BubbleSortDistribution.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "BubbleSortDistribution",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AuFp4-lIVthX"
      },
      "source": [
        "# **Laboratorio 10**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qhJ-36m-ciQE"
      },
      "source": [
        "**PARTE 1.** ***Bubble Sort Distribution***\r\n",
        "\r\n",
        "\r\n",
        "Reproduce the **Bubble Sort** *(optimized – stops if in a round does not do swaps)* time distribución calculated in ungrid in a Colab notebook using permutations from itertools and histogram from matplotlib and upload the notebook in *BubbleSortDistribution.ipynb* in the group’s github.\r\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A2JTdtzwvQDT"
      },
      "source": [
        "# **Solución**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_qPa9rPFvUdx"
      },
      "source": [
        "**Import Libraries.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yS5GccUJqAXu"
      },
      "source": [
        "# import libraries\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "import itertools as it\r\n",
        "import numpy as np\r\n",
        "import pandas as pd"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H8yPEiI3s_Ow"
      },
      "source": [
        "**Bubble Sort.** Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3eEZ5LaQt5lv"
      },
      "source": [
        "def bubbleSort(v): #Algoritmo bubbleSort Simple\r\n",
        "    s = 0 \r\n",
        "    c = v[:] \r\n",
        "    for i in range(len(c)-1): \r\n",
        "  \r\n",
        "        for j in reversed(range(i+1,len(c))): \r\n",
        "            s += 1\r\n",
        "            if (c[j] < c[j-1]) : \r\n",
        "                swap(c,j,j-1)\r\n",
        "    return  s, c\r\n",
        "  \r\n",
        "def swap(v,i,j):\r\n",
        "  t = v[i]\r\n",
        "  v[i] = v[j]\r\n",
        "  v[j] = t"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-NQrh4g5tNJ6"
      },
      "source": [
        "**Bubble Sort Optimizado.** The above function always runs O(n^2) time even if the array is sorted. It can be optimized by stopping the algorithm if inner loop didn’t cause any swap."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QKXSr5NqgCBg"
      },
      "source": [
        "\r\n",
        "def BubbleSortOptimizado(v): #Algoritmo bubbleShortOptimizado\r\n",
        "    s = 0 \r\n",
        "    c = v[:]\r\n",
        "    for i in range(len(c)-1): \r\n",
        "        flag = False\r\n",
        "        for j in reversed(range(i+1,len(c))): \r\n",
        "            s += 1\r\n",
        "            if (c[j] < c[j-1]) : \r\n",
        "                swap(c,j,j-1)\r\n",
        "                flag = True\r\n",
        "                s += 1\r\n",
        "        if flag == False: \r\n",
        "            break\r\n",
        "    return s, c\r\n",
        "\r\n",
        "def swap(v,i,j):\r\n",
        "  t = v[i]\r\n",
        "  v[i] = v[j]\r\n",
        "  v[j] = t\r\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uo1JgLFiq3eR"
      },
      "source": [
        "from collections import Counter\r\n",
        "def plotBubbleSort(n):\r\n",
        "  \r\n",
        "   # Grafica los pasos que se demora el algoritmo bubble sort.\r\n",
        "   # n: es el tamaño de la lista a ordenar\r\n",
        "  v = [i+1 for i in range(n)] # Vector con n elementos\r\n",
        "  pobj = it.permutations(v)   # Se calculan para n! permutaciones\r\n",
        "  permutaciones = list(pobj)\r\n",
        "  xhist = []     \r\n",
        "  for p in permutaciones: #Ejecuta bubbleSort\r\n",
        "    pl = list(p)\r\n",
        "    t, po = bubbleSort(pl)\r\n",
        "    xhist.append(t)\r\n",
        "    titulo = \"Bubble Sort time distribution\".format(n)\r\n",
        "\r\n",
        "  plt.hist(xhist, density=True)\r\n",
        "  plt.title(titulo)\r\n",
        "  plt.ylabel(\"density\")\r\n",
        "  plt.xlabel(\"time complexity\")\r\n",
        "  plt.show()\r\n",
        "\r\n",
        "  for i in range(min(xhist), max(xhist)+1):\r\n",
        "    porcentaje = xhist.count(i)/len(xhist)*100\r\n",
        "    print(\"P({0}) = {1} %\".format(i,porcentaje))\r\n",
        "  print(\"\\nAvg:\",sum(xhist)/len(xhist))"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "id": "AjNIOOtSsZCP",
        "outputId": "89bc05d0-9788-481a-c2dd-064483985eaf"
      },
      "source": [
        "plotBubbleSort(1)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(0) = 100.0 %\n",
            "\n",
            "Avg: 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f_YmEPDMrGDQ"
      },
      "source": [
        "from collections import Counter\r\n",
        "def plotBubbleSort(n):\r\n",
        "  \r\n",
        "   # Grafica los pasos que se demora el algoritmo bubble sort.\r\n",
        "   # n: es el tamaño de la lista a ordenar\r\n",
        "  v = [i+1 for i in range(n)] # Vector con n elementos\r\n",
        "  pobj = it.permutations(v)   # Se calculan para n! permutaciones\r\n",
        "  permutaciones = list(pobj)\r\n",
        "  xhist = []          \r\n",
        "  for p in permutaciones: #Ejecuta optimizedBubbleSort\r\n",
        "    pl = list(p)\r\n",
        "    t, po = BubbleSortOptimizado(pl)\r\n",
        "    xhist.append(t)\r\n",
        "  titulo = \"Bubble Sort Optimized time distribution\".format(n)\r\n",
        " \r\n",
        "  \r\n",
        "  plt.hist(xhist, density=True)\r\n",
        "  plt.title(titulo)\r\n",
        "  plt.ylabel(\"density\")\r\n",
        "  plt.xlabel(\"time complexity\")\r\n",
        "  plt.show()\r\n",
        "\r\n",
        "  for i in range(min(xhist), max(xhist)+1):\r\n",
        "    porcentaje = xhist.count(i)/len(xhist)*100\r\n",
        "    print(\"P({0}) = {1} %\".format(i,porcentaje))\r\n",
        "  print(\"\\nAvg:\",sum(xhist)/len(xhist))"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F0-QDH8LygGC"
      },
      "source": [
        "Bubble Sort Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LC6ajeSIvHz4"
      },
      "source": [
        "from collections import Counter\r\n",
        "def plotBubbleSortOptimizado(n):\r\n",
        "  \r\n",
        "   # Grafica los pasos que se demora el algoritmo bubble sort.\r\n",
        "   # n: es el tamaño de la lista a ordenar\r\n",
        "  v = [i+1 for i in range(n)] # Vector con n elementos\r\n",
        "  pobj = it.permutations(v)   # Se calculan para n! permutaciones\r\n",
        "  permutaciones = list(pobj)\r\n",
        "  xhist = []          \r\n",
        "  for p in permutaciones: #Ejecuta optimizedBubbleSort\r\n",
        "    pl = list(p)\r\n",
        "    t, po = BubbleSortOptimizado(pl)\r\n",
        "    xhist.append(t)\r\n",
        "  titulo = \"Bubble Sort Optimized time distribution\".format(n)\r\n",
        " \r\n",
        "  \r\n",
        "  plt.hist(xhist, density=True)\r\n",
        "  plt.title(titulo)\r\n",
        "  plt.ylabel(\"density\")\r\n",
        "  plt.xlabel(\"time complexity\")\r\n",
        "  plt.show()\r\n",
        "\r\n",
        "  for i in range(min(xhist), max(xhist)+1):\r\n",
        "    porcentaje = xhist.count(i)/len(xhist)*100\r\n",
        "    print(\"P({0}) = {1} %\".format(i,porcentaje))\r\n",
        "  print(\"\\nAvg:\",sum(xhist)/len(xhist))"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "id": "qE0gkgJEjw8d",
        "outputId": "25a8b15d-34f0-485d-c0e2-0f98553e760b"
      },
      "source": [
        "plotBubbleSortOptimizado(1)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GDP6I2Cd/37qacszMrN2aHaRt176B1CQdLulMSVu2tzQzM2uHZm/n/G/gOUlvBI4njdlzYduqMjOztmk2+JdFRADjgXMi4lukWzrNzGyEaXbIhkWSTgQOB3bLY/Ov1b6yzMysXYYyHv+LwMQ8uubmwBltq8rMzNqmqTP+HPZn1kw/RBql08zMRphm7+o5UNJsSQslPSNpkaRn2l2cmZm1XrN9/F8H9o2IWe0sxszM2q/ZPv75Dn0zs9VDs2f80yRdBlxFusgLQERc0ZaqzMysbZoN/vWA54B31zwWgIPfzGyEafauHn8mrpnZaqLZu3r+TtINkmbk6R0kfbG9pZmZWTs0e3H3e8CJwFKAiPgtcGi7ijIzs/ZpNvhHR8RddY8ta3UxZmbWfs0G/+OSXkO6oIukg4F5bavKzMzaptm7ej4BTAZeJ+kR4AHgg22ryszM2mbA4Jd0XM3kz4CbSP8lPAscRM34PWZmNjIMdsbfN+b+a4E3A1eTPnf3CKC+z9/MzEaAwT5z98sAkm4Gdo6IRXn6ZODatldnZmYt1+zF3Y2BJTXTS/JjZmY2wjR7cfcC4C5JV+bp/YHz21KRmZm1VbNDNpwq6Trg7fmhD0fEPe0ry8zM2qXZM34i4m7g7jbWYmZmFWi2j9/MzFYTDn4zs8J0LPglrSnpHkk/7VQNZmYl6uQZ/6cAf5yjmVnFOhL8kjYH3gec24n2zcxK1qkz/m8CJwDL+1tA0lGSpkma1tvbW11lZmarucqDX9I+wIKImD7QchExOSJ6IqKnq6urourMzFZ/nTjj3xXYT9KDwKXAuyRd1IE6zMyKVHnwR8SJEbF5RHSTPr7xxog4vOo6zMxK5fv4zcwK0/SQDe0QEVOBqZ2swcysND7jNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MClN58EvaQtJNku6TNFPSp6quwcysZKM60OYy4PiIuFvSusB0SddHxH0dqMXMrDiVn/FHxLyIuDv/vAiYBWxWdR1mZqXqaB+/pG5gJ+DOBvOOkjRN0rTe3t6qSzMzW211LPgljQF+DHw6Ip6pnx8RkyOiJyJ6urq6qi/QzGw11ZHgl7QWKfQvjogrOlGDmVmpOnFXj4DvA7Mi4syq2zczK10nzvh3BY4A3iXpN/nrvR2ow8ysSJXfzhkRtwKqul0zM0v8zl0zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8I4+M3MCuPgNzMrjIPfzKwwDn4zs8J0JPglvUfSHyTdL2lSJ2owMytV5cEvaU3gW8DewBuAwyS9oeo6zMxK1Ykz/l2A+yNiTkQsAS4FxnegDjOzIo3qQJubAQ/XTM8F3lK/kKSjgKPy5GJJf6igtlYaCzze6SIq5m2ukE7vRKuAf88jyVaNHuxE8DclIiYDkztdx3BJmhYRPZ2uo0re5jJ4m0e+TnT1PAJsUTO9eX7MzMwq0Ing/zWwraStJa0NHApc04E6zMyKVHlXT0Qsk3QM8AtgTeC8iJhZdR0VGLHdVCvB21wGb/MIp4jodA1mZlYhv3PXzKwwDn4zs8I4+FtI0kaSrpc0O3/fcIBl15M0V9I5VdbYSs1sr6QdJd0uaaak30o6pBO1rqzBhhmR9DJJl+X5d0rqrr7K1mpim4+TdF/+vd4gqeE94yNJs8PJSDpIUkgakbd4OvhbaxJwQ0RsC9yQp/vzVeDmSqpqn2a29zngQxGxHfAe4JuSNqiwxpXW5DAjE4GnImIb4BtA595e1QJNbvM9QE9E7ABMAb5ebZWt1exwMpLWBT4F3Fltha3j4G+t8cAP888/BPZvtJCkNwEbA7+sqK52GXR7I+KPETE7//wosADoqqzC1mhmmJHafTEF2EOSKqyx1Qbd5oi4KSKey5N3kN6TM5I1O5zMV0kv7C9UWVwrOfhba+OImJd/fowU7i8haQ3gP4HPVllYmwy6vbUk7QKsDfyp3YW1WKNhRjbrb5mIWAYsBF5ZSXXt0cw215oIXNfWitpv0G2WtDOwRURcW2VhrbbKDtmwqpL0K2CTBrO+UDsRESGp0b2yHwd+FhFzR8IJYQu2t28944ALgSMjYnlrq7ROknQ40APs3ula2imftJ0JTOhwKSvNwT9EEbFnf/MkzZc0LiLm5aBb0GCxfwTeLunjwBhgbUmLI2KV/FyCFmwvktYDrgW+EBF3tKnUdmpmmJG+ZeZKGgWsDzxRTXlt0dTQKpL2JJ0E7B4RL1ZUW7sMts3rAtsDU/NJ2ybANZL2i4hplVXZAu7qaa1rgCPzz0cCV9cvEBEfjIgtI6Kb1N1zwaoa+k0YdHvzsBxXkrZzSoW1tVIzw4zU7ouDgRtjZL87ctBtlrQT8F1gv4ho+KI/wgy4zRGxMCLGRkR3/vu9g7TtIyr0wcHfal8D9pI0G9gzTyOpR9K5Ha2sPZrZ3g8AuwETJP0mf+3YmXKHJ/fZ9w0zMgu4PCJmSvqKpP3yYt8HXinpfuA4Br6ja5XX5DafQfqv9X/y73VEj7nV5DavFjxkg5lZYXzGb2ZWGAe/mVlhHPxmZoVx8JuZFcbBb2ZWGAe/rdIkbZDf7NY3vamkkfp+gL+StHiYz+uR9F/553dIemtrK7MS+HZOW6Xl4Y1/GhHbd7iUlsrv1h6zkus4GVgcEf/RmqqsFD7jt1Xd14DX5DcInSGpW9IMAEkTJF2VPwvgQUnH5DHi75F0h6SN8nKvkfRzSdMl3SLpdfWNSBoj6QeSfpfHlz8oP35YfmyGpNNrll+c65kp6VeSdpE0VdKcvjf75Pquzo/PlnRSow2U9DlJv87tfjk/doDSGPeSNE7SHyVtks/yf5pfEI8GPpP3zdslPSBprfz89WqnzWo5+G1VNwn4U0TsGBGfazB/e+BA4M3AqcBzEbETcDvwobzMZODYiHgTaZiMbzdYz5eAhRHx93l8+RslbUoafvddwI7AmyX1DT39CtKwDNsBi4BTgL2AA4Cv1Kx3F+AgYAfg/ar74A5J7wa2zcvtCLxJ0m4RcSUwD/gE8D3gpIh4rO95EfEg8B3gG3nf3AJMBd6XFzkUuCIiljbYViucB2mzke6miFgELJK0EPhJfvx3wA6SxgBvJQ0r0PeclzVYz56ksAQgIp6StBswNSJ6ASRdTBp+4ipgCfDzmrZejIilkn4HdNes9/qIeCI//wrgbUDt2C7vzl/35OkxpBeCm4FjgRnAHRFxSRP74lzghFzfh4GPNvEcK5CD30a62hEhl9dMLycd32sAT0dEq8cHWlozCNtf242I5Xl0zj71F9HqpwWcFhHfbdDG5nndG0taY7DhrCPittwV9g5gzYiY0eS2WGHc1WOrukWk4XCHJSKeAR6Q9H6A3Gf+xgaLXk/qViEvtyFwF7C7pLFKH8t3GPC/QyxhL6XPJn456RPKbqub/wvgX/J/JkjaTNKr8ovHebnNWaSB3+o12jcXAD8CfjDEOq0gDn5bpeVuktvyxdUzhrmaDwITJd0LzKTxx+mdAmyY27kXeGf+dLFJwE3AvcD0iFhh6OlB3AX8GPgt8OP6IXwj4pekoL49dxNNIYX554FbIuJWUuh/RNLr69b9E+CAvou7+bGLgQ2BZrqGrFC+ndOsTSRNIH0Y+TEVtnkwMD4ijqiqTRt53MdvtpqQdDawN/DeTtdiqzaf8ZuZFcZ9/GZmhXHwm5kVxsFvZlYYB7+ZWWEc/GZmhfl/waJ9lfH/fFsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(0) = 100.0 %\n",
            "\n",
            "Avg: 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        },
        "id": "7XwlumGej6J1",
        "outputId": "5bb53446-12ef-48d1-aa61-b0b6960f05db"
      },
      "source": [
        "plotBubbleSortOptimizado(2)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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I1e5QBUskHQXsC2yfx4YfX19ZZmY2WP0ZD/4F4ICIeIQ0vvuJtVVlZmaD1tYefA71kyq3HyCNKmlmZiNUu2fR7CnpD5KelvSMpCWSnqm7ODMzG7h2++C/DuwWEfPrLMbMzDqn3T74Rx3uZmajS7t78LMlnQdcTDrYCkBEXFhLVWZmNmjtBvwrgeeA91TuC8ABb2Y2QrV7Fs3+dRdiZmad1e5ZNH8t6SpJc/Ptt0j6Qr2lmZnZYLR7kPX7wFHAMvjzD2rvXVdRZmY2eO0G/FoRcWvDfcs7XYyZmXVOuwH/mKRNSQdWkbQXsLC2qszMbNDaPYvmIGAm8AZJDwP3AR+rrSozMxu0lgEv6bDKzV8A15D2+p8FPkhlfBozMxtZ+tqD7xnz/fXA3wGXkH6XdT+gsU/ezMxGkL5+k/VYAEnXAVtFxJJ8+xjgstqrMzOzAWv3IOt6wIuV2y/m+8zMbIRq9yDrmcCtki7Kt3cHZtVSkZmZdUS7QxUcJ+ly4O35rv0j4vb6yjIzs8Fqdw+eiLgNuK3GWszMrIPa7YM3M7NRxgFvZlao2gJe0kaSrpF0j6R5kg6tqy0zM1tV233wA7AcODwibpM0EZgj6cqIuKfGNs3MLKttDz4iFuYDs+QvSM0HNqirPTMzW9mQ9MFL6ga2BG5pMm2GpNmSZi9evHgoyjEzGxNqD3hJE4CfAp+JiGcap0fEzIiYGhFTu7q66i7HzGzMqDXgJY0nhfvZEeEf6DYzG0J1nkUj4AfA/IjwsMJmZkOszj34bUnDCr9T0h358r4a2zMzs4raTpOMiBtIY8ebmdkw8DdZzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQjngzcwK5YA3MyuUA97MrFAOeDOzQtUW8JLOkLRI0ty62jAzs97VuQc/C9i5xuWbmVkLtQV8RFwHPFHX8s3MrLVh74OXNEPSbEmzFy9ePNzlmJkVY9gDPiJmRsTUiJja1dU13OWYmRVj2APezMzq4YA3MytUnadJngPcBLxe0kOSDqirLTMzW9W4uhYcEfvUtWwzM+ubu2jMzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzArlgDczK5QD3sysUA54M7NCOeDNzApVa8BL2lnS7yTdK+nIOtsyM7OV1RbwklYHvg3sArwR2EfSG+tqz8zMVlbnHvzWwL0RsSAiXgTOBabV2J6ZmVWMq3HZGwAPVm4/BGzTOJOkGcCMfHOppN8NsL1JwGMDfOyA6YShbnElw7LOw2ysrfNYW18Yg+usEwa1zhv3NqHOgG9LRMwEZg52OZJmR8TUDpQ0anidyzfW1he8zp1UZxfNw8BGldsb5vvMzGwI1BnwvwE2k7SJpL8A9gZ+VmN7ZmZWUVsXTUQsl3Qw8EtgdeCMiJhXV3t0oJtnFPI6l2+srS94nTtGEVHHcs3MbJj5m6xmZoVywJuZFWpUBbykMyQtkjS3l+mS9K08NMJdkrYa6ho7rY11/lhe17sl/VrSFkNdY6f1tc6V+f5O0nJJew1VbXVpZ50l7SjpDknzJP3PUNbXaW1s16+S9HNJd+b13X+oa+w0SRtJukbSPXmdDm0yT0czbFQFPDAL2LnF9F2AzfJlBvCfQ1BT3WbRep3vA3aIiL8BvkIZB6hm0Xqde4bCOAH41VAUNARm0WKdJa0NfAf4QES8CfjQENVVl1m0fo0PAu6JiC2AHYFv5LPxRrPlwOER8UbgbcBBTYZv6WiGjaqAj4jrgCdazDINODOSm4G1JU0emurq0dc6R8SvI+LJfPNm0vcNRrU2XmeAQ4CfAovqr6h+bazzR4ELI+KBPP+oXu821jeAiZIETMjzLh+K2uoSEQsj4rZ8fQkwn/SN/6qOZtioCvg2NBseofEJLNkBwOXDXUTdJG0A7EEZn9Da9dfAOpKulTRH0seHu6CanQZsDvwRuBs4NCJWDG9JnSOpG9gSuKVhUkczbNiHKrDOkPQOUsBvN9y1DIGTgX+JiBVpB29MGAf8LfAuYE3gJkk3R8Tvh7es2rwXuAN4J7ApcKWk6yPimeEta/AkTSB9+vxM3etTWsCPyeERJL0FOB3YJSIeH+56hsBU4Nwc7pOA90laHhEXD29ZtXoIeDwingWelXQdsAVQasDvD3wt0hd17pV0H/AG4NbhLWtwJI0nhfvZEXFhk1k6mmGlddH8DPh4PhL9NuDpiFg43EXVSdIU4EJgv4L35lYSEZtERHdEdAMXAJ8qPNwBLgG2kzRO0lqkkVnnD3NNdXqA9GkFSesBrwcWDGtFg5SPJ/wAmB8RJ/UyW0czbFTtwUs6h3REfZKkh4AvA+MBIuK7wC+A9wH3As+R9gJGtTbW+UvAXwHfyXu0y0f7SHxtrHNx+lrniJgv6QrgLmAFcHpEtDyNdCRr4zX+CjBL0t2ASF1yo30I4W2B/YC7Jd2R7zsamAL1ZJiHKjAzK1RpXTRmZpY54M3MCuWANzMrlAPezKxQDngzs0I54G1EkLS2pE9Vbq8v6YLhrKkTJC0d4OOmSvpWvr6jpL/vbGU2Fvg0SRsR8tgcl0bEm4e5lI6StDQiJgxyGccASyPiPzpTlY0V3oO3keJrwKZ5vPMTJXX3jBUuabqkiyVdKel+SQdLOkzS7ZJulrRunm9TSVfkwbiul/SGxkYkTZD0wzx+/l2SPpjv3yffN1fSCZX5l+Z65kn6b0lb5wG/Fkj6QKW+S/L9f5D05WYrKOnzkn6T2z0237eHpKvyNxcnS/q9pNfkvfZL8xvfgcBn83Pzdkn35a+8I+mV1dtmK4kIX3wZ9gvQDcxtdhuYTvpm30SgC3gaODBP+yZp0CaAq4DN8vVtgKubtHMCcHLl9jrA+qSvxneRvt19NbB7nh6kMX4ALiKNPz+eNA7MHZX6FpK+UbwmMBeYmqctzX/fQxqrX6Qdq0uB7fO0s4CD83375Pt2JH2iATgG+Fyl5h9W6psBfGO4Xz9fRuZlVA1VYGPaNZHG0F4i6Wng5/n+u4G35BH6/h74r8oIk69ospx3A3v33IiIJyVtD1wbEYsBJJ0NbA9cDLwIXFFp64WIWJa/Qt9dWe6VkQd6k3QhaVTP2ZXp78mX2/PtCaQfdbiONLb9XODmiDinjefidOCIXN/+wD+28RgbgxzwNlq8ULm+onJ7BWk7Xg14KiLe2uF2l0VEz4GqP7cbaaji6v9P48GsxtsCjo+I7zVpY8O87PUkrRZ9jHseETfmLqwdgdVjFI9JY/VyH7yNFEtIXTADEmlc7fskfQj+/NuWzX6f9krSz8GR51uHNATtDpImKf0U4D5Af3/zdCdJ60paE9gduLFh+i+Bf8ifNJC0gaRX5zeJM3Kb84HDmiy72XNzJvATUneNWVMOeBsRcvfGjfkg54kDXMzHgAMk3QnMI/38WaOvkn4ZaW6e7x2RhmM9ErgGuBOYExGX9LPtW0njfN8F/DQiqt0zRMSvSIF8U+7euYAU2kcD10fEDaRw/6SkzRuW/XNgj56DrPm+s0nHD9rp0rExyqdJmg2SpOmkg6oHD2GbewHTImK/oWrTRh/3wZuNMpJOBXYhjRtu1ivvwZuZFcp98GZmhXLAm5kVygFvZlYoB7yZWaEc8GZmhfp/87/nCLZq7IYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(1) = 50.0 %\n",
            "P(2) = 50.0 %\n",
            "\n",
            "Avg: 1.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 422
        },
        "id": "ZAXOYSv1kFuj",
        "outputId": "03841c21-c546-415b-d043-b1fae67dcdca"
      },
      "source": [
        "plotBubbleSortOptimizado(3)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(2) = 16.666666666666664 %\n",
            "P(3) = 0.0 %\n",
            "P(4) = 33.33333333333333 %\n",
            "P(5) = 33.33333333333333 %\n",
            "P(6) = 16.666666666666664 %\n",
            "\n",
            "Avg: 4.333333333333333\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "-DsW09ITkZta",
        "outputId": "e00467cd-dfd2-4fba-c8f6-1aa73e985d20"
      },
      "source": [
        "plotBubbleSortOptimizado(4)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(3) = 4.166666666666666 %\n",
            "P(4) = 0.0 %\n",
            "P(5) = 0.0 %\n",
            "P(6) = 12.5 %\n",
            "P(7) = 12.5 %\n",
            "P(8) = 12.5 %\n",
            "P(9) = 20.833333333333336 %\n",
            "P(10) = 20.833333333333336 %\n",
            "P(11) = 12.5 %\n",
            "P(12) = 4.166666666666666 %\n",
            "\n",
            "Avg: 8.583333333333334\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 640
        },
        "id": "KXsM56PRp8tG",
        "outputId": "18bc7ebf-77db-4694-a9d9-f64a6c0579b3"
      },
      "source": [
        "plotBubbleSortOptimizado(5)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "P(4) = 0.8333333333333334 %\n",
            "P(5) = 0.0 %\n",
            "P(6) = 0.0 %\n",
            "P(7) = 0.0 %\n",
            "P(8) = 3.3333333333333335 %\n",
            "P(9) = 5.0 %\n",
            "P(10) = 3.3333333333333335 %\n",
            "P(11) = 3.3333333333333335 %\n",
            "P(12) = 7.5 %\n",
            "P(13) = 11.666666666666666 %\n",
            "P(14) = 13.333333333333334 %\n",
            "P(15) = 14.166666666666666 %\n",
            "P(16) = 14.166666666666666 %\n",
            "P(17) = 11.666666666666666 %\n",
            "P(18) = 7.5 %\n",
            "P(19) = 3.3333333333333335 %\n",
            "P(20) = 0.8333333333333334 %\n",
            "\n",
            "Avg: 14.258333333333333\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}