Day_12_Subterranean_Sustainability.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPItuD0QdltccwPgZcldoEl",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/elichen/aoc2018/blob/main/Day_12_Subterranean_Sustainability.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nQv1H1Q3FiKy"
      },
      "outputs": [],
      "source": [
        "init = \"#..#.#..##......###...###\"\n",
        "data = \"\"\"...## => #\n",
        "..#.. => #\n",
        ".#... => #\n",
        ".#.#. => #\n",
        ".#.## => #\n",
        ".##.. => #\n",
        ".#### => #\n",
        "#.#.# => #\n",
        "#.### => #\n",
        "##.#. => #\n",
        "##.## => #\n",
        "###.. => #\n",
        "###.# => #\n",
        "####. => #\"\"\".split('\\n')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "init = \"#.#.#..##.#....#.#.##..##.##..#..#...##....###..#......###.#..#.....#.###.#...#####.####...#####.#.#\"\n",
        "data = \"\"\"..#.. => .\n",
        "#...# => .\n",
        ".#... => #\n",
        "#.##. => .\n",
        "..#.# => #\n",
        "#.#.# => .\n",
        "###.. => #\n",
        "###.# => #\n",
        "..... => .\n",
        "....# => .\n",
        ".##.. => #\n",
        "##### => .\n",
        "####. => .\n",
        "..##. => .\n",
        "##.#. => #\n",
        ".#..# => #\n",
        "##..# => .\n",
        ".##.# => .\n",
        ".#### => #\n",
        "..### => .\n",
        "...## => #\n",
        "#..## => #\n",
        "#.... => .\n",
        "##.## => .\n",
        "#.#.. => .\n",
        "##... => .\n",
        ".#.## => #\n",
        ".###. => #\n",
        "...#. => .\n",
        "#.### => .\n",
        "#..#. => #\n",
        ".#.#. => .\"\"\".split('\\n')"
      ],
      "metadata": {
        "id": "BXbImborRuXj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "parsed_dict = {item.split(\" => \")[0]: item.split(\" => \")[1] for item in data}"
      ],
      "metadata": {
        "id": "8inFEyvVFrbS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def transform_string_with_conditional_padding(input_string, left_offset, mapping_dict):\n",
        "    # Padding with \".\" only if necessary to ensure at least 3 \".\" on both sides\n",
        "    left_padding = 3\n",
        "    right_padding = 3 - (len(input_string) - input_string.rfind('#') - 1) if (len(input_string) - input_string.rfind('#') - 1) < 3 else 0\n",
        "\n",
        "    extended_string = (\".\" * left_padding) + input_string + (\".\" * right_padding)\n",
        "\n",
        "    # Initializing the output string\n",
        "    output_string = \"\"\n",
        "\n",
        "    # Iterating through each sequence of 5 characters in the extended string\n",
        "    for i in range(len(extended_string) - 4):\n",
        "        sequence = extended_string[i:i + 5]\n",
        "        # Looking up the sequence in the dictionary and appending to the output string\n",
        "        c = mapping_dict.get(sequence, \".\")\n",
        "        if i > 0:\n",
        "          output_string += c\n",
        "        elif c == \"#\":\n",
        "          left_offset += 1\n",
        "          output_string += c\n",
        "\n",
        "    return output_string, left_offset"
      ],
      "metadata": {
        "id": "YPgoPYZFGSLi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "s = init\n",
        "left_offset = 0\n",
        "for i in range(1,21):\n",
        "  s,left_offset = transform_string_with_conditional_padding(s, left_offset, parsed_dict)\n",
        "  # print(i,s,left_offset)\n",
        "indices = [index-left_offset for index, char in enumerate(s) if char == '#']\n",
        "sum(indices)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fyjx0zHlH7AN",
        "outputId": "c968953e-8ce6-40d9-eebc-922e0acefd0d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1917"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "s = init\n",
        "left_offset = 0\n",
        "seq = []\n",
        "for i in range(1,1000+1):\n",
        "  s,left_offset = transform_string_with_conditional_padding(s, left_offset, parsed_dict)\n",
        "  indices = [index-left_offset for index, char in enumerate(s) if char == '#']\n",
        "  seq.append(sum(indices))\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(seq)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 445
        },
        "id": "ymx8lyLtLh-F",
        "outputId": "ded47c5e-2306-4c31-e838-0f1c96500e7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "6041-6016, 6066-6041, 6091-6066"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gzhIuGCaWeo8",
        "outputId": "2a485b1e-3ad8-4068-dd94-47c0b5fdd111"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(25, 25, 25)"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = 50000000000-1\n",
        "m = 25\n",
        "b = 1016\n",
        "m*x+b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PjNOtGO6WqKc",
        "outputId": "88fafa6c-21c1-45c0-ee12-0849c03fd204"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1250000000991"
            ]
          },
          "metadata": {},
          "execution_count": 108
        }
      ]
    }
  ]
}