TeamOptimization.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/NicolasChagnet/pokemon-team-optimizer/blob/main/TeamOptimization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DDlvcWdHl_OL"
      },
      "source": [
        "# Pokemon Team Optimization\n",
        "\n",
        "The goal of this notebook is to find an optimal Pokemon team using the [Pokemon dataset](https://www.kaggle.com/datasets/rounakbanik/pokemon) (with data up to Gen VII) and the Pulp package of solvers for optimization problems.\n",
        "\n",
        "The problem is defined by the following constraints:\n",
        "- A team must have up to 6 Pokemon in total.\n",
        "- The coverage of the team should be maximized.\n",
        "- The weaknesses of the team should be minimized.\n",
        "- The base total (sum of all stats of each Pokemon) should be maximized.\n",
        "\n",
        "Eventually, the final team will be further constrained to have:\n",
        "- No legendaries or pseudo-legendaries.\n",
        "- No dragon Pokemon (they tend to make things a bit too easy).\n",
        "- At most 1 starter Pokemon."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PNMvmWSTnsZx"
      },
      "source": [
        "## Initializations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bpq_3BMcrkQJ",
        "outputId": "2def1907-3f12-43ed-cd6a-11c5ba8f49dc"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "\n",
        "drive.mount(\"/content/drive\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c9KJr3-xoP5l",
        "outputId": "a9fe2976-e9dd-4206-db60-b3140761901c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "/content/drive/MyDrive/Colab Notebooks\n",
            "/content/drive/MyDrive/Colab Notebooks/pokemon-team-optimization\n",
            "/content/drive/MyDrive/Colab Notebooks/pokemon-team-optimization/data\n",
            "--2024-06-18 17:25:00--  https://raw.githubusercontent.com/NicolasChagnet/pokemon-team-optimization/main/data/pokemon.csv\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 160616 (157K) [text/plain]\n",
            "Saving to: ‘pokemon.csv’\n",
            "\n",
            "pokemon.csv         100%[===================>] 156.85K  --.-KB/s    in 0.03s   \n",
            "\n",
            "2024-06-18 17:25:00 (5.22 MB/s) - ‘pokemon.csv’ saved [160616/160616]\n",
            "\n",
            "/content/drive/MyDrive/Colab Notebooks/pokemon-team-optimization\n"
          ]
        }
      ],
      "source": [
        "%cd /content/drive/MyDrive/Colab\\ Notebooks\n",
        "%mkdir -p pokemon-team-optimization\n",
        "%cd pokemon-team-optimization\n",
        "%mkdir -p data\n",
        "%cd data\n",
        "!wget \"https://raw.githubusercontent.com/NicolasChagnet/pokemon-team-optimization/main/data/pokemon.csv\"\n",
        "%cd .."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D3fuP8bikwIb",
        "outputId": "63280ac4-165f-4981-8263-f04207fad299"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
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          ]
        }
      ],
      "source": [
        "# Download dependencies\n",
        "%pip install pandas numpy matplotlib seaborn pulp pokebase ipywidgets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "WFVZBjX5lFrq"
      },
      "outputs": [],
      "source": [
        "# Imports\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "from matplotlib import pyplot as plt\n",
        "import requests\n",
        "import os\n",
        "import pulp\n",
        "import pokebase\n",
        "from IPython.display import Image\n",
        "import ipywidgets as widgets\n",
        "from IPython.display import HTML"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NFA4qBoRl73o"
      },
      "source": [
        "Let us start by loading the Pokemon data. An important note: the columns \"against_XXX\" denote the damage factor taken by the Pokemon against an attack of that type."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "rQYdCHlvr478"
      },
      "outputs": [],
      "source": [
        "GENERATION_CAP = 4\n",
        "NTYPES = 18\n",
        "pks = pd.read_csv(\"data/pokemon.csv\")\n",
        "# Drop the Pokemon above the Generation cap and columns we will not use\n",
        "pks = pks.drop(pks.loc[pks[\"generation\"] > GENERATION_CAP].index)\n",
        "pks = pks.drop(\n",
        "    [\n",
        "        \"abilities\",\n",
        "        \"attack\",\n",
        "        \"base_egg_steps\",\n",
        "        \"base_happiness\",\n",
        "        \"capture_rate\",\n",
        "        \"classfication\",\n",
        "        \"defense\",\n",
        "        \"experience_growth\",\n",
        "        \"height_m\",\n",
        "        \"hp\",\n",
        "        \"japanese_name\",\n",
        "        \"percentage_male\",\n",
        "        \"sp_attack\",\n",
        "        \"sp_defense\",\n",
        "        \"speed\",\n",
        "        \"weight_kg\",\n",
        "    ],\n",
        "    axis=1,\n",
        ")\n",
        "pks[\"name\"] = pks[\"name\"].str.lower()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "A3zAb58lBfnW"
      },
      "outputs": [],
      "source": [
        "# This will be useful for later\n",
        "list_starters_final_stage = [\n",
        "    \"venusaur\",\n",
        "    \"charizard\",\n",
        "    \"blastoise\",\n",
        "    \"typhlosion\",\n",
        "    \"meganium\",\n",
        "    \"feraligatr\",\n",
        "    \"swampert\",\n",
        "    \"blaziken\",\n",
        "    \"sceptile\",\n",
        "    \"torterra\",\n",
        "    \"infernape\",\n",
        "    \"empoleon\",\n",
        "    \"serperior\",\n",
        "    \"emboar\",\n",
        "    \"samurott\",\n",
        "    \"chesnaught\",\n",
        "    \"delphox\",\n",
        "    \"greninja\",\n",
        "    \"decidueye\",\n",
        "    \"incineroar\",\n",
        "    \"primarina\",\n",
        "    \"rillaboom\",\n",
        "    \"cinderace\",\n",
        "    \"inteleon\",\n",
        "    \"meowscarada\",\n",
        "    \"skeledirge\",\n",
        "    \"quaquaval\",\n",
        "]\n",
        "pks[\"starter\"] = pks[\"name\"].isin(list_starters_final_stage).astype(int)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 396
        },
        "id": "V4uPbAIjzhGc",
        "outputId": "dbbacb65-34c5-4d96-9dc9-3d6c4abfefa0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Index(['against_bug', 'against_dark', 'against_dragon', 'against_electric',\n",
              "       'against_fairy', 'against_fight', 'against_fire', 'against_flying',\n",
              "       'against_ghost', 'against_grass', 'against_ground', 'against_ice',\n",
              "       'against_normal', 'against_poison', 'against_psychic', 'against_rock',\n",
              "       'against_steel', 'against_water', 'base_total', 'name',\n",
              "       'pokedex_number', 'type1', 'type2', 'generation', 'is_legendary',\n",
              "       'starter'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "pks"
            },
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>against_bug</th>\n",
              "      <th>against_dark</th>\n",
              "      <th>against_dragon</th>\n",
              "      <th>against_electric</th>\n",
              "      <th>against_fairy</th>\n",
              "      <th>against_fight</th>\n",
              "      <th>against_fire</th>\n",
              "      <th>against_flying</th>\n",
              "      <th>against_ghost</th>\n",
              "      <th>against_grass</th>\n",
              "      <th>...</th>\n",
              "      <th>against_steel</th>\n",
              "      <th>against_water</th>\n",
              "      <th>base_total</th>\n",
              "      <th>name</th>\n",
              "      <th>pokedex_number</th>\n",
              "      <th>type1</th>\n",
              "      <th>type2</th>\n",
              "      <th>generation</th>\n",
              "      <th>is_legendary</th>\n",
              "      <th>starter</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.25</td>\n",
              "      <td>...</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>318</td>\n",
              "      <td>bulbasaur</td>\n",
              "      <td>1</td>\n",
              "      <td>grass</td>\n",
              "      <td>poison</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.25</td>\n",
              "      <td>...</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>405</td>\n",
              "      <td>ivysaur</td>\n",
              "      <td>2</td>\n",
              "      <td>grass</td>\n",
              "      <td>poison</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.25</td>\n",
              "      <td>...</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>625</td>\n",
              "      <td>venusaur</td>\n",
              "      <td>3</td>\n",
              "      <td>grass</td>\n",
              "      <td>poison</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.50</td>\n",
              "      <td>...</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.0</td>\n",
              "      <td>309</td>\n",
              "      <td>charmander</td>\n",
              "      <td>4</td>\n",
              "      <td>fire</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.50</td>\n",
              "      <td>...</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.0</td>\n",
              "      <td>405</td>\n",
              "      <td>charmeleon</td>\n",
              "      <td>5</td>\n",
              "      <td>fire</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 26 columns</p>\n",
              "</div>\n",
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              "      fill: #FFFFFF;\n",
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              "\n",
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              "        document.querySelector('#df-04c4196d-0412-41fa-a8a9-5cbec86cc1aa button.colab-df-convert');\n",
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              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
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              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "\n",
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              "\n",
              "  .colab-df-quickchart {\n",
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              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
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              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-fa8bb281-1491-4cbc-80af-c9c32b4f496f button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "   against_bug  against_dark  against_dragon  against_electric  against_fairy  \\\n",
              "0          1.0           1.0             1.0               0.5            0.5   \n",
              "1          1.0           1.0             1.0               0.5            0.5   \n",
              "2          1.0           1.0             1.0               0.5            0.5   \n",
              "3          0.5           1.0             1.0               1.0            0.5   \n",
              "4          0.5           1.0             1.0               1.0            0.5   \n",
              "\n",
              "   against_fight  against_fire  against_flying  against_ghost  against_grass  \\\n",
              "0            0.5           2.0             2.0            1.0           0.25   \n",
              "1            0.5           2.0             2.0            1.0           0.25   \n",
              "2            0.5           2.0             2.0            1.0           0.25   \n",
              "3            1.0           0.5             1.0            1.0           0.50   \n",
              "4            1.0           0.5             1.0            1.0           0.50   \n",
              "\n",
              "   ...  against_steel  against_water  base_total        name  pokedex_number  \\\n",
              "0  ...            1.0            0.5         318   bulbasaur               1   \n",
              "1  ...            1.0            0.5         405     ivysaur               2   \n",
              "2  ...            1.0            0.5         625    venusaur               3   \n",
              "3  ...            0.5            2.0         309  charmander               4   \n",
              "4  ...            0.5            2.0         405  charmeleon               5   \n",
              "\n",
              "   type1   type2  generation  is_legendary starter  \n",
              "0  grass  poison           1             0       0  \n",
              "1  grass  poison           1             0       0  \n",
              "2  grass  poison           1             0       1  \n",
              "3   fire     NaN           1             0       0  \n",
              "4   fire     NaN           1             0       0  \n",
              "\n",
              "[5 rows x 26 columns]"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "display(pks.columns)\n",
        "type_columns = [col for col in pks.columns if \"against\" in col]\n",
        "pks.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "u_IBsc5REYjj"
      },
      "outputs": [],
      "source": [
        "def display_team(team):\n",
        "    \"\"\"Displays images of Pokemon in a row\n",
        "\n",
        "    Args:\n",
        "        team (list(str)): Names of Pokemon on the team\n",
        "    \"\"\"\n",
        "    style = \"<style>#output-body{display:flex; flex-direction: row;}</style>\"\n",
        "    style_none = \"<style>#output-body{display:none; flex-direction: none;}</style>\"\n",
        "    display(HTML(style))\n",
        "    for pkm in team[\"name\"].values:\n",
        "        display(Image(pokebase.pokemon(pkm).sprites.front_default))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6nf0yhg6DB3"
      },
      "source": [
        "## Optimization problem"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NCM-_hX26FJS"
      },
      "source": [
        "Let us start with the first part of the optimization problem using the dataset as it is. We can denote by $x_i$ whether a Pokemon is in the team or not, which means that the constraint of having a full team is $\\sum_i x_i = 6$.\n",
        "\n",
        "Furthermore, denoting by $b_i$ the base total of the Pokemon $i$, maximizing the base state means finding $x_i = \\arg \\max_{x_i} x_i b_i$ under the previous constraint.\n",
        "\n",
        "Finally, we want to reduce the weaknesses of our team. We can denote the damage multiple for the Pokemon $i$ against the type $A$ as $w_{iA}$. We want to ensure there is at least one resistant Pokemon to every type i.e. for every $A \\in [1, 18]$, we want to impose $\\min x_i w_{i A} \\leq 1.0$.\n",
        "\n",
        "Note that such minimizations are difficult to add with PulP. The trick explained [here](https://stackoverflow.com/questions/51939363/pulp-milp-constraint-at-least-one-variable-must-be-below-0) is to define extra boolean variables $y_{A i}$ such that for all $i,A$, we impose $x_i w_{i A} \\leq 1.0 + m*(1-y_{Ai})$ and $\\sum_i y_{Ai} \\geq 1$. The last constraint means that for each $A$, there must be one $i$ with $y_{Ai} = 1$. For $m$ sufficiently large, $y_{Ai} = 0$ for the others is not a constraint."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "RaiWtz0Z9iBr"
      },
      "outputs": [],
      "source": [
        "def present_solution_weaknesses(team, types):\n",
        "    \"\"\"Given a subset of Pokemon, highlights which Pokemon is resistant for each type.\n",
        "\n",
        "    Args:\n",
        "        team (pandas.DataFrame): DataFrame with the Pokemon team.\n",
        "        types (list(str)): List of type columns to consider.\n",
        "\n",
        "    Returns:\n",
        "        pandas.DataFrame: DataFrame indexed by type and with columns the team Pokemon as well as the minimal damage value and the Pokemon for which it happens.\n",
        "    \"\"\"\n",
        "    team_by_name = team.set_index(\"name\")\n",
        "    team_by_types = team_by_name[types].transpose()\n",
        "    team_by_types[\"min_val\"] = team_by_types.min(axis=1)\n",
        "    team_by_types[\"min_pkmn\"] = team_by_types.idxmin(axis=1)\n",
        "    team_by_types[\"type1\"] = team_by_name.loc[team_by_types[\"min_pkmn\"].values, \"type1\"].values\n",
        "    team_by_types[\"type2\"] = team_by_name.loc[team_by_types[\"min_pkmn\"].values, \"type2\"].values\n",
        "    return team_by_types\n",
        "\n",
        "\n",
        "def optimize_team_weakness(pkms, types, size_team=6):\n",
        "    prob = pulp.LpProblem(\"Pokemon_Team_Optimization\", pulp.LpMaximize)\n",
        "\n",
        "    # Define the boolean variables\n",
        "    x = pulp.LpVariable.dicts(\"x\", range(len(pkms)), cat=\"Binary\")\n",
        "    y = pulp.LpVariable.dicts(\"y\", (range(len(types)), range(len(pkms))), cat=\"Binary\")\n",
        "\n",
        "    # Define the size constraint\n",
        "    prob += pulp.lpSum(x[i] for i in range(len(pkms))) == size_team, \"Team Size\"\n",
        "\n",
        "    # Define the base total sum\n",
        "    prob += pulp.lpSum(pkmn[\"base_total\"] * x[i] for i, pkmn in pkms.iterrows()), \"Maximal base total\"\n",
        "\n",
        "    # Define the weakness sum bound for each type\n",
        "    # Based on https://stackoverflow.com/questions/51939363/pulp-milp-constraint-at-least-one-variable-must-be-below-0\n",
        "    m = 100\n",
        "    for a, type_col in enumerate(types):\n",
        "        prob += pulp.lpSum(y[a][i] for i in range(len(pkms))) >= 1  # Overall constraint for each type\n",
        "        for i, pkmn in pkms.iterrows():\n",
        "            prob += x[i] * pkmn[type_col] <= 0.5 + m * (1 - y[a][i]), f\"Weakness {type_col} for pokemon {i}\"\n",
        "\n",
        "    out_code = prob.solve()\n",
        "    display(print(f\"Out code: {out_code}\"))\n",
        "\n",
        "    if out_code == 1:\n",
        "        idxs_sol = [i for i in range(len(pkms)) if pulp.value(x[i]) == 1]\n",
        "        pkms_selected = pkms.loc[idxs_sol]\n",
        "        return pkms_selected\n",
        "    return None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "h6v7K5nvGVig",
        "outputId": "efd8f430-dff7-4f12-941c-e71ff70fa864"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pkmns_weakness = optimize_team_weakness(pks, type_columns)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "KzNUlmUbGfZT",
        "outputId": "dabb7695-5a60-49ef-c432-48525542bdc7"
      },
      "outputs": [
        {
          "data": {
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      ],
      "source": [
        "display_team(pkmns_weakness)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "8yQgb9M5D_CC",
        "outputId": "6656fbf6-7f94-4bc1-c23b-6706ebff58d1"
      },
      "outputs": [
        {
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            "text/plain": [
              "         name    type1   type2\n",
              "149    mewtwo  psychic     NaN\n",
              "381    kyogre    water     NaN\n",
              "382   groudon   ground     NaN\n",
              "383  rayquaza   dragon  flying\n",
              "444  garchomp   dragon  ground\n",
              "492    arceus   normal     NaN"
            ]
          },
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              "    <tr style=\"text-align: right;\">\n",
              "      <th>name</th>\n",
              "      <th>min_val</th>\n",
              "      <th>min_pkmn</th>\n",
              "      <th>type1</th>\n",
              "      <th>type2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>against_bug</th>\n",
              "      <td>0.50</td>\n",
              "      <td>rayquaza</td>\n",
              "      <td>dragon</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dark</th>\n",
              "      <td>1.00</td>\n",
              "      <td>kyogre</td>\n",
              "      <td>water</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dragon</th>\n",
              "      <td>1.00</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_electric</th>\n",
              "      <td>0.00</td>\n",
              "      <td>groudon</td>\n",
              "      <td>ground</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fairy</th>\n",
              "      <td>1.00</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fight</th>\n",
              "      <td>0.50</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fire</th>\n",
              "      <td>0.50</td>\n",
              "      <td>kyogre</td>\n",
              "      <td>water</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_flying</th>\n",
              "      <td>1.00</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ghost</th>\n",
              "      <td>0.00</td>\n",
              "      <td>arceus</td>\n",
              "      <td>normal</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_grass</th>\n",
              "      <td>0.25</td>\n",
              "      <td>rayquaza</td>\n",
              "      <td>dragon</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ground</th>\n",
              "      <td>0.00</td>\n",
              "      <td>rayquaza</td>\n",
              "      <td>dragon</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ice</th>\n",
              "      <td>0.50</td>\n",
              "      <td>kyogre</td>\n",
              "      <td>water</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_normal</th>\n",
              "      <td>1.00</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_poison</th>\n",
              "      <td>0.50</td>\n",
              "      <td>groudon</td>\n",
              "      <td>ground</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_psychic</th>\n",
              "      <td>0.50</td>\n",
              "      <td>mewtwo</td>\n",
              "      <td>psychic</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_rock</th>\n",
              "      <td>0.50</td>\n",
              "      <td>groudon</td>\n",
              "      <td>ground</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_steel</th>\n",
              "      <td>0.50</td>\n",
              "      <td>kyogre</td>\n",
              "      <td>water</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_water</th>\n",
              "      <td>0.50</td>\n",
              "      <td>kyogre</td>\n",
              "      <td>water</td>\n",
              "      <td>NaN</td>\n",
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            ],
            "text/plain": [
              "name              min_val  min_pkmn    type1   type2\n",
              "against_bug          0.50  rayquaza   dragon  flying\n",
              "against_dark         1.00    kyogre    water     NaN\n",
              "against_dragon       1.00    mewtwo  psychic     NaN\n",
              "against_electric     0.00   groudon   ground     NaN\n",
              "against_fairy        1.00    mewtwo  psychic     NaN\n",
              "against_fight        0.50    mewtwo  psychic     NaN\n",
              "against_fire         0.50    kyogre    water     NaN\n",
              "against_flying       1.00    mewtwo  psychic     NaN\n",
              "against_ghost        0.00    arceus   normal     NaN\n",
              "against_grass        0.25  rayquaza   dragon  flying\n",
              "against_ground       0.00  rayquaza   dragon  flying\n",
              "against_ice          0.50    kyogre    water     NaN\n",
              "against_normal       1.00    mewtwo  psychic     NaN\n",
              "against_poison       0.50   groudon   ground     NaN\n",
              "against_psychic      0.50    mewtwo  psychic     NaN\n",
              "against_rock         0.50   groudon   ground     NaN\n",
              "against_steel        0.50    kyogre    water     NaN\n",
              "against_water        0.50    kyogre    water     NaN"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness[[\"name\", \"type1\", \"type2\"]])\n",
        "display(present_solution_weaknesses(pkmns_weakness, type_columns)[[\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X3rQiEAFfpPB"
      },
      "source": [
        "We see an issue here: some weaknesses are still at least equal to 1.\n",
        "\n",
        "The constraint to have one $y_{Ai} = 1$ for all $A$ does not mean these coincide with the Pokemon selected for the team. So we need more variables. The idea is to create variables $z_{Ai}$ under the constraint:\n",
        "$$\n",
        "\\begin{aligned}\n",
        "  z_{Ai} \\leq x_i~,\\\\\n",
        "  z_{Ai} \\leq y_{Ai}~,\\\\\n",
        "  z_{Ai} \\geq x_i + y_{Ai} - 1~.\n",
        "\\end{aligned}\n",
        "$$\n",
        "More can be found [here](https://stackoverflow.com/questions/31173983/python-pulp-integer-linear-program-with-dynamic-constraint). For a given $A$ and $i$, we see that if $x_i = y_{Ai} = 1$, then $z_{Ai} = 1$. Otherwise, if one of them is $0$, the first two constraints impose that $z_{Ai} = 0$.\n",
        "\n",
        "Finally, the constraint $\\sum_i y_{Ai} \\geq 1$ should be changed to $\\sum_i z_{Ai} \\geq 1$ to impose that **both** $y_{Ai}$ and $x_i$ are equal to 1 for some $i$, for every $A$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "Y7SPoySUDgYp"
      },
      "outputs": [],
      "source": [
        "def optimize_team_weakness_improved(pkms, types, size_team=6):\n",
        "    prob = pulp.LpProblem(\"Pokemon_Team_Optimization\", pulp.LpMaximize)\n",
        "\n",
        "    # Define the boolean variables\n",
        "    x = pulp.LpVariable.dicts(\"x\", range(len(pkms)), cat=\"Binary\")\n",
        "    y = pulp.LpVariable.dicts(\"y\", (range(len(types)), range(len(pkms))), cat=\"Binary\")\n",
        "    z = pulp.LpVariable.dicts(\"z\", (range(len(types)), range(len(pkms))), cat=\"Binary\")\n",
        "\n",
        "    # Define the size constraint\n",
        "    prob += pulp.lpSum(x[i] for i in range(len(pkms))) == size_team, \"Team Size\"\n",
        "\n",
        "    # Define the base total sum\n",
        "    prob += pulp.lpSum(pkmn[\"base_total\"] * x[i] for i, pkmn in pkms.iterrows()), \"Maximal base total\"\n",
        "\n",
        "    # Define the weakness sum bound for each type\n",
        "    # Based on https://stackoverflow.com/questions/51939363/pulp-milp-constraint-at-least-one-variable-must-be-below-0\n",
        "    m = 100\n",
        "    for a, type_col in enumerate(types):\n",
        "        prob += pulp.lpSum(z[a][i] for i in range(len(pkms))) >= 1  # Overall constraint for each type\n",
        "        for i, pkmn in pkms.iterrows():\n",
        "            prob += z[a][i] <= x[i], f\"Contraint z 1 for {a},{i}\"\n",
        "            prob += z[a][i] <= y[a][i], f\"Contraint z 2 for {a},{i}\"\n",
        "            prob += z[a][i] >= x[i] + y[a][i] - 1, f\"Contraint z 3 for {a},{i}\"\n",
        "            prob += x[i] * pkmn[type_col] <= 0.5 + m * (1 - y[a][i]), f\"Weakness {type_col} for pokemon {i}\"\n",
        "\n",
        "    out_code = prob.solve()\n",
        "    display(print(f\"Out code: {out_code}\"))\n",
        "\n",
        "    if out_code == 1:\n",
        "        idxs_sol = [i for i in range(len(pkms)) if pulp.value(x[i]) == 1]\n",
        "        pkms_selected = pkms.loc[idxs_sol]\n",
        "        return pkms_selected\n",
        "    return None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "2ngRspSRGlZF",
        "outputId": "584e9f14-96a4-410f-ca92-aa7bcfaf57a3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pkmns_weakness_optimized = optimize_team_weakness_improved(pks, type_columns)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "ZqVbmuOpGqEp",
        "outputId": "1cf931d6-3dc2-4bdc-a3df-a6b463c16857"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
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              "<IPython.core.display.HTML object>"
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            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
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            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "4nmE_NhtiUQv",
        "outputId": "dc7212d6-aee3-41fd-feb2-921e445378ba"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "summary": "{\n  \"name\": \"display(present_solution_weaknesses(pkmns_weakness_optimized, type_columns)[[\\\"min_val\\\", \\\"min_pkmn\\\", \\\"type1\\\", \\\"type2\\\"]])\",\n  \"rows\": 6,\n  \"fields\": [\n    {\n      \"column\": \"name\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"mewtwo\",\n          \"tyranitar\",\n          \"rayquaza\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type1\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"psychic\",\n          \"rock\",\n          \"dragon\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type2\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"dark\",\n          \"psychic\",\n          \"flying\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
              "type": "dataframe"
            },
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              "      <td>rayquaza</td>\n",
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              "        document.querySelector('#df-0e1e3fac-f703-4487-bd2a-f2f99473081e button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
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              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
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              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
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              "\n",
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              "\n",
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              "\n",
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              "  </div>\n"
            ],
            "text/plain": [
              "          name    type1    type2\n",
              "149     mewtwo  psychic      NaN\n",
              "247  tyranitar     rock     dark\n",
              "375  metagross    steel  psychic\n",
              "381     kyogre    water      NaN\n",
              "382    groudon   ground      NaN\n",
              "383   rayquaza   dragon   flying"
            ]
          },
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              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-6d82e7d0-7820-49b5-abb1-e9fbd6ea752d');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-0932bab8-549f-48f4-84d2-8f2e7187485d\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-0932bab8-549f-48f4-84d2-8f2e7187485d')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-0932bab8-549f-48f4-84d2-8f2e7187485d button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "name              min_val   min_pkmn    type1    type2\n",
              "against_bug          0.50   rayquaza   dragon   flying\n",
              "against_dark         0.50  tyranitar     rock     dark\n",
              "against_dragon       0.50  metagross    steel  psychic\n",
              "against_electric     0.00    groudon   ground      NaN\n",
              "against_fairy        0.50  metagross    steel  psychic\n",
              "against_fight        0.50     mewtwo  psychic      NaN\n",
              "against_fire         0.50  tyranitar     rock     dark\n",
              "against_flying       0.50  tyranitar     rock     dark\n",
              "against_ghost        0.50  tyranitar     rock     dark\n",
              "against_grass        0.25   rayquaza   dragon   flying\n",
              "against_ground       0.00   rayquaza   dragon   flying\n",
              "against_ice          0.50  metagross    steel  psychic\n",
              "against_normal       0.50  tyranitar     rock     dark\n",
              "against_poison       0.00  metagross    steel  psychic\n",
              "against_psychic      0.00  tyranitar     rock     dark\n",
              "against_rock         0.50  metagross    steel  psychic\n",
              "against_steel        0.50  metagross    steel  psychic\n",
              "against_water        0.50     kyogre    water      NaN"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness_optimized[[\"name\", \"type1\", \"type2\"]])\n",
        "display(present_solution_weaknesses(pkmns_weakness_optimized, type_columns)[[\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_H2nGxp4ioht"
      },
      "source": [
        "Finally we found a method which works! All types are covered in our team! However, as expected, the team is full of legendary and pseudo-legendaries. The base total requirement almost ensures this, so let's try to just remove legendaries from the dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "VvbidSnVGxAs",
        "outputId": "bf615952-5e7d-4f33-ec8c-eeb85795697b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pks_no_legendaries = pks.loc[pks[\"is_legendary\"] == 0].reset_index().drop(columns=[\"index\"])\n",
        "pkmns_weakness_optimized_nolegendaries = optimize_team_weakness_improved(pks_no_legendaries, type_columns)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "almgy2atGuqA",
        "outputId": "876b1ed0-ad32-449a-d307-b3287e243ca2"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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              "<IPython.core.display.Image object>"
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          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "n111mLiXiYa6",
        "outputId": "15ed3258-bb58-45ba-ad76-748f7266ccf6"
      },
      "outputs": [
        {
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              "type": "dataframe"
            },
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-978a76c4-3edd-4b14-b747-fd453a0626fd button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "          name   type1    type2\n",
              "129   gyarados   water   flying\n",
              "239  tyranitar    rock     dark\n",
              "277    slaking  normal      NaN\n",
              "361  salamence  dragon   flying\n",
              "364  metagross   steel  psychic\n",
              "423   garchomp  dragon   ground"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "summary": "{\n  \"name\": \")\",\n  \"rows\": 18,\n  \"fields\": [\n    {\n      \"column\": \"min_val\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.2291109557951332,\n        \"min\": 0.0,\n        \"max\": 0.5,\n        \"num_unique_values\": 3,\n        \"samples\": [\n          0.5,\n          0.0,\n          0.25\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"min_pkmn\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"gyarados\",\n          \"tyranitar\",\n          \"salamence\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type1\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 5,\n        \"samples\": [\n          \"rock\",\n          \"normal\",\n          \"steel\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type2\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"dark\",\n          \"ground\",\n          \"flying\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
              "type": "dataframe"
            },
            "text/html": [
              "\n",
              "  <div id=\"df-4aa2d7b7-f2e3-49d2-941a-8a4a072bcb7a\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
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              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>name</th>\n",
              "      <th>min_val</th>\n",
              "      <th>min_pkmn</th>\n",
              "      <th>type1</th>\n",
              "      <th>type2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>against_bug</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dark</th>\n",
              "      <td>0.50</td>\n",
              "      <td>tyranitar</td>\n",
              "      <td>rock</td>\n",
              "      <td>dark</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dragon</th>\n",
              "      <td>0.50</td>\n",
              "      <td>metagross</td>\n",
              "      <td>steel</td>\n",
              "      <td>psychic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_electric</th>\n",
              "      <td>0.00</td>\n",
              "      <td>garchomp</td>\n",
              "      <td>dragon</td>\n",
              "      <td>ground</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fairy</th>\n",
              "      <td>0.50</td>\n",
              "      <td>metagross</td>\n",
              "      <td>steel</td>\n",
              "      <td>psychic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fight</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fire</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_flying</th>\n",
              "      <td>0.50</td>\n",
              "      <td>tyranitar</td>\n",
              "      <td>rock</td>\n",
              "      <td>dark</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ghost</th>\n",
              "      <td>0.00</td>\n",
              "      <td>slaking</td>\n",
              "      <td>normal</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_grass</th>\n",
              "      <td>0.25</td>\n",
              "      <td>salamence</td>\n",
              "      <td>dragon</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ground</th>\n",
              "      <td>0.00</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ice</th>\n",
              "      <td>0.50</td>\n",
              "      <td>metagross</td>\n",
              "      <td>steel</td>\n",
              "      <td>psychic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_normal</th>\n",
              "      <td>0.50</td>\n",
              "      <td>tyranitar</td>\n",
              "      <td>rock</td>\n",
              "      <td>dark</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_poison</th>\n",
              "      <td>0.00</td>\n",
              "      <td>metagross</td>\n",
              "      <td>steel</td>\n",
              "      <td>psychic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_psychic</th>\n",
              "      <td>0.00</td>\n",
              "      <td>tyranitar</td>\n",
              "      <td>rock</td>\n",
              "      <td>dark</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_rock</th>\n",
              "      <td>0.50</td>\n",
              "      <td>metagross</td>\n",
              "      <td>steel</td>\n",
              "      <td>psychic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_steel</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_water</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "    <div class=\"colab-df-buttons\">\n",
              "\n",
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              "    .colab-df-convert:hover {\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-4aa2d7b7-f2e3-49d2-941a-8a4a072bcb7a button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-4aa2d7b7-f2e3-49d2-941a-8a4a072bcb7a');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
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              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
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              "      border-left-color: var(--fill-color);\n",
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              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-59bc905c-fa2a-4af8-88ea-8b80f5d9d14b button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "name              min_val   min_pkmn   type1    type2\n",
              "against_bug          0.50   gyarados   water   flying\n",
              "against_dark         0.50  tyranitar    rock     dark\n",
              "against_dragon       0.50  metagross   steel  psychic\n",
              "against_electric     0.00   garchomp  dragon   ground\n",
              "against_fairy        0.50  metagross   steel  psychic\n",
              "against_fight        0.50   gyarados   water   flying\n",
              "against_fire         0.50   gyarados   water   flying\n",
              "against_flying       0.50  tyranitar    rock     dark\n",
              "against_ghost        0.00    slaking  normal      NaN\n",
              "against_grass        0.25  salamence  dragon   flying\n",
              "against_ground       0.00   gyarados   water   flying\n",
              "against_ice          0.50  metagross   steel  psychic\n",
              "against_normal       0.50  tyranitar    rock     dark\n",
              "against_poison       0.00  metagross   steel  psychic\n",
              "against_psychic      0.00  tyranitar    rock     dark\n",
              "against_rock         0.50  metagross   steel  psychic\n",
              "against_steel        0.50   gyarados   water   flying\n",
              "against_water        0.50   gyarados   water   flying"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness_optimized_nolegendaries[[\"name\", \"type1\", \"type2\"]])\n",
        "display(\n",
        "    present_solution_weaknesses(pkmns_weakness_optimized_nolegendaries, type_columns)[\n",
        "        [\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]\n",
        "    ]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IGnBncDfkVVr"
      },
      "source": [
        "This is great, but again now the team is as expected dominated by dragons because they have the most resistance! It would be interesting to restrict ourselves to non-dragons."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "bIIYVoFzG7Vf",
        "outputId": "7b507336-fe1a-436f-f5d0-404e250780cb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pks_no_legendaries_no_dragons = (\n",
        "    pks_no_legendaries.loc[(pks_no_legendaries[\"type1\"] != \"dragon\") & (pks_no_legendaries[\"type2\"] != \"dragon\")]\n",
        "    .reset_index()\n",
        "    .drop(columns=[\"index\"])\n",
        ")\n",
        "pkmns_weakness_optimized_nolegendaries_nodragons = optimize_team_weakness_improved(\n",
        "    pks_no_legendaries_no_dragons, type_columns\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "8q_mrOACG9yK",
        "outputId": "c83dbb04-a0e4-4f27-9587-83a7cb39d553"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
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        },
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              "<IPython.core.display.Image object>"
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          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "KkkhP0iAjKvv",
        "outputId": "74ba5510-138b-4022-83bd-0b2b6ed5a782"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "summary": "{\n  \"name\": \")\",\n  \"rows\": 6,\n  \"fields\": [\n    {\n      \"column\": \"name\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"charizard\",\n          \"gyarados\",\n          \"metagross\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type1\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 5,\n        \"samples\": [\n          \"water\",\n          \"steel\",\n          \"rock\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type2\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"dark\",\n          \"psychic\",\n          \"flying\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
              "type": "dataframe"
            },
            "text/html": [
              "\n",
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              "      <th>5</th>\n",
              "      <td>charizard</td>\n",
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              "      <th>129</th>\n",
              "      <td>gyarados</td>\n",
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              "      <th>235</th>\n",
              "      <td>tyranitar</td>\n",
              "      <td>rock</td>\n",
              "      <td>dark</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>244</th>\n",
              "      <td>swampert</td>\n",
              "      <td>water</td>\n",
              "      <td>ground</td>\n",
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              "    <tr>\n",
              "      <th>273</th>\n",
              "      <td>slaking</td>\n",
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              "      <td>NaN</td>\n",
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              "    <tr>\n",
              "      <th>354</th>\n",
              "      <td>metagross</td>\n",
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              "        document.querySelector('#df-cd50aef3-ce66-4026-b5f8-88a85b527908 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-cd50aef3-ce66-4026-b5f8-88a85b527908');\n",
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              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
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              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
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              "  </button>\n",
              "\n",
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              "    fill: var(--button-hover-fill-color);\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
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              "\n",
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              "      border-right-color: var(--fill-color);\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
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              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "          name   type1    type2\n",
              "5    charizard    fire   flying\n",
              "129   gyarados   water   flying\n",
              "235  tyranitar    rock     dark\n",
              "244   swampert   water   ground\n",
              "273    slaking  normal      NaN\n",
              "354  metagross   steel  psychic"
            ]
          },
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        {
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              "\n",
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              "\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
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              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-7a3fb5b6-3804-4fb1-9eff-ca7b7c1b14fe button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
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              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-7a3fb5b6-3804-4fb1-9eff-ca7b7c1b14fe');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-22b31e30-d186-4166-9d38-62e73f38ae90\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-22b31e30-d186-4166-9d38-62e73f38ae90')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-22b31e30-d186-4166-9d38-62e73f38ae90 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "name              min_val   min_pkmn   type1    type2\n",
              "against_bug          0.25  charizard    fire   flying\n",
              "against_dark         0.50  tyranitar    rock     dark\n",
              "against_dragon       0.50  metagross   steel  psychic\n",
              "against_electric     0.00   swampert   water   ground\n",
              "against_fairy        0.50  charizard    fire   flying\n",
              "against_fight        0.50  charizard    fire   flying\n",
              "against_fire         0.50  charizard    fire   flying\n",
              "against_flying       0.50  tyranitar    rock     dark\n",
              "against_ghost        0.00    slaking  normal      NaN\n",
              "against_grass        0.25  charizard    fire   flying\n",
              "against_ground       0.00  charizard    fire   flying\n",
              "against_ice          0.50  metagross   steel  psychic\n",
              "against_normal       0.50  tyranitar    rock     dark\n",
              "against_poison       0.00  metagross   steel  psychic\n",
              "against_psychic      0.00  tyranitar    rock     dark\n",
              "against_rock         0.50   swampert   water   ground\n",
              "against_steel        0.50  charizard    fire   flying\n",
              "against_water        0.50   gyarados   water   flying"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness_optimized_nolegendaries_nodragons[[\"name\", \"type1\", \"type2\"]])\n",
        "display(\n",
        "    present_solution_weaknesses(pkmns_weakness_optimized_nolegendaries_nodragons, type_columns)[\n",
        "        [\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]\n",
        "    ]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k7LRANxo6r3e"
      },
      "source": [
        "Another restriction we can self-impose is about pseudo-legendaries: those Pokemon appearing each generation with a much higher base total than usual Pokemon. In that sense they are closer to legendaries. But the issue is they usually can only be obtained late in the game (usually close to the last badge if not later). In any game, you would ideally want to get your dream team as early as possible. So let's remove these Pokemon."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "SK9pcNt2HDUn",
        "outputId": "8f81901c-a07e-494f-ae1e-270a36358db9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "list_pseudo_legendaries = [\n",
        "    \"Dragonite\",\n",
        "    \"Tyranitar\",\n",
        "    \"Salamence\",\n",
        "    \"Metagross\",\n",
        "    \"Garchomp\",\n",
        "    \"Hydreigon\",\n",
        "    \"Goodra\",\n",
        "    \"Kommo-o\",\n",
        "    \"Dragapult\",\n",
        "    \"Hisuian Goodra\",\n",
        "    \"Baxcalibur\",\n",
        "]\n",
        "list_pseudo_legendaries = [pkmn.lower() for pkmn in list_pseudo_legendaries]\n",
        "pks_no_legendaries_no_dragons_no_pl = (\n",
        "    pks_no_legendaries_no_dragons.loc[-pks_no_legendaries_no_dragons[\"name\"].isin(list_pseudo_legendaries)]\n",
        "    .reset_index()\n",
        "    .drop(columns=[\"index\"])\n",
        ")\n",
        "pkmns_weakness_optimized_nolegendaries_nodragons_nopl = optimize_team_weakness_improved(\n",
        "    pks_no_legendaries_no_dragons_no_pl, type_columns\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "n7t1lCFeHF9O",
        "outputId": "04a12b28-2522-4ada-e4af-011e95c7c7f6"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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              "<IPython.core.display.Image object>"
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            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons_nopl)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "e9yvbvRm1oIn",
        "outputId": "5d10c85a-8cb1-419a-a93e-57e665d8cc96"
      },
      "outputs": [
        {
          "data": {
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              "summary": "{\n  \"name\": \")\",\n  \"rows\": 6,\n  \"fields\": [\n    {\n      \"column\": \"name\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"charizard\",\n          \"gyarados\",\n          \"aggron\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type1\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"water\",\n          \"steel\",\n          \"fire\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type2\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"fighting\",\n          \"rock\",\n          \"flying\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
              "type": "dataframe"
            },
            "text/html": [
              "\n",
              "  <div id=\"df-372edb04-f904-4afd-bf1c-3401728ef3ba\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>name</th>\n",
              "      <th>type1</th>\n",
              "      <th>type2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>129</th>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>240</th>\n",
              "      <td>blaziken</td>\n",
              "      <td>fire</td>\n",
              "      <td>fighting</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>243</th>\n",
              "      <td>swampert</td>\n",
              "      <td>water</td>\n",
              "      <td>ground</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>272</th>\n",
              "      <td>slaking</td>\n",
              "      <td>normal</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>289</th>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-372edb04-f904-4afd-bf1c-3401728ef3ba')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-372edb04-f904-4afd-bf1c-3401728ef3ba button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-372edb04-f904-4afd-bf1c-3401728ef3ba');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-c448e316-f2ac-4b2a-a993-92d447b0315a\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-c448e316-f2ac-4b2a-a993-92d447b0315a')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
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              "        document.querySelector('#df-c448e316-f2ac-4b2a-a993-92d447b0315a button');\n",
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              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "          name   type1     type2\n",
              "5    charizard    fire    flying\n",
              "129   gyarados   water    flying\n",
              "240   blaziken    fire  fighting\n",
              "243   swampert   water    ground\n",
              "272    slaking  normal       NaN\n",
              "289     aggron   steel      rock"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "summary": "{\n  \"name\": \")\",\n  \"rows\": 18,\n  \"fields\": [\n    {\n      \"column\": \"min_val\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.21004201260420147,\n        \"min\": 0.0,\n        \"max\": 0.5,\n        \"num_unique_values\": 3,\n        \"samples\": [\n          0.25,\n          0.5,\n          0.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"min_pkmn\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 6,\n        \"samples\": [\n          \"charizard\",\n          \"blaziken\",\n          \"gyarados\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type1\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"steel\",\n          \"normal\",\n          \"fire\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"type2\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"fighting\",\n          \"ground\",\n          \"flying\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
              "type": "dataframe"
            },
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              "\n",
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              "    }\n",
              "\n",
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              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>name</th>\n",
              "      <th>min_val</th>\n",
              "      <th>min_pkmn</th>\n",
              "      <th>type1</th>\n",
              "      <th>type2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>against_bug</th>\n",
              "      <td>0.25</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dark</th>\n",
              "      <td>0.50</td>\n",
              "      <td>blaziken</td>\n",
              "      <td>fire</td>\n",
              "      <td>fighting</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_dragon</th>\n",
              "      <td>0.50</td>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_electric</th>\n",
              "      <td>0.00</td>\n",
              "      <td>swampert</td>\n",
              "      <td>water</td>\n",
              "      <td>ground</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fairy</th>\n",
              "      <td>0.50</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fight</th>\n",
              "      <td>0.50</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_fire</th>\n",
              "      <td>0.50</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_flying</th>\n",
              "      <td>0.25</td>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ghost</th>\n",
              "      <td>0.00</td>\n",
              "      <td>slaking</td>\n",
              "      <td>normal</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_grass</th>\n",
              "      <td>0.25</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ground</th>\n",
              "      <td>0.00</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_ice</th>\n",
              "      <td>0.50</td>\n",
              "      <td>blaziken</td>\n",
              "      <td>fire</td>\n",
              "      <td>fighting</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_normal</th>\n",
              "      <td>0.25</td>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_poison</th>\n",
              "      <td>0.00</td>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_psychic</th>\n",
              "      <td>0.50</td>\n",
              "      <td>aggron</td>\n",
              "      <td>steel</td>\n",
              "      <td>rock</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_rock</th>\n",
              "      <td>0.50</td>\n",
              "      <td>swampert</td>\n",
              "      <td>water</td>\n",
              "      <td>ground</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_steel</th>\n",
              "      <td>0.50</td>\n",
              "      <td>charizard</td>\n",
              "      <td>fire</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>against_water</th>\n",
              "      <td>0.50</td>\n",
              "      <td>gyarados</td>\n",
              "      <td>water</td>\n",
              "      <td>flying</td>\n",
              "    </tr>\n",
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              "\n",
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              "          + ' to learn more about interactive tables.';\n",
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              "\n",
              "  .colab-df-quickchart:hover {\n",
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              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "  }\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-46fa86b1-7a4b-4d34-8cd7-921f0b803022 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "name              min_val   min_pkmn   type1     type2\n",
              "against_bug          0.25  charizard    fire    flying\n",
              "against_dark         0.50   blaziken    fire  fighting\n",
              "against_dragon       0.50     aggron   steel      rock\n",
              "against_electric     0.00   swampert   water    ground\n",
              "against_fairy        0.50  charizard    fire    flying\n",
              "against_fight        0.50  charizard    fire    flying\n",
              "against_fire         0.50  charizard    fire    flying\n",
              "against_flying       0.25     aggron   steel      rock\n",
              "against_ghost        0.00    slaking  normal       NaN\n",
              "against_grass        0.25  charizard    fire    flying\n",
              "against_ground       0.00  charizard    fire    flying\n",
              "against_ice          0.50   blaziken    fire  fighting\n",
              "against_normal       0.25     aggron   steel      rock\n",
              "against_poison       0.00     aggron   steel      rock\n",
              "against_psychic      0.50     aggron   steel      rock\n",
              "against_rock         0.50   swampert   water    ground\n",
              "against_steel        0.50  charizard    fire    flying\n",
              "against_water        0.50   gyarados   water    flying"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness_optimized_nolegendaries_nodragons_nopl[[\"name\", \"type1\", \"type2\"]])\n",
        "display(\n",
        "    present_solution_weaknesses(pkmns_weakness_optimized_nolegendaries_nodragons_nopl, type_columns)[\n",
        "        [\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]\n",
        "    ]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UePzqI758nUK"
      },
      "source": [
        "This is better, but again there is an issue: there are 3 starters in this team only. It is unrealistic in a game to have more than one starter. To remedy this issue, we will add an extra constraint that there should only be at most one starter."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "-P-xXvCOAEbX"
      },
      "outputs": [],
      "source": [
        "def optimize_team_weakness_improved_starter_cst(pkms, types, size_team=6):\n",
        "    prob = pulp.LpProblem(\"Pokemon_Team_Optimization\", pulp.LpMaximize)\n",
        "\n",
        "    # Define the boolean variables\n",
        "    x = pulp.LpVariable.dicts(\"x\", range(len(pkms)), cat=\"Binary\")\n",
        "    y = pulp.LpVariable.dicts(\"y\", (range(len(types)), range(len(pkms))), cat=\"Binary\")\n",
        "    z = pulp.LpVariable.dicts(\"z\", (range(len(types)), range(len(pkms))), cat=\"Binary\")\n",
        "\n",
        "    # Define the size constraint\n",
        "    prob += pulp.lpSum(x[i] for i in range(len(pkms))) == size_team, \"Team Size\"\n",
        "\n",
        "    # Starter constraint\n",
        "    prob += pulp.lpSum(x[i] * pkmn[\"starter\"] for i, pkmn in pkms.iterrows()) <= 1, \"Number starter\"\n",
        "\n",
        "    # Define the base total sum\n",
        "    prob += pulp.lpSum(pkmn[\"base_total\"] * x[i] for i, pkmn in pkms.iterrows()), \"Maximal base total\"\n",
        "\n",
        "    # Define the weakness sum bound for each type\n",
        "    # Based on https://stackoverflow.com/questions/51939363/pulp-milp-constraint-at-least-one-variable-must-be-below-0\n",
        "    m = 100\n",
        "    for a, type_col in enumerate(types):\n",
        "        prob += pulp.lpSum(z[a][i] for i in range(len(pkms))) >= 1  # Overall constraint for each type\n",
        "        for i, pkmn in pkms.iterrows():\n",
        "            prob += z[a][i] <= x[i], f\"Contraint z 1 for {a},{i}\"\n",
        "            prob += z[a][i] <= y[a][i], f\"Contraint z 2 for {a},{i}\"\n",
        "            prob += z[a][i] >= x[i] + y[a][i] - 1, f\"Contraint z 3 for {a},{i}\"\n",
        "            prob += x[i] * pkmn[type_col] <= 0.5 + m * (1 - y[a][i]), f\"Weakness {type_col} for pokemon {i}\"\n",
        "\n",
        "    out_code = prob.solve()\n",
        "    display(print(f\"Out code: {out_code}\"))\n",
        "\n",
        "    if out_code == 1:\n",
        "        idxs_sol = [i for i in range(len(pkms)) if pulp.value(x[i]) == 1]\n",
        "        pkms_selected = pkms.loc[idxs_sol]\n",
        "        return pkms_selected\n",
        "    return None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "8PZuTwRZHJlN",
        "outputId": "da40736c-bd1e-4744-cfb9-9a56431cfd8b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter = optimize_team_weakness_improved_starter_cst(\n",
        "    pks_no_legendaries_no_dragons_no_pl, type_columns\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "NzVyaLTyHK9Z",
        "outputId": "1875d81b-30ee-4a37-98c4-4562396aa894"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "id": "Z8AfIp80AhO-",
        "outputId": "fbb4edeb-e17c-40da-ea57-89ad29fd457f"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
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            ],
            "text/plain": [
              "          name     type1   type2\n",
              "129   gyarados     water  flying\n",
              "243   swampert     water  ground\n",
              "265  gardevoir   psychic   fairy\n",
              "272    slaking    normal     NaN\n",
              "289     aggron     steel    rock\n",
              "411    lucario  fighting   steel"
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-254bd0da-3b1c-43df-8983-5b16f1a10305 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-254bd0da-3b1c-43df-8983-5b16f1a10305');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-006b4e18-b1cf-4b83-9a0e-0126545c3e7c\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-006b4e18-b1cf-4b83-9a0e-0126545c3e7c')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-006b4e18-b1cf-4b83-9a0e-0126545c3e7c button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "name              min_val   min_pkmn     type1   type2\n",
              "against_bug          0.25    lucario  fighting   steel\n",
              "against_dark         0.50    lucario  fighting   steel\n",
              "against_dragon       0.00  gardevoir   psychic   fairy\n",
              "against_electric     0.00   swampert     water  ground\n",
              "against_fairy        0.50     aggron     steel    rock\n",
              "against_fight        0.25  gardevoir   psychic   fairy\n",
              "against_fire         0.50   gyarados     water  flying\n",
              "against_flying       0.25     aggron     steel    rock\n",
              "against_ghost        0.00    slaking    normal     NaN\n",
              "against_grass        0.50    lucario  fighting   steel\n",
              "against_ground       0.00   gyarados     water  flying\n",
              "against_ice          0.50     aggron     steel    rock\n",
              "against_normal       0.25     aggron     steel    rock\n",
              "against_poison       0.00     aggron     steel    rock\n",
              "against_psychic      0.50  gardevoir   psychic   fairy\n",
              "against_rock         0.25    lucario  fighting   steel\n",
              "against_steel        0.50   gyarados     water  flying\n",
              "against_water        0.50   gyarados     water  flying"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter[[\"name\", \"type1\", \"type2\"]])\n",
        "display(\n",
        "    present_solution_weaknesses(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter, type_columns)[\n",
        "        [\"min_val\", \"min_pkmn\", \"type1\", \"type2\"]\n",
        "    ]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KeYhSagrA1fK"
      },
      "source": [
        "**Perfect**! We finally have a team which can resist every possible encounter and is made of achievable Pokemon! Out of curiosity, let's just look at the various generations restrictions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 122
        },
        "id": "80fad7CsCDGp",
        "outputId": "09514134-fbae-42b7-a2c7-83df36ff8c1c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Out code: 1\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen1 = optimize_team_weakness_improved_starter_cst(\n",
        "    pks_no_legendaries_no_dragons_no_pl.loc[pks_no_legendaries_no_dragons_no_pl[\"generation\"] <= 1], type_columns\n",
        ")\n",
        "pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen2 = optimize_team_weakness_improved_starter_cst(\n",
        "    pks_no_legendaries_no_dragons_no_pl.loc[pks_no_legendaries_no_dragons_no_pl[\"generation\"] <= 2], type_columns\n",
        ")\n",
        "pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen3 = optimize_team_weakness_improved_starter_cst(\n",
        "    pks_no_legendaries_no_dragons_no_pl.loc[pks_no_legendaries_no_dragons_no_pl[\"generation\"] <= 3], type_columns\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "CMvTdY6AsYZP",
        "outputId": "cfe6e90a-dc90-41f9-ed8c-f269c8362f82"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "5mKJrg2lCP3N",
        "outputId": "b3c0476f-a120-4f21-8dee-835d793a7409"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
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            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
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            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 113
        },
        "id": "W16CsS9qCaKU",
        "outputId": "69729b37-f0f7-4a0c-eefd-ba85e9f1b8e0"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<style>#output-body{display:flex; flex-direction: row;}</style>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAABgBAMAAAAQtmoLAAAAMFBMVEUAAAAYGBgYQXMYYpQgi6xBtO5aQSBqGCBze3t71e69MWLNtHvV3vbuYkH25qz29vYds8NdAAAAAXRSTlMAQObYZgAABc5JREFUWMPt10FoG0cUANBZKQ067tgrx7aUxlqtS4KDa3nlQmguI30VgnqxrIHkEmLaqAWBIZeqBNI6DSWCCEQbfNCxl+ZUihLVOQyUSoYgyoBvPQR86MG5GBbSXnwQbP+sFMeSNpF8LVksTOR5O//P/zO7IeTd9b++9JOCxAnHh3ZONkVoJAjaS6//YZJKWb49puAKz78WyfOVtlz2HbjZ/ZU2Oef5uVff3ktJKe/5xRQ69H4B5xMocp4IlMk9uCilbxJVd5OECNS2OA8jyHvRXSzLJE6xM+c3g/sHqRi1Wg1H4xQZb8zlttzBKdr+4DAkZ47AfE59Gce7w7L0X6aqe1cBDIkvOj0QuCy9mHwBToFAjUewv8j1oykuvgl0KjM4+vq+B/b13hQK+Bei2pG4Ptcdh6ec/KKz6n0Zr2BMbT8QolUpm8AdBTgsHnRBYPlNoOqWpWxxuO7s8xTAQoN1vw+cb6Xjc77AxSZY4QmH51PZxwDsVfuZ6bhva5xzO3IH2yich5Q4Bohp+4FNoiGYx1UyIFsUxWMgsEz1oT4NNYkW7bRUEVhWIGhA7OjvsfTEQJ/qpNIkRlQqkGdCFLdFA6yj2wbTT/T+dA/1kNQN5kWUh8g2TtFINfRXmySZ7Qch1305LZs9AAgKQghvXbubJJn9rD+Jsus2K9KAyxkFspF1HD8hhAKuTjY3NWoP16BdaUEaVETZ+pQQFLIKVF0aarc1gIHKhaqqaHEzlsGIsnWxPiUaXXAYjbbbcYDUUKci2MnwGAAIFRGuUsMDMior1hAIlTsKqDUFSvWiEgC6CgmTU6Du03jYRygoz/cAq6stgkBaGOZQ0p0ewB9dU4BFxDSC6aaUMfrx+mDS/2AS36vDAtdVJ1iH7c9BnCu7MtqM4gzmjcGkrQ9VCh7AXIsFsygw60O3LfVoC7x8+q8eUBExclqYOZU1c/Fc1QMKsCGwLNtdgDc7/ZibamEZZtYkAcy5MQwSFS9p3G06CcxfjXhgF3c5MXOW8AOmia1Hw/mkjuMrHsCGl5sTta2caNSHQ4LMj/M5CENSx/FtD1gIzGt4eC7AMEjAta2cwbABqVWRTVW5VIPJtnkBQS47uEqnFOCrYFCDaVelfIAgtSAYneY5PD1zYhBcsRKZGscJgJnhLqgb2K+ruAwXuJOnxwcHemBrNcmAhfMGntgvCwWsnDDUsyXlOPm+7WDNkVM/gG3wSduADFdg9+UDr8Mjv4VxnZ2D/kJbqS5gdgJUZ6Tlrus+8BoWs3AasNjoBxrMvacATpBRnZGWbg+ksGeRYaUHALuCgNqJjOoMmt7FXSA8gC2BwBisggHUBHPSTiQVMNK4l+56uxR3GlMFH9w+GtjLALZt7PBM3jA+RUAVwAMZ746fviqYJiGTdhJBIvovAsoUaKN4vNDwAIscr0KAgxmjtgUpO/FrB/BYothAshmhU7izGwww776qEdPCu0waCGbvdNSxBAyB6yUhBPagGDzDWqYBLAZ2/OxZPPgwNtaku66ujldRV5/BPq3IlpFu2TZdU68xSWC6Tqbd7kGAmdSHdnMIjxH4czJRU/ttrbfd1SOnULiBH5+HlTqpbBp+mCncVGByadQ7nQKprcxaQWwjYMMHxOClyRZ8ZPGCcyDCPMkojHqH1DoWbLwoOC8Kxe2bSUaM9KjXTNf6ZHvDqdPdKbGeBl0bDb4zv3xWKJWqtCgmMaDkqLTLhHywe6ZU+prSiFAxjVwnzKOKoERRPGH4WB7jfXl6XYHZRxSfyBobA2iReunW7N7zW9g6YwGSiJy5tbe39xOC4DggCImnswh+RpBcGgekSeRODxjjgl8QFBHMjAm023t7zzdujAkwcAR/fbGhnwA8vf3tMwUuPRwPhO7ffuSBIILg0ugcpt3SV98cKFBbIpfevimCSwjev1/63fHOiJmHdm0EWFvBVXKcv6e8cVqtRkdEtMIxZnr0ekrpyDLY7/7H/e46dv0HVGzR1Ud+I4oAAAAASUVORK5CYII=",
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              "<IPython.core.display.Image object>"
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          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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            "text/plain": [
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          "metadata": {},
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        },
        {
          "data": {
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            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
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        "display_team(pkmns_weakness_optimized_nolegendaries_nodragons_nopl_starter_gen3)"
      ]
    }
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