Análise de algoritmos de busca no problema Sliding puzzle.ipynb

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    "%matplotlib inline\n",
    "import helper\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
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    "# Análise de algoritmos de busca no problema *Sliding puzzle*\n",
    "\n",
    "**Nome:** Paulo Mateus Moura da Silva - mateus.moura@hotmail.com\n",
    "\n",
    "**Professor:** Ajalmar Rêgo da Rocha Neto - ajalmar@gmail.com\n",
    "\n",
    "_**Resumo:** Este relatório apresenta uma análise comparativa de tempo de algorimos de busca no problema **Sliding Puzzle**, também conhecido como quebra cabeça de oito peças. Após uma descrição na introdução de como o trabalho foi desenvolvido, serão apresentados gráficos dos resultados e, por fim, uma breve discussão dos resultados._\n",
    "\n",
    "## 1. Introdução\n",
    "\n",
    "Serão analisados algoritmos de busca no problema **Sliding Puzzle**, buscando demonstrar a importância do uso de algoritmos que utilizam heurísticas para problemas de resolução de problemas por meio de busca.\n",
    "\n",
    "### 1.1 Sliding Puzzle\n",
    "\n",
    "Também conhecido como *8/15 Puzzle* e *Quebra cabeças de 8* ou *15 peças*, o jogo consiste em mover as peças do quebra-cabeças nos sentidos horizontais/verticais para organizá-las em uma ordem lógica (de 1 a 8 da esquerda para a direita, de cima para baixo).\n",
    "\n",
    "### 1.2. Algoritmos testados\n",
    "\n",
    "Foram implementados e testados os seguintes algoritmos de busca:\n",
    "\n",
    " * **Algoritmos de busca sem informação**\n",
    "   * Busca em largura/extensão;\n",
    "   * Busca em profunidade grafo (não caminhos repetidos);\n",
    "   * Busca em profundidade limitada;\n",
    "   * Busca em aprofundamento interativo;\n",
    "\n",
    "\n",
    " * **Algoritmos de busca com informação**\n",
    "   * Busca A\\* (A star): Heurística Distância Manhattan;\n",
    "     * **Heurística**: Soma da distância quarteirão de cada peça para a posição correta\n",
    "   * Busca A\\* (A star): Heurística Distância Hamming.\n",
    "     * **Heurística**: Contabilização de quantas peças estão no canto errado.\n",
    "\n",
    "A medida que o campo aumenta, o custo de tempo de alguns algoritmos aumenta drasticamente. Desta forma, foi escolhido retirar alguns algoritmos da análise a partir de uma configuração de tamanho $3x3$.\n",
    "\n",
    "## 2. Método de análise\n",
    "\n",
    "Os algorimos de busca foram testados $10$ (dez) vezes a partir de um estado aleatório inicial. \n",
    "\n",
    "Para cada teste, foram computados o tempo inicial e o tempo final da execução de um algoritmo de busca. O tempo utilizado foi o **tempo do processo**, de forma a evitar a adição de tempo que o processo está em _Sleep status_.\n",
    "\n",
    "> **```time.process_time()```**\n",
    "\n",
    "> Return the value (in fractional seconds) of the sum of the system and user CPU time of the current process. It does not include time elapsed during sleep. It is process-wide by definition. The reference point of the returned value is undefined, so that only the difference between the results of consecutive calls is valid.\n",
    "\n",
    "> -- <cite>[Python documentation](https://docs.python.org/3.5/library/time.html#time.process_time) - 2017</cite>\n",
    "\n",
    "O estado inicial foi definido antes da execução dos algoritmos de busca: foram realizadas 150 movimentos aleatórios a partir do estado objetivo.\n",
    "\n",
    "```python\n",
    "def shuffle(puzzle, n):\n",
    "    last_movement = SlidingMovement.FROM_BOTTOM\n",
    "    while n > 0:\n",
    "        movement = random.choice(puzzle.possible_movements)\n",
    "        # Não desfazer o movimento anterior\n",
    "        if movement == ~last_movement:\n",
    "            continue\n",
    "\n",
    "        puzzle.move(movement)\n",
    "\n",
    "        last_movement = movement\n",
    "        n -= 1\n",
    "```\n",
    "\n",
    "Para facilitar a implementação, **o estado objetivo** foi definido como a sequência $[0 .. (largura*altura - 1)]$.\n",
    "\n",
    "### 2.1 Configurações de testes\n",
    "\n",
    "As configurações de tamanho do quebra cabeça são\n",
    "\n",
    "* 2 x 2\n",
    "* 2 x 3\n",
    "* 3 x 3 - Quebra cabeças de 8 peças\n",
    "* 3 x 4\n",
    "\n",
    "### 2.2 Ambiente de testes\n",
    "\n",
    "Foi utilizado um Notebook com as seguintes características:\n",
    "\n",
    "* **Memória RAM**: 7,7 GiB\n",
    "* **Processador**: Intel® Core™ i5-5200U CPU @ 2.20GHz × 4 \n",
    "* **Sistema Operacional**: Ubuntu 16.04 LTS - 64-bit\n",
    "\n",
    "### 2.3 Linguagem de programação\n",
    "\n",
    "O código foi implementado com a linguagem Python versão 3.5.2 - distribuição Anaconda 4.2.0 (64-bit).\n",
    "\n",
    "Para a manipulação de arrays, foi utilizada a biblioteca [NumPy](http://www.numpy.org/) \"o pacote fundamenta para computação científica em Python\" (NumPy 2017).\n",
    "\n",
    "O código pode ser encontrado no repositório oficial do projeto: https://github.com/IFCE-Ciencia-da-Computacao-2011-2/UDM.279-Inteligencia-Artificial\n",
    "\n",
    "## 3. Resultados\n",
    "\n",
    "A análise dos dados consiste basicamente a partir da média das execuções. Foi percebido que aleatoriamente algoritmos apresentaram um desvio padrão alto, ocasionado por demoras excessivas em uma única das execuções. A fim de amenizar o problema, considerou ser mais justo remover da análise a execução mais rápida e a mais lenta."
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    "### 3.1 Tamanho:  (2, 2)\n",
    "\n",
    "* **Estado inicial**:\n",
    "```\n",
    "[[3 2]\n",
    " [1 0]]\n",
    "```\n",
    "* **Mínimo de movimentos para solucionar**: 6\n"
   ]
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       "      <th></th>\n",
       "      <th>A* - Distância Manhattan</th>\n",
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       "   A* - Distância Manhattan  A* - Distância Hamming  \\\n",
       "0                         6                       6   \n",
       "\n",
       "   Profundidade limitada - 15  Aprofundamento Interativo  \\\n",
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QXFyMO3fu4ObNm1Cr1eW2qMXExKB9+/YwMzPDrVu3kJiYCEEQ4O7uXm4MERERcHZ2Lnet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\nK0wsERERERERERGRVphYIiIiIiIiIiI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fce8dd2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = helper.carregar_json('data.json')\n",
    "resultado_2_x_2 = helper.processar_resultados(data['(2, 2)'])\n",
    "helper.grafico_desvio_padrao(resultado_2_x_2[0], figsize=(12, 3))\n",
    "\n",
    "resultado_2_x_2[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Tamanho: (2, 3)\n",
    "\n",
    "* **Estado inicial**:\n",
    "```\n",
    "[[5 2]\n",
    " [4 3]\n",
    " [0 1]]\n",
    "```\n",
    "* **Mínimo de movimentos para solucionar**: 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A* - Distância Manhattan</th>\n",
       "      <th>A* - Distância Hamming</th>\n",
       "      <th>Profundidade limitada - 15</th>\n",
       "      <th>Aprofundamento Interativo</th>\n",
       "      <th>Profundidade (grafo)</th>\n",
       "      <th>Largura</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14</td>\n",
       "      <td>14</td>\n",
       "      <td>14</td>\n",
       "      <td>14</td>\n",
       "      <td>118</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A* - Distância Manhattan  A* - Distância Hamming  \\\n",
       "0                        14                      14   \n",
       "\n",
       "   Profundidade limitada - 15  Aprofundamento Interativo  \\\n",
       "0                          14                         14   \n",
       "\n",
       "   Profundidade (grafo)  Largura  \n",
       "0                   118       14  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wEDExMbXqV6FQYOzYsbVqAwBKSkowbdo0JCQk1LqtqigqKsLSpUvh5+cHHx8f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\nERERERFpCSaCiIiIiIiIiIi0xGubCEp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fcac04f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resultado_2_x_3 = helper.processar_resultados(data['(2, 3)'])\n",
    "helper.grafico_desvio_padrao(resultado_2_x_3[0], figsize=(12, 3))\n",
    "\n",
    "resultado_2_x_3[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Tamanho: (3, 3)\n",
    "\n",
    "* **Estado inicial**:\n",
    "```\n",
    "[[2 6 3]\n",
    " [5 1 8]\n",
    " [0 4 7]]\n",
    "```\n",
    "* **Mínimo de movimentos para solucionar**: 24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A* - Distância Manhattan</th>\n",
       "      <th>A* - Distância Hamming</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A* - Distância Manhattan  A* - Distância Hamming\n",
       "0                        24                      24"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fce654978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resultado_3_x_3 = helper.processar_resultados(data['(3, 3)'])\n",
    "helper.grafico_desvio_padrao(resultado_3_x_3[0], figsize=(12, 2))\n",
    "\n",
    "resultado_3_x_3[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Tamanho: (3, 4)\n",
    "\n",
    "* **Estado inicial**:\n",
    "```\n",
    "[[ 5  7 11]\n",
    " [ 4 10  2]\n",
    " [ 3  1  0]\n",
    " [ 6  8  9]]\n",
    "```\n",
    "* **Mínimo de movimentos para solucionar**: 32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A* - Distância Manhattan</th>\n",
       "      <th>A* - Distância Hamming</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A* - Distância Manhattan  A* - Distância Hamming\n",
       "0                        32                      32"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fce60edd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resultado_3_x_4 = helper.processar_resultados(data['(3, 4)'])\n",
    "helper.grafico_desvio_padrao(resultado_3_x_4[0], figsize=(12, 3))\n",
    "\n",
    "resultado_3_x_4[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.5 Análise Manhattan\n",
    "\n",
    "A partir de uma solução com $n$ passos, é possível obter $m = n+1$ estados com $0,1,2,3..n$ passos necessários para solucionar o problema.\n",
    "Para cada um dos $m$ estado, foi realizada 10 (dez) execuções _A\\* - Heurística Distância Manhattan_. O gráfico a seguir apresenta a média dos resultados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f5fca6ecc18>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kiKIosmHDhhLr3rNnjyiKIs2aNZNx48bJTz/9VO4yjz/+uISEhIhOpzOavnPn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\nN1cL6qcG1KULqB/qUGdOof5djVZ9BO3oQWhvQ/t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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fcabaf3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_quarteirao = helper.carregar_json('astar-quarteirao-analise.json')\n",
    "\n",
    "analise = helper.processar_resultados_crescente(data_quarteirao)\n",
    "helper.grafico_desvio_padrao(analise, kind='line', title='A* - Heurística Distância Manhattan\\n $n^o\\ passos\\ x\\ Tempo\\ (segundos)$', figsize=(4, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Discussão e conclusões\n",
    "\n",
    "Como esperado, a utilização de algorítmos de busca com informação para melhor seleção dos próximos nós a expandir trouxe resultados melhores que algoritmos de busca com sem informação. A partir de um quebra cabeças de tamanho $2x3$, já foi apresentado uma diferença significativa entre os algoritmos sem e com informação.\n",
    "\n",
    "A partir do quebra cabeças de 8 peças ($3x3$), o tempo de execução de busca sem informação foi significativamente grande, a ponto de desconsiderar da análise.\n",
    "\n",
    "Comparando as heurísticas utilizadas para o algorítmo A\\*, a distância Manhattan demonstrou ser mais performático que a distância Hamming: Uma solução de 32 passos necessitava de cerca de **uma hora** para o _Hamming_ e cerca de três minutos para a distância **Manhattan**.\n",
    "\n",
    "No gráfico $n^o\\ passos\\ x\\ Tempo$ para _A\\* - Manhattan_, é possível perceber um crescimento semelhante à uma função exponencial. \n",
    "\n",
    "\n",
    "## 5. Referências\n",
    "\n",
    "\\_\\_\\_\\_\\_\\_\\_. [\"8 Puzzle\"](http://www.cs.princeton.edu/courses/archive/spring09/cos226/assignments/8puzzle.html). Computer Science 226, Algorithms and Data Structures, Spring 2009. Acessado em 16 de abril \n",
    "\n",
    "Parberry, I (1995). \"A Real-Time Algorithm for the $(n^2 − 1)$-puzzle\". Information Processing Letters\n",
    "\n",
    "\n",
    "\n"
   ]
  }
 ],
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