias a partir da Cidade A:\n",
      "Cidade A: $0\n",
      "Cidade B: $5\n",
      "Cidade C: $8\n",
      "Cidade D: $7\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exercício de Bellman-Ford:\n",
    "\n",
    "Suponha que temos um conjunto de cidades e estradas entre elas, e\n",
    "queremos encontrar o caminho mais barato da Cidade A para a Cidade D.\n",
    "\n",
    "Exemplo Visual\n",
    "\n",
    "Descrição do gráfico:\n",
    "\n",
    "    Cidade A tem uma estrada para a Cidade B com um custo de $5.\n",
    "    Cidade A tem uma estrada para a Cidade C com um custo de $8.\n",
    "    Cidade B tem uma estrada para a Cidade D com um custo de $2.\n",
    "    Cidade C tem uma estrada para a Cidade D com um custo de $4.\n",
    "\n",
    "Com base neste gráfico, o caminho mais barato da Cidade A para a \n",
    "Cidade D é A -> B -> D com um custo total de $7.\n",
    "\n",
    "Crie um código que crie um Grafo com esse dados destacando o \n",
    "caminho mais barato.\n",
    "\"\"\"\n",
    "\n",
    "# Solução\n",
    "\n",
    "# Importando as bibliotecas necessárias\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Inicializando um grafo direcionado. Um grafo direcionado é um \n",
    "# conjunto de vértices (cidades) e arestas direcionadas (estradas) entre esses vértices.\n",
    "grafo = nx.DiGraph()\n",
    "\n",
    "# Adicionando arestas ao grafo para representar estradas entre\n",
    "# cidades. O parâmetro 'weight' indica o custo de viajar por essa estrada.\n",
    "grafo.add_edge('Cidade A', 'Cidade B', weight=5)\n",
    "grafo.add_edge('Cidade A', 'Cidade C', weight=8)\n",
    "grafo.add_edge('Cidade B', 'Cidade D', weight=2)\n",
    "grafo.add_edge('Cidade C', 'Cidade D', weight=4)\n",
    "\n",
    "# Aplicando o algoritmo de Bellman-Ford para calcular o caminho mais\n",
    "# barato de 'Cidade A' para todas as outras cidades no grafo.\n",
    "predecessores, distancias = nx.bellman_ford_predecessor_and_distance(grafo, 'Cidade A')\n",
    "\n",
    "# Imprimindo as distâncias (ou custos) calculadas da 'Cidade A' para \n",
    "# todas as outras cidades no grafo.\n",
    "# A função print é usada para exibir uma mensagem no console ou terminal.\n",
    "print(\"Distâncias a partir da Cidade A:\")\n",
    "\n",
    "# O loop for é usado para iterar sobre cada item no dicionário 'distancias'. \n",
    "# O dicionário 'distancias' contém cada cidade como chave e a \n",
    "# distância (ou custo) da 'Cidade A' para essa cidade como valor.\n",
    "for cidade, distancia in distancias.items():\n",
    "    \n",
    "    # Dentro do loop, a função print é usada novamente para \n",
    "    # exibir a cidade e sua respectiva distância.\n",
    "    # O f-string (indicado pelo prefixo 'f') permite incorporar \n",
    "    # valores de variáveis diretamente na string.\n",
    "    print(f\"{cidade}: ${distancia}\")\n",
    "    \n",
    "\n",
    "# Iniciando o processo de reconstrução do caminho mais barato da 'Cidade A' para a 'Cidade D'.\n",
    "# Começamos com a 'Cidade D' porque queremos reconstruir o caminho de volta para a 'Cidade A'.\n",
    "caminho = ['Cidade D']\n",
    "\n",
    "# A variável 'no_atual' é usada para acompanhar a cidade atual enquanto reconstruímos o caminho.\n",
    "# Como estamos reconstruindo de trás para frente, começamos com a 'Cidade D'.\n",
    "no_atual = 'Cidade D'\n",
    "\n",
    "# O loop while continuará enquanto 'no_atual' não for 'Cidade A', \n",
    "# ou seja, até que o caminho completo seja reconstruído.\n",
    "while no_atual != 'Cidade A':\n",
    "    \n",
    "    # Atualizando 'no_atual' para ser a cidade predecessora da \n",
    "    # cidade atual no caminho mais barato.\n",
    "    # O dicionário 'predecessores' fornece a cidade \n",
    "    # predecessora para cada cidade no grafo.\n",
    "    no_atual = predecessores[no_atual][0]\n",
    "    \n",
    "    # Adicionando a cidade predecessora à lista 'caminho'.\n",
    "    caminho.append(no_atual)\n",
    "    \n",
    "# Como o caminho foi construído começando pela 'Cidade D' e \n",
    "# terminando na 'Cidade A', ele está ao contrário.\n",
    "# Portanto, usamos o método reverse() para inverter a lista e \n",
    "# obter o caminho correto da 'Cidade A' para a 'Cidade D'.\n",
    "caminho.reverse()\n",
    "\n",
    "# Usando o layout \"spring\" para determinar a disposição dos \n",
    "# vértices (neste caso, as cidades) no espaço bidimensional.\n",
    "# Esta disposição tenta posicionar os vértices de forma que as\n",
    "# arestas tenham aproximadamente o mesmo comprimento e haja pouca sobreposição.\n",
    "pos = nx.spring_layout(grafo)\n",
    "\n",
    "# Desenhando o grafo no espaço determinado pelo layout 'spring'.\n",
    "# O parâmetro 'with_labels=True' indica que queremos que os nomes das cidades sejam exibidos.\n",
    "# 'node_color' define a cor dos círculos que representam as cidades.\n",
    "nx.draw(grafo, pos, with_labels=True, node_color='lightblue')\n",
    "\n",
    "# Recuperando os pesos (ou custos) associados a cada aresta (neste caso, estrada) no grafo.\n",
    "# Estes serão usados para mostrar os custos das estradas entre as cidades.\n",
    "etiquetas_arestas = nx.get_edge_attributes(grafo, 'weight')\n",
    "\n",
    "# Adicionando rótulos às arestas (estradas) usando os custos recuperados anteriormente.\n",
    "# 'edge_labels' especifica a informação que queremos mostrar em cada aresta.\n",
    "nx.draw_networkx_edge_labels(grafo, pos, edge_labels=etiquetas_arestas)\n",
    "\n",
    "# Para destacar o caminho mais barato de 'Cidade A' para 'Cidade D', criamos\n",
    "# uma lista de arestas que compõem esse caminho.\n",
    "# A função zip() é usada para combinar cada cidade no 'caminho' com a \n",
    "# cidade seguinte, criando pares que representam as arestas.\n",
    "caminho_arestas = list(zip(caminho, caminho[1:]))\n",
    "\n",
    "\n",
    "# Desenhando as arestas do caminho mais barato com uma cor vermelha e uma espessura de linha de 2.\n",
    "# 'edgelist' especifica quais arestas queremos desenhar, e 'edge_color' \n",
    "# e 'width' definem a cor e a espessura da linha, respectivamente.\n",
    "nx.draw_networkx_edges(grafo, pos, edgelist=caminho_arestas, edge_color='r', width=2)\n",
    "\n",
    "# Usando a função 'show' da biblioteca Matplotlib para exibir o gráfico gerado.\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Ao executar o código acima, você obterá a distância mais curta \n",
    "da Cidade A para todas as outras cidades e uma visualização do \n",
    "grafo. Isso deve fornecer uma representação clara e simples do \n",
    "algoritmo de Bellman-Ford em ação.\n",
    "\"\"\"\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "866b3a21",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2d68e008",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Arestas da Árvore Geradora Mínima:\n",
      "(A, D): $3\n",
      "(A, B): $5\n",
      "(C, D): $8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Grafos\n",
    "            \n",
    "            Algoritmos Clássicos\n",
    "\n",
    "                Algoritmo de Kruskal para Árvores Geradoras Mínimas\n",
    "                \n",
    "                \n",
    "\n",
    "O algoritmo de Kruskal é usado para encontrar uma árvore geradora \n",
    "mínima em um grafo conectado e ponderado. Uma árvore geradora mínima \n",
    "é um subgrafo que conecta todos os vértices do grafo original\n",
    "sem formar ciclos e tem o menor peso total possível.\n",
    "\n",
    "Vamos usar um exemplo prático envolvendo um sistema de distribuição de energia:\n",
    "\n",
    "Enunciado:\n",
    "\n",
    "Imagine que temos várias cidades e queremos conectá-las com linhas de transmissão\n",
    "de energia. Cada possível conexão entre duas cidades tem um custo associado. \n",
    "\n",
    "Nosso objetivo é construir uma rede de transmissão que conecte todas as \n",
    "cidades e tenha o menor custo total.\n",
    "\n",
    "Descrição do gráfico:\n",
    "\n",
    "    Cidade A e Cidade B podem ser conectadas com um custo de $5.\n",
    "    Cidade A e Cidade C podem ser conectadas com um custo de $10.\n",
    "    Cidade A e Cidade D podem ser conectadas com um custo de $3.\n",
    "    Cidade B e Cidade D podem ser conectadas com um custo de $7.\n",
    "    Cidade C e Cidade D podem ser conectadas com um custo de $8.\n",
    "\n",
    "Vamos agora codificar o exemplo:\n",
    "\"\"\"\n",
    "\n",
    "# Importando as bibliotecas necessárias\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Importa a biblioteca NetworkX para manipulação de grafos\n",
    "import networkx as nx\n",
    "\n",
    "# Inicializa uma instância da classe Graph do NetworkX, que representa um grafo não-direcionado.\n",
    "# Neste ponto, o grafo está vazio, sem vértices ou arestas.\n",
    "grafo = nx.Graph()\n",
    "\n",
    "# Utiliza o método 'add_edge' para adicionar uma aresta entre os vértices 'A' e 'B' com um peso de 5.\n",
    "# Se 'A' e 'B' não existem ainda no grafo, eles são adicionados automaticamente.\n",
    "grafo.add_edge('A', 'B', weight=5)\n",
    "\n",
    "# Adiciona uma aresta entre 'A' e 'C' com um peso de 10.\n",
    "# Novamente, se os vértices não existem, são adicionados.\n",
    "grafo.add_edge('A', 'C', weight=10)\n",
    "\n",
    "# Adiciona uma aresta entre 'A' e 'D' com um peso de 3.\n",
    "grafo.add_edge('A', 'D', weight=3)\n",
    "\n",
    "# Adiciona uma aresta entre 'B' e 'D' com um peso de 7.\n",
    "grafo.add_edge('B', 'D', weight=7)\n",
    "\n",
    "# Adiciona uma aresta final entre 'C' e 'D' com um peso de 8.\n",
    "grafo.add_edge('C', 'D', weight=8)\n",
    "\n",
    "\n",
    "# Utiliza a função 'minimum_spanning_edges' do NetworkX para obter\n",
    "# as arestas que compõem a Árvore Geradora Mínima (AGM)\n",
    "# do grafo usando o algoritmo de Kruskal.\n",
    "# - O parâmetro 'algorithm=\"kruskal\"' especifica que queremos usar o algoritmo de Kruskal.\n",
    "# - O parâmetro 'data=True' garante que os dados associados a cada \n",
    "# aresta (como o peso) sejam retornados junto com a aresta.\n",
    "arvore_geradora_minima = list(nx.minimum_spanning_edges(grafo, algorithm=\"kruskal\", data=True))\n",
    "\n",
    "# Imprime a mensagem inicial para indicar a listagem das arestas da AGM.\n",
    "print(\"Arestas da Árvore Geradora Mínima:\")\n",
    "\n",
    "# Itera sobre cada aresta na árvore geradora mínima.\n",
    "# Cada item (u, v, w) consiste em:\n",
    "# - 'u' e 'v': os dois vértices que a aresta conecta.\n",
    "# - 'w': um dicionário contendo os atributos da aresta (neste \n",
    "# caso, estamos interessados no peso, que é acessado com 'w['weight']').\n",
    "for u, v, w in arvore_geradora_minima:\n",
    "    \n",
    "    # Imprime a aresta e seu peso no formato \"(vértice1, vértice2): $peso\".\n",
    "    print(f\"({u}, {v}): ${w['weight']}\")\n",
    "    \n",
    "\n",
    "# Define a posição dos nós do grafo usando o \"spring layout\", \n",
    "# que posiciona os nós usando uma simulação de forças\n",
    "# em que arestas são tratadas como molas que se repeliriam ou \n",
    "# atraem. Isso ajuda a distribuir os nós de forma que\n",
    "# o grafo seja esteticamente agradável e fácil de entender.\n",
    "pos = nx.spring_layout(grafo)\n",
    "\n",
    "# Desenha o grafo na posição definida anteriormente.\n",
    "# 'with_labels=True' indica que os rótulos (neste caso, os nomes) dos nós devem ser desenhados.\n",
    "# 'node_color='lightblue'' define a cor de fundo dos nós.\n",
    "nx.draw(grafo, pos, with_labels=True, node_color='lightblue')\n",
    "\n",
    "# Obtém os pesos (atributos 'weight') de todas as arestas do grafo. \n",
    "# Isso nos dá um dicionário onde as chaves são pares de \n",
    "# nós (representando arestas) e os valores são os pesos correspondentes.\n",
    "etiquetas_arestas = nx.get_edge_attributes(grafo, 'weight')\n",
    "\n",
    "\n",
    "# Desenha as etiquetas (neste caso, os pesos) nas arestas do grafo.\n",
    "# 'edge_labels=etiquetas_arestas' indica que as etiquetas das arestas \n",
    "# são os pesos que acabamos de obter.\n",
    "nx.draw_networkx_edge_labels(grafo, pos, edge_labels=etiquetas_arestas)\n",
    "\n",
    "\n",
    "# Destaca as arestas que fazem parte da árvore geradora mínima.\n",
    "# 'edgelist' especifica a lista de arestas que queremos desenhar. Neste caso, estamos construindo essa lista a partir \n",
    "# da árvore geradora mínima que foi calculada anteriormente.\n",
    "# 'edge_color='r'' define a cor das arestas como vermelho, o que as destaca em relação às outras arestas.\n",
    "# 'width=2' especifica a largura da linha usada para desenhar as arestas.\n",
    "# nx.draw_networkx_edges(grafo, pos, edgelist=[(u, v) for u, v, w in arvore_geradora_minima], edge_color='r', width=2)\n",
    "\n",
    "# Construir a lista de arestas que pertencem à árvore geradora mínima.\n",
    "# Esta lista contém os pares de nós (u, v) que representam as arestas da árvore geradora mínima.\n",
    "arestas_mst = [(u, v) for u, v, w in arvore_geradora_minima]\n",
    "\n",
    "# Desenhar as arestas da árvore geradora mínima em destaque.\n",
    "# 'edgelist' especifica quais arestas desenhar. Estamos fornecendo a lista que acabamos de construir.\n",
    "# 'edge_color' define a cor das arestas (neste caso, vermelho).\n",
    "# 'width' define a largura das linhas que representam as arestas. Um valor maior do que o padrão destaca as arestas.\n",
    "nx.draw_networkx_edges(grafo, pos, edgelist=arestas_mst, edge_color='r', width=2)\n",
    "\n",
    "\n",
    "# Exibe o grafo desenhado.\n",
    "# Este comando é essencial quando se usa a biblioteca matplotlib para visualização, pois instrui o matplotlib a \n",
    "# renderizar e exibir o plot/gráfico que foi construído até agora.\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Neste exemplo, você verá o grafo com as possíveis conexões entre as cidades \n",
    "e a árvore geradora mínima destacada em vermelho, representando o menor custo \n",
    "total para conectar todas as cidades.\n",
    "\n",
    "\n",
    "Resultado:\n",
    "\n",
    "O algoritmo de Kruskal procura a árvore geradora mínima de um grafo conectado, \n",
    "ou seja, um subconjunto das arestas que conecta todos os vértices juntos sem\n",
    "formar qualquer ciclo e com o peso total mínimo.\n",
    "\n",
    "Neste exemplo, as arestas selecionadas para a árvore geradora mínima foram:\n",
    "\n",
    "    ('A', 'D') com peso 3\n",
    "    ('A', 'B') com peso 5\n",
    "    ('B', 'D') com peso 7\n",
    "\n",
    "Estas arestas foram selecionadas porque formam uma árvore (ou seja, não\n",
    "têm ciclos) e têm o peso total mínimo possível, que é 15.\n",
    "\n",
    "\n",
    "    Cidade A e Cidade B podem ser conectadas com um custo de $5.\n",
    "    Cidade A e Cidade C podem ser conectadas com um custo de $10.\n",
    "    Cidade A e Cidade D podem ser conectadas com um custo de $3.\n",
    "    Cidade B e Cidade D podem ser conectadas com um custo de $7.\n",
    "    Cidade C e Cidade D podem ser conectadas com um custo de $8.\n",
    "\"\"\"\n",
    "print()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80956e72",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1b8dc4f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Arestas da Árvore Geradora Mínima:\n",
      "(F, J): $1\n",
      "(D, F): $2\n",
      "(A, D): $3\n",
      "(C, F): $4\n",
      "(A, B): $5\n",
      "(B, E): $6\n",
      "(D, G): $11\n",
      "(E, H): $12\n",
      "(E, I): $13\n",
      "Custo total da Árvore Geradora Mínima: $57\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exemplo mais completo de Algoritmo de Kruskal para Árvores Geradoras Mínimas\n",
    "\"\"\"\n",
    "\n",
    "# Importando a biblioteca para trabalhar com grafos.\n",
    "import networkx as nx\n",
    "\n",
    "# Importando a biblioteca para visualização gráfica.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Inicializando um grafo não direcionado. Um grafo não direcionado não possui direção nas arestas.\n",
    "grafo_cidades = nx.Graph()\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'A' e 'B' com um peso de 5.\n",
    "grafo_cidades.add_edge('A', 'B', weight=5)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'A' e 'C' com um peso de 10.\n",
    "grafo_cidades.add_edge('A', 'C', weight=10)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'A' e 'D' com um peso de 3.\n",
    "grafo_cidades.add_edge('A', 'D', weight=3)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'B' e 'D' com um peso de 7.\n",
    "grafo_cidades.add_edge('B', 'D', weight=7)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'B' e 'E' com um peso de 6.\n",
    "grafo_cidades.add_edge('B', 'E', weight=6)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'C' e 'E' com um peso de 9.\n",
    "grafo_cidades.add_edge('C', 'E', weight=9)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'C' e 'F' com um peso de 4.\n",
    "grafo_cidades.add_edge('C', 'F', weight=4)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'D' e 'F' com um peso de 2.\n",
    "grafo_cidades.add_edge('D', 'F', weight=2)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'D' e 'G' com um peso de 11.\n",
    "grafo_cidades.add_edge('D', 'G', weight=11)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'E' e 'H' com um peso de 12.\n",
    "grafo_cidades.add_edge('E', 'H', weight=12)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'E' e 'I' com um peso de 13.\n",
    "grafo_cidades.add_edge('E', 'I', weight=13)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'F' e 'J' com um peso de 1.\n",
    "grafo_cidades.add_edge('F', 'J', weight=1)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'G' e 'J' com um peso de 14.\n",
    "grafo_cidades.add_edge('G', 'J', weight=14)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'H' e 'I' com um peso de 15.\n",
    "grafo_cidades.add_edge('H', 'I', weight=15)\n",
    "\n",
    "# Adicionando uma aresta entre os vértices/nós 'I' e 'J' com um peso de 16.\n",
    "grafo_cidades.add_edge('I', 'J', weight=16)\n",
    "\n",
    "\n",
    "# Utilizar o algoritmo de Kruskal para encontrar a árvore geradora mínima do grafo 'grafo_cidades'.\n",
    "\n",
    "# O conceito de uma \"árvore geradora mínima\" (AGM) é central em teoria dos grafos e aplicações práticas em redes.\n",
    "# Uma AGM é um subconjunto de arestas de um grafo conectado, sem ciclos, que conecta todos os vértices juntos \n",
    "# com o mínimo de peso total.\n",
    "\n",
    "# A biblioteca 'networkx' oferece uma função chamada 'minimum_spanning_edges' que retorna as arestas da AGM de um grafo.\n",
    "# Essa função utiliza vários algoritmos para encontrar a AGM. Um dos mais populares é o algoritmo de Kruskal.\n",
    "\n",
    "# Ao chamar a função:\n",
    "# - Primeiro argumento: é o grafo para o qual queremos encontrar a AGM, que neste caso é 'grafo_cidades'.\n",
    "# - 'algorithm=\"kruskal\"': especifica que o algoritmo de Kruskal deve ser usado. Existem outros algoritmos possíveis, mas Kruskal é uma escolha comum.\n",
    "# - 'data=True': indica que queremos que os dados associados a cada aresta (neste caso, o peso) sejam retornados junto com a aresta.\n",
    "\n",
    "# A função 'minimum_spanning_edges' retorna um gerador, o que significa que não retorna todos os resultados de uma vez, \n",
    "# mas permite que você itere sobre eles um de cada vez. \n",
    "# Para converter esse gerador em uma lista (para que possamos trabalhar com os resultados mais facilmente ou referenciá-los várias vezes), \n",
    "# usamos a função 'list'.\n",
    "arvore_minima = list(nx.minimum_spanning_edges(grafo_cidades, algorithm=\"kruskal\", data=True))\n",
    "\n",
    "\n",
    "# Calcular o custo total (ou peso) da árvore geradora mínima.\n",
    "\n",
    "# Usamos uma compreensão de lista para iterar sobre cada aresta na árvore geradora mínima.\n",
    "# Cada aresta na 'arvore_minima' é representada por uma tupla (cidade1, cidade2, peso).\n",
    "# O underscore (_) é usado para descartar temporariamente os dois primeiros valores da tupla (cidade1 e cidade2), \n",
    "# já que estamos interessados apenas no 'peso'.\n",
    "# O 'peso' é um dicionário que contém informações adicionais sobre a aresta. \n",
    "# Neste caso, estamos interessados no valor associado à chave 'weight', que representa o peso da aresta.\n",
    "# 'sum()' é uma função que soma todos os valores produzidos pela compreensão de lista.\n",
    "# O resultado é o custo total (ou peso) de todas as arestas na árvore geradora mínima.\n",
    "custo_arvore_minima = sum(peso['weight'] for _, _, peso in arvore_minima)\n",
    "\n",
    "\n",
    "# Exibir as arestas que fazem parte da árvore geradora mínima.\n",
    "print(\"Arestas da Árvore Geradora Mínima:\")\n",
    "\n",
    "# Iterar sobre as arestas na árvore geradora mínima e exibir cada aresta junto com seu peso.\n",
    "\n",
    "# A estrutura 'for' permite-nos percorrer cada aresta da 'arvore_minima'.\n",
    "# Cada aresta é uma tupla que consiste em dois nós (representando as cidades) e um dicionário (peso).\n",
    "# 'cidade1' e 'cidade2' representam os dois nós da aresta, enquanto 'peso' é um dicionário contendo informações adicionais sobre a aresta.\n",
    "\n",
    "# No loop:\n",
    "for cidade1, cidade2, peso in arvore_minima:\n",
    "    \n",
    "    # A função 'print' é usada para exibir a informação.\n",
    "\n",
    "    # Usamos uma string formatada (f-string) para inserir os valores de 'cidade1', 'cidade2', e o peso da aresta \n",
    "    # diretamente na string a ser impressa.\n",
    "    # Dentro da f-string, {cidade1} e {cidade2} são substituídos pelos nomes das cidades da aresta atual.\n",
    "    # {peso['weight']} acessa o valor associado à chave 'weight' no dicionário 'peso', que é o peso da aresta.\n",
    "    # O resultado final é uma string que mostra as duas cidades conectadas pela aresta e o peso dessa conexão.\n",
    "    print(f\"({cidade1}, {cidade2}): ${peso['weight']}\")\n",
    "\n",
    "\n",
    "# Exibir o custo total (ou peso) da árvore geradora mínima.\n",
    "print(f\"Custo total da Árvore Geradora Mínima: ${custo_arvore_minima}\")\n",
    "\n",
    "\n",
    "# Desenhar o grafo 'grafo_cidades'.\n",
    "\n",
    "# Utilizar o layout de mola (spring layout) para determinar a posição dos nós no gráfico.\n",
    "# O layout de mola posiciona os nós usando um sistema de forças simuladas.\n",
    "# Em termos simples, ele faz com que os nós que estão diretamente conectados fiquem próximos,\n",
    "# enquanto os nós que não estão conectados se repelem.\n",
    "posicionamento = nx.spring_layout(grafo_cidades)\n",
    "\n",
    "# Usar a função 'nx.draw()' para desenhar o grafo.\n",
    "# 'grafo_cidades' é o grafo que queremos desenhar.\n",
    "# 'posicionamento' é um dicionário que mapeia cada nó para uma posição no plano.\n",
    "# 'with_labels=True' indica que os nós devem ser rotulados com seus nomes.\n",
    "# 'node_color' define a cor dos nós. Aqui, todos os nós são coloridos de azul claro ('lightblue').\n",
    "nx.draw(grafo_cidades, posicionamento, with_labels=True, node_color='lightblue')\n",
    "\n",
    "# Obter as etiquetas (pesos) das arestas/conexões do grafo 'grafo_cidades'.\n",
    "# 'nx.get_edge_attributes()' é uma função que recupera os atributos das arestas.\n",
    "# Aqui, estamos interessados nos pesos das arestas, que é indicado pelo atributo 'weight'.\n",
    "etiquetas_conexoes = nx.get_edge_attributes(grafo_cidades, 'weight')\n",
    "\n",
    "# Desenhar as etiquetas (pesos) nas arestas/conexões do grafo.\n",
    "# 'grafo_cidades' é o grafo que estamos desenhando.\n",
    "# 'posicionamento' é o dicionário que mapeia cada nó para uma posição no plano.\n",
    "# 'edge_labels' é um dicionário que mapeia cada aresta para seu peso.\n",
    "# Portanto, cada conexão/aresta será rotulada com seu respectivo peso.\n",
    "nx.draw_networkx_edge_labels(grafo_cidades, posicionamento, edge_labels=etiquetas_conexoes)\n",
    "\n",
    "\n",
    "# Destacar a Árvore Geradora Mínima no grafo.\n",
    "\n",
    "# Utilizar a função 'nx.draw_networkx_edges()' para desenhar apenas as arestas da árvore geradora mínima.\n",
    "# 'grafo_cidades' é o grafo no qual estamos trabalhando.\n",
    "# 'posicionamento' define a posição de cada nó no gráfico.\n",
    "# 'edgelist=arvore_minima' especifica que queremos desenhar apenas as arestas presentes na árvore geradora mínima.\n",
    "# 'edge_color=\"vermelho\"' define a cor das arestas da árvore geradora mínima como vermelho. \n",
    "# (Nota: o correto seria 'edge_color=\"red\"' para que a cor seja de fato reconhecida como vermelho.)\n",
    "# 'width=2' define a largura das linhas das arestas para 2, tornando-as mais destacadas.\n",
    "nx.draw_networkx_edges(grafo_cidades, posicionamento, edgelist=arvore_minima, edge_color='red', width=2)\n",
    "\n",
    "# Exibir o gráfico desenhado.\n",
    "# 'plt.show()' é uma função da biblioteca matplotlib que exibe a figura atual.\n",
    "# Ela renderiza o gráfico na tela, permitindo visualizar todas as adições e modificações feitas anteriormente.\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "No exemplo acima, temos 10 cidades (A a J) com várias conexões e pesos entre\n",
    "elas. Depois de aplicar o algoritmo de Kruskal, obtemos a árvore geradora \n",
    "mínima. Ao visualizar o grafo, as arestas pertencentes à árvore geradora \n",
    "mínima são destacadas em vermelho.\n",
    "\"\"\"\n",
    "print()"
   ]
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