TNN_Total_n00b_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TNN: Total n00b Notebook\n",
    "\n",
    "I have a very limited understanding of this challenge (other than knowing what a Rubik’s Cube is), but it seems very interesting. I have no hopes of making it high on the leaderboard, but it seems worthwhile to learn more about the techniques involved in the challenge.\n",
    "\n",
    "Because I assume that other people are in my situation, I am working with ChatGPT to better understand the nature of the challenge. \n",
    "\n",
    "The first step in my journey is taking the **very simple** puzzle from the \"getting started\" notebook and creating some visuals to better understand the move steps.\n",
    "\n",
    "I am a Physician and Data Science hobbyist, so I am using GPT and Copilot to help with writing code. But the ideas in this notebook are my own.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from ast import literal_eval\n",
    "from pathlib import Path\n",
    "from pprint import pprint\n",
    "from sympy.combinatorics import Permutation\n",
    "\n",
    "# Here is a very simple puzzle\n",
    "solution_state = ['R', 'G', 'B']\n",
    "initial_state = ['B', 'G', 'R']\n",
    "moves = {\n",
    "    'r': [1, 2, 0],\n",
    "    's': [1, 0, 2],\n",
    "}\n",
    "r = moves['r']\n",
    "s = moves['s']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a function that plots the current state of the 3 element puzzle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "\n",
    "def plot_state_squares(state, title, scale=0.75):\n",
    "    \"\"\"\n",
    "    Plot a state of the puzzle with each element represented as a true square.\n",
    "    \n",
    "    :param state: List of color initials (e.g., ['R', 'G', 'B'])\n",
    "    :param title: Title of the plot\n",
    "    :param scale: Scale factor for the size of squares (default is 0.75)\n",
    "    \"\"\"\n",
    "    color_map = {'R': 'red', 'G': 'green', 'B': 'blue'}\n",
    "    fig_size = len(state) * scale\n",
    "    fig, ax = plt.subplots(figsize=(fig_size, scale))\n",
    "\n",
    "    # Calculate the offset and size of each square based on the scale factor\n",
    "    offset = (1 - scale) / 2\n",
    "    size = scale\n",
    "\n",
    "    # Create a true square for each element in the state\n",
    "    for i, color_initial in enumerate(state):\n",
    "        color = color_map.get(color_initial, 'white')  # Default to white if unknown color\n",
    "        rect = patches.Rectangle((i + offset, offset), size, size, linewidth=1, edgecolor='black', facecolor=color)\n",
    "        ax.add_patch(rect)\n",
    "\n",
    "    # Setting the limits and removing the axes for clarity\n",
    "    ax.set_xlim(0, len(state))\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.set_aspect('equal')  # Ensuring squares are displayed as true squares\n",
    "    ax.axis('off')\n",
    "    ax.set_title(title)\n",
    "\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Look at what the 2 moves, \"r\" and \"s\", do to the puzzle\n",
    "\n",
    "```\n",
    "moves = {\n",
    "    'r': [1, 2, 0],\n",
    "    's': [1, 0, 2],\n",
    "}\n",
    "```\n",
    "- ```r``` effectively rotates the color of the squares, moving each square rightwards in a circular manner.\n",
    "- ```s``` swaps the position of the first 2 squares and leaves the 3rd unchanged\n",
    "\n",
    "Initially, I am just manipulating the state using a list comprehension.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['G', 'R', 'B']\n",
      "['R', 'B', 'G']\n",
      "['B', 'G', 'R']\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Applying 3 r moves in a row\n",
    "first_move = [initial_state[i] for i in r]\n",
    "print(first_move)\n",
    "second_move = [first_move[i] for i in r]\n",
    "print(second_move)\n",
    "third_move = [second_move[i] for i in r]\n",
    "print(third_move)\n",
    "\n",
    "# Re-plotting the initial state, the state after each move, and the solution state with smaller squares\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "plot_state_squares(first_move, \"After Move 'r'\")\n",
    "plot_state_squares(second_move, \"After Move 'r'\")\n",
    "plot_state_squares(third_move, \"After Move 'r'\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Looking at the intial state and the solution state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAABiCAYAAADpyrfcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAAALHklEQVR4nO3dbUxbZRsH8P8pLRwoJst6aBlsFJwOmOm6PBISX4ebug3FuSdEN4MwEtwUtixkQcPMMkycSDeDizJIZnSZOCKJOCMizggYXxjwwcWIJPOFQhenrsVN5+jWlev5MHukK3RQulGe+/ol/cA597nPdZ3233NOWZlERATGBKaZ7QIYm20cAiY8DgETHoeACY9DwITHIWDC4xAw4XEImPA4BEx4ER+Cnp4erF+/HikpKYiJiYHJZMIdd9yBHTt2hDTfpk2bkJqaGtK2X3/9NaqqqnD27NmAdTk5OcjJyQlp3plyOBwoLS3FkiVLEBsbi/nz58NiseCpp56Cw+FQx7W1taGqqmpG+zpy5AheffXVmRUcaSiCtba2kkajoZUrV1JTUxN1dXVRU1MT7dixg5KTk0Oas6ioiMxmc0jb7t27lwDQ4OBgwLr+/n7q7+8Pad6ZcDgcpCgK3XLLLVRfX08dHR30/vvv0549e8hqtVJXV5c6tqysjGb6lD/00EMhH79IpZ3tEAZjs9mQlpaGTz75BFrtv6Vu2LABNpttFisLtHTp0lnZ78GDB+F0OtHb24u0tDR1+aOPPoqdO3dibGxsVuqaSyL6csjlckFRFL8A+Gg0/qWPjY3BZrMhIyMDMTExMBqNKCwsxKlTp4Luw263Q5IkHDp0KGCdJEnq5UNVVRUqKioAAGlpaZAkCZIkoaurC8DEl0MjIyMoLS1FcnIyoqOjcfPNN+P555/HxYsXA/azdetWvP3228jMzERcXBysVitaW1uD1g5cOUYajQZGo3HC9b7jtGnTJtTV1an78z3sdjsAoK6uDvfeey+MRiP0ej0sFgtsNhs8Ho86V05ODj766CMMDQ35zeFz6dIlvPjii+pzkJCQgOLiYpw5c+aafcyq2T4VBVNSUkIAaNu2bXT8+HG6dOnSpGM3b95MAGjr1q3U3t5ODQ0NlJCQQIsWLaIzZ86o466+HBocHCQA9NZbbwXMCYB2795NRFcuO7Zt20YAqKWlhbq7u6m7u5vOnTtHREQrVqygFStWqNuOjo7SsmXLSK/X0759++jYsWO0a9cu0mq1lJubG7Cf1NRUys7OpubmZmpra6OcnBzSarX0008/BT1GjY2NBIAefPBBam9vV+u52o8//kj5+fkEQK29u7ub3G43ERGVl5dTfX09tbe3U0dHB9XW1pKiKFRcXKzO0d/fT3fddRclJib6zUFE5PV6ac2aNaTX6+mFF16gTz/9lN544w1KTk6mpUuX0oULF4L2MZsiOgROp5PuvvtuAkAASKfT0Z133knV1dX0119/qeMGBgYIAJWWlvpt39PTQwBo586d6rJQQ0AU/J7g6hA0NDQQAGpubvYbV1NTQwDo2LFjfvsxmUz0559/qst+/fVX0mg0VF1dPdnhISKisbEx2rJlC2k0GgJAkiRRZmYmlZeXB9Q51XsCr9dLHo+HDh8+TFFRUTQyMqKum+yeoKmpiQDQe++957e8r6+PANCBAweuud/ZEtGXQwaDAV988QX6+vrw8ssvY926dTh58iQqKythsVjgdDoBAJ2dnQCunPLHy87ORmZmJj777LMbXTo6Ojqg1+uRn5/vt9xX49U13XfffbjpppvUn00mE4xGI4aGhoLuR5IkNDQ04Oeff8aBAwdQXFwMj8eD2tpa3Hbbbfj888+nVO8333yDRx55BAaDAVFRUdDpdCgsLITX68XJkyevuX1rayvmzZuHvLw8XL58WX0sX74ciYmJ6mVjJIroG2OfrKwsZGVlAQA8Hg+ee+451NbWwmazwWazweVyAQAWLFgQsG1SUtI1X0jXg8vlQmJiot81MwAYjUZotVq1Zh+DwRAwR0xMDEZHR6e0P7PZjGeeeUb9ubm5GRs3bkRFRQV6e3uDbjs8PIx77rkH6enp2L9/P1JTUyHLMnp7e1FWVjalGn777TecPXsW0dHRE673vWFFojkRgvF0Oh12796N2tpafPfddwD+fQGdPn0aCxcu9Bv/yy+/QFGUSeeTZRkAAm5Wr36RTpfBYEBPTw+IyC8Iv//+Oy5fvhy0pnB47LHHUF1drR6jYI4ePYq///4bLS0tMJvN6vITJ05MeX+KosBgMKC9vX3C9ePPcpEmoi+HTp8+PeHygYEBAFfe5QFg5cqVAIDGxka/cX19fRgYGMCqVasm3YfJZIIsy/j222/9ln/wwQcBY2NiYgBgSu+Mq1atwvnz53H06FG/5YcPH1bXh8Nkx+j8+fNwOBzqMQImr98XUt96ACAiHDx4MGDeyc5ODz/8MFwuF7xer3rmHv9IT0+ffnM3SESfCVavXo2FCxciLy8PGRkZGBsbw4kTJ/DKK68gPj4e27dvBwCkp6dj8+bNeO2116DRaLB27VrY7Xbs2rULixYtQnl5+aT7kCQJBQUFePPNN7F48WJYrVb09vbiyJEjAWMtFgsAYP/+/SgqKoJOp0N6evqE73KFhYWoq6tDUVER7HY7LBYLvvzyS7z00kvIzc3F/fffH5ZjtGfPHnz11Vd4/PHHsXz5csTGxmJwcBCvv/46XC4X9u7dG1B/TU0N1q5di6ioKCxbtgwPPPAAoqOjsXHjRjz77LNwu92or6/HH3/8MeExaGlpQX19PW6//XZoNBpkZWVhw4YNeOedd5Cbm4vt27cjOzsbOp0Op06dQmdnJ9atW4f169eHpeewm+0782DeffddeuKJJ+jWW2+l+Ph40ul0lJKSQk8++SR9//33fmO9Xi/V1NTQkiVLSKfTkaIoVFBQQA6Hw2/cRL8xPnfuHJWUlJDJZCK9Xk95eXlkt9sDPh0iIqqsrKSkpCT105jOzk4iCvx0iIjI5XLR008/TQsWLCCtVktms5kqKyvVjyV9AFBZWVlA/2azmYqKioIeo+PHj1NZWRlZrVaaP38+RUVFUUJCAq1Zs4ba2tr8xl68eJFKSkooISGBJEny+6Trww8/JKvVSrIsU3JyMlVUVNDHH3/s1yMR0cjICOXn59O8efPUOXw8Hg/t27dPnSc+Pp4yMjJoy5Yt9MMPPwTtYzZJRPzXJpjYIvqegLEbgUPAhMchYMLjEDDhcQiY8DgETHgcAiY8DgETHoeACY9DwITHIWDC4xAw4XEImPDC8n2C4eHhiP763NUURUFKSsq0t5tLfYbaIyBOn6qZ/lvsoaEhipNl9S9CzIVHnCzT0NDQtPuUY+dOn3Ls9HtU+5TjZr3+Kfcpx4XU53gzPhM4nU5ccLvRCCBzppPdAAMACtxuOJ3Oab2DOJ1OuEfdwH8BXN+vB8+cE3C3TL9H4J8+3ReAOfGMDsDtLgipz/HC9vXKTAD/CddkkUwBkHTNUf8HhHlG+caYMQ4BEx6HgAmPQ8CExyFgwuMQMOFxCJjwOARMeBwCJjwOARMeh4AJj0PAhMchYMLjEDDhcQiY8DgETHgcAiY8DgETHoeACY9DwITHIWDC4xAw4XEImPA4BEx4HAImPA4BEx6HgAmPQ8CExyFgwuMQMOFxCJjwOARMeBwCJjwOARMeh4AJj0PAhMchYMLjEDDhcQiY8DgETHhh+8+8B8I10XU24zqd4ajiOgtLjXPhGQ1PjTMOgaIoiJNlFLjd4ajnhoiTZSiKMq1tFEWBHCvD3TI3+pRjp98j8E+fchzc7oLrUFX4yXJcSH2OJxERzbSQ4eFhOJ1z4S3yCkVRkJKSMu3t5lKfofYIiNOnT1hCwNhcxjfGTHgcAiY8DgETHoeACY9DwITHIWDC4xAw4XEImPA4BEx4HAImPA4BEx6HgAmPQ8CExyFgwvsf/bv3oRMrpyIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot initial state\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "# plot solution state  \n",
    "plot_state_squares(solution_state, \"Solution State\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that moving the puzzle one step to the right places the blue square in the correct position. After that, it is just a matter of switching the first 2 square (function ```s```). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Does second_move == solution_state?  True\n"
     ]
    }
   ],
   "source": [
    "# plot initial state\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "\n",
    "first_move = [initial_state[i] for i in r]\n",
    "plot_state_squares(first_move, \"After RIGHT move\")\n",
    "\n",
    "second_move = [first_move[i] for i in s]\n",
    "plot_state_squares(second_move, \"After SWAP move\")\n",
    "\n",
    "plot_state_squares(solution_state, \"Solution State\")\n",
    "\n",
    "print(\"Does second_move == solution_state? \", second_move == solution_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I understand how a game state and a moves dictionary can be used to transition game states. I was a little confused about converting the state from a ```list``` to an ```np.array```. \n",
    "\n",
    "But it does simplify the transition because you can just input the array from the move dictionary to transition the state, i.e. ```initial_state_np[r]```. So this now makes some sense to me.\n",
    "\n",
    "This simplifies the syntax for state transitions, and transitions can be performed in sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial_state = ['B' 'G' 'R']\n",
      "initial_state[r] = ['G' 'R' 'B']\n",
      "initial_state[r][r] = ['R' 'B' 'G']\n",
      "initial_state[r][s] = ['R' 'G' 'B']\n",
      "Does two_moves == solution_state? True\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# convert initial_state to an np.array\n",
    "initial_state_np = np.array(initial_state)\n",
    "solution_state_np = np.array(solution_state)\n",
    "\n",
    "# reiterating the moves dictionary\n",
    "moves = {\n",
    "    'r': [1, 2, 0],\n",
    "    's': [1, 0, 2],\n",
    "}\n",
    "r = moves['r']\n",
    "s = moves['s']\n",
    "\n",
    "print(f\"initial_state = {initial_state_np}\")\n",
    "\n",
    "# apply 1 r move to initial state\n",
    "print(f\"initial_state[r] = {initial_state_np[r]}\")\n",
    "\n",
    "# apply 2 r moves to initial state\n",
    "print(f\"initial_state[r][r] = {initial_state_np[r][r]}\")\n",
    "\n",
    "# apply 1 r move followed by 1 s move to initial state\n",
    "two_moves = initial_state_np[r][s]\n",
    "print(f\"initial_state[r][s] = {two_moves}\")\n",
    "\n",
    "# check if two_moves is the same as solution_state for all positions\n",
    "result = (two_moves == solution_state_np).all()\n",
    "\n",
    "print(f\"Does two_moves == solution_state? {(two_moves == solution_state).all()}\")\n",
    "\n",
    "plot_state_squares(initial_state_np, \"Initial State\")\n",
    "plot_state_squares(initial_state_np[r], \"After RIGHT move\")\n",
    "plot_state_squares(initial_state_np[r][s], \"After RIGHT and SWAP moves\")\n",
    "plot_state_squares(solution_state, \"Solution State\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm still grappling with the concept of permutation arrays. While I can follow the logic when I'm actively working with them, it's challenging to keep a clear understanding in my mind.\n",
    "\n",
    "- **Permutation Array**: In a permutation array, each element specifies the new position of the element at that index. For example, consider `r = [1, 2, 0]`:\n",
    "    - Here, `r[0] = 1` implies that the first element in the transformed state takes its value from the second element in the initial state (since indexing starts at 0). So, if `initial_state[1]` is 'G', then `transformed_state[0]` will be 'G'.\n",
    "    - This concept is somewhat clear to me, but it still feels a bit perplexing at times.\n",
    "\n",
    "- **Inverse Permutation Array**: Applying `np.argsort(r)` to a permutation array `r` returns the indices that would sort the array. When used on a permutation array, `np.argsort(r)` yields the inverse permutation. This inverse indicates the final positions of the elements from the original array in their sorted order. \n",
    "\n",
    "I'm getting a grasp of these ideas, but I can't say I've fully internalized them just yet. 🤯😓\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 0, 2]\n",
      "[1, 0, 2]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_inv = np.argsort(r).tolist()\n",
    "s_inv = np.argsort(s).tolist()\n",
    "\n",
    "# there is no inverse for the swap move\n",
    "print(s)\n",
    "print(s_inv)\n",
    "\n",
    "plot_state_squares(initial_state_np, \"Initial State\")\n",
    "plot_state_squares(initial_state_np[r], \"After RIGHT move\")\n",
    "plot_state_squares(initial_state_np[r_inv], \"After RIGHT Inverse move (AKA LEFT move)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring SymPy and Permutations in Puzzle Solving\n",
    "\n",
    "- **Discovering SymPy**: The example notebook introduced the SymPy library, and it's quite fascinating. It specializes in symbolic computation, handling mathematical expressions as symbols rather than through numerical approximations. It's like translating emojis in math: 😀 + 🔥 equals 🥵! The library covers a broad spectrum, including algebra, calculus, discrete math, geometry, plotting, and even code generation. It's definitely on my list for deeper exploration.\n",
    "\n",
    "- **The `Permutation` Function**: The `Permutation` function in `sympy.combinatorics` seems helpful for solving these puzzles, where permutation operations are more intuitively expressed and computed using a specialized class.\n",
    "\n",
    "- **Applicability for Puzzles**: While the `Permutation` class might be excessive for simpler puzzles, it seems highly promising for tackling more complex challenges in my upcoming puzzle-solving endeavors.\n",
    "\n",
    "- **Understanding Disjoint Cycle Form**: The concept of \"disjoint cycle form\" in permutations is still a bit of a puzzle to me 🤔. From what I gather, it involves breaking down a sequence of moves into cycles that are independent of each other, streamlining the process of understanding and executing these moves.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r: (0 1 2) \tSends 0 -> 1, 1 -> 2, and 2 -> 0.\n",
      "s: (2)(0 1) \tSends 0 -> 1, 1 -> 0, and 2 stays fixed.\n",
      "Effect of r: ['G', 'R', 'B']\n",
      "Effect of s: ['G', 'B', 'R']\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# reminder about the import call\n",
    "from sympy.combinatorics import Permutation\n",
    "\n",
    "# this is from the tutorial\n",
    "rp = Permutation(r)\n",
    "sp = Permutation(s)\n",
    "print('r:', rp, \"\\tSends 0 -> 1, 1 -> 2, and 2 -> 0.\")\n",
    "print('s:', sp, \"\\tSends 0 -> 1, 1 -> 0, and 2 stays fixed.\" )\n",
    "\n",
    "# A Permutation is a function which you can apply to a state with a function call\n",
    "print(\"Effect of r:\", rp(initial_state))\n",
    "print(\"Effect of s:\", sp(initial_state))\n",
    "\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "plot_state_squares(rp(initial_state), \"After RIGHT move using Permutation\")\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "plot_state_squares(sp(initial_state), \"After SWAP move using Permutation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Progress and Challenges with Understanding Permutations\n",
    "\n",
    "- **Current Understanding**: So far, I'm making progress (sort of) with understanding permutations. While there's more to learn, I'm able to follow along for the most part. \n",
    "\n",
    "- **Struggling with Inverse Permutations**: I'm encountering some difficulty in grasping why the inverse of a permutation is represented as the negative power of the function, like `rp_inv = rp ** -1`. \n",
    "\n",
    "    - **Permutation Function Basics**: A permutation function maps a set of elements to itself but in a different order. The inverse of this permutation effectively undoes this mapping, bringing the elements back to their original order.\n",
    "\n",
    "    - **Inverse Operations in SymPy**: In SymPy, the `Permutation` class facilitates inverse operations using the negative power notation. This approach is rooted in group theory in mathematics, where raising an element to a negative power is equivalent to finding its inverse in the group context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 225x75 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rp_inv = rp**-1\n",
    "sp_inv = sp**-1\n",
    "\n",
    "plot_state_squares(initial_state, \"Initial State\")\n",
    "next_state = rp(initial_state)\n",
    "plot_state_squares(next_state, \"After RIGHT move using Permutation\")\n",
    "return_state = rp_inv(next_state)\n",
    "plot_state_squares(return_state, \"After RIGHT Inverse move using Permutation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring the 6x6 Wreath Puzzle\n",
    "\n",
    "### Initial Steps\n",
    "\n",
    "I'm now turning my attention to the **6x6 Wreath Puzzle**, as it appears to be one of the more approachable challenges. My initial focus will be on two key aspects:\n",
    "\n",
    "1. **Loading Puzzles**: Understanding how to import or load puzzles into my working environment. This is the first step in interacting with the puzzle data.\n",
    "\n",
    "2. **Loading Available Moves**: Figuring out how to access and comprehend the set of possible moves. This is crucial for devising strategies to solve the puzzle.\n",
    "\n",
    "### Visualization and Strategy Development\n",
    "\n",
    "- Once the puzzles and moves are loaded, the next step will be to explore ways to **visualize the wreath puzzle**. Visualization is a powerful tool to keep track of the moves and to understand the state of the puzzle at any given moment.\n",
    "\n",
    "- Additionally, visualization will aid in **evaluating the distance to the solution**. By having a clear picture of the puzzle's current state, I can better assess how close I am to solving it and adjust my strategies accordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "# local data_dir\n",
    "data_dir = Path(\"data\")\n",
    "\n",
    "puzzle_info = pd.read_csv(data_dir / 'puzzle_info.csv', index_col='puzzle_type')\n",
    "# Parse allowed_moves\n",
    "puzzle_info['allowed_moves'] = puzzle_info['allowed_moves'].apply(literal_eval)\n",
    "\n",
    "puzzles_all = pd.read_csv(data_dir / 'puzzles.csv', index_col='id')\n",
    "# Parse color states\n",
    "puzzles_all = puzzles_all.assign(\n",
    "    initial_state=lambda df: df['initial_state'].str.split(';'),\n",
    "    solution_state=lambda df: df['solution_state'].str.split(';')\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['l', 'r']\n"
     ]
    }
   ],
   "source": [
    "wreath_6_6_info = puzzle_info.loc['wreath_6/6', 'allowed_moves']\n",
    "# convert keys from wreath_6_6_info to a list\n",
    "wreath_6_6_moves = list(wreath_6_6_info.keys())\n",
    "print(wreath_6_6_moves)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'l': [1, 2, 3, 4, 5, 0, 6, 7, 8, 9], 'r': [6, 1, 8, 3, 4, 5, 7, 2, 9, 0]}\n",
      "    puzzle_type                  solution_state  \\\n",
      "id                                                \n",
      "284  wreath_6/6  [C, A, C, A, A, A, B, B, B, B]   \n",
      "285  wreath_6/6  [C, A, C, A, A, A, B, B, B, B]   \n",
      "286  wreath_6/6  [C, A, C, A, A, A, B, B, B, B]   \n",
      "287  wreath_6/6  [C, A, C, A, A, A, B, B, B, B]   \n",
      "288  wreath_6/6  [C, A, C, A, A, A, B, B, B, B]   \n",
      "\n",
      "                      initial_state  num_wildcards  \n",
      "id                                                  \n",
      "284  [A, A, A, A, B, C, B, C, B, B]              0  \n",
      "285  [B, A, B, A, B, A, C, A, B, C]              2  \n",
      "286  [A, B, C, A, A, C, B, B, B, A]              2  \n",
      "287  [B, C, B, C, A, A, B, A, B, A]              2  \n",
      "288  [A, A, C, B, C, A, B, B, A, B]              0  \n"
     ]
    }
   ],
   "source": [
    "# Extracting info for 'wreath_6/6' puzzles\n",
    "wreath_6_6_moves_dict = puzzle_info.loc['wreath_6/6', 'allowed_moves']\n",
    "moves = list(wreath_6_6_moves_dict.keys())\n",
    "\n",
    "wreath_6_6_puzzles = puzzles_all[puzzles_all['puzzle_type'] == 'wreath_6/6']\n",
    "# get a list of loc indices for wreath_6/6 puzzles\n",
    "wreath_6_6_idx = wreath_6_6_puzzles.index.tolist()\n",
    "\n",
    "\n",
    "\n",
    "# Now you can access the allowed moves for 'wreath_6/6' using the dictionary\n",
    "# For example:\n",
    "print(allowed_moves_dict['wreath_6/6'])\n",
    "\n",
    "# And you have the wreath_6_6_puzzles DataFrame containing all puzzles of this type\n",
    "print(wreath_6_6_puzzles.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenges in Visualizing the Puzzle\n",
    "\n",
    "### Current Approach\n",
    "\n",
    "The current code is designed to visualize the puzzle as two rings (left and right), each with the capability of independent rotation, and sharing two common points. This model attempts to reflect the mechanics of the puzzle's movement.\n",
    "\n",
    "### Issues Encountered\n",
    "\n",
    "However, upon closer examination of the permutations `l` and `r`, several discrepancies have emerged:\n",
    "\n",
    "- **L-Permutation Complexity**:\n",
    "  - The `l-permutation` seems to only affect the early elements in the puzzle. This observation suggests a simpler pattern of movement than initially thought.\n",
    "\n",
    "- **R-Permutation Complexity**:\n",
    "  - Conversely, the `r-permutation` appears to induce more complex changes. These changes aren't adequately represented by the current model of two independently rotating rings with two shared points.\n",
    "\n",
    "### Next Steps\n",
    "\n",
    "- At this point, the path forward for the visualization is unclear. The simplistic model does not capture the intricacies revealed by the permutations.\n",
    "- A deeper analysis or a different approach to modeling might be necessary to develop a more accurate visualization of the puzzle dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial State:\n",
      "   A   A      C   B\n",
      "A         C          B\n",
      "     l          r\n",
      "B         B          A\n",
      "   C   B     C  B\n",
      "---------------------------------------------\n",
      "Solution State:\n",
      "   A   C      B   B\n",
      "C         A          B\n",
      "     l          r\n",
      "A         B          A\n",
      "   A   B     B  B\n"
     ]
    }
   ],
   "source": [
    "def print_wreath_puzzle(state):\n",
    "    \"\"\"\n",
    "    Print a text-based visualization of the wreath_6/6 puzzle.\n",
    "\n",
    "    :param state: List representing the state of each point on the wreath puzzle (10 elements).\n",
    "    \"\"\"\n",
    "    # Ensuring the state has 10 elements\n",
    "    if len(state) != 10:\n",
    "        raise ValueError(\"State must have 10 elements.\")\n",
    "\n",
    "    # Constructing the layout\n",
    "    # Note: Points at index 5 and 6 are the common points between the two rings\n",
    "\"\"\"     layout = [\n",
    "        f\"   {state[1]}   {state[2]}      {state[7]}   {state[8]}\",\n",
    "        f\"{state[0]}         {state[5]}          {state[9]}\",\n",
    "        \"     l          r\",\n",
    "        f\"{state[4]}         {state[6]}          {state[3]}\",\n",
    "        f\"   {state[5]}   {state[6]}     {state[7]}  {state[8]}\"\n",
    "    ] \"\"\"\n",
    "\n",
    "    layout = [\n",
    "        f\"         {state[4]}      {state[7]}   {state[8]}\",\n",
    "        f\"{state[3]}         {state[5]}          {state[9]}\",\n",
    "        \"     l          r\",\n",
    "        f\"{state[2]}         {state[6]}          {state[3]}\",\n",
    "        f\"   {state[0]}   {state[6]}     {state[7]}  {state[8]}\"\n",
    "    ]\n",
    "\n",
    "    # Printing the layout\n",
    "    for line in layout:\n",
    "        print(line)\n",
    "\n",
    "# get first puzzle index\n",
    "idx = wreath_6_6_idx[0]\n",
    "puzzle_initial = wreath_6_6_puzzles.loc[idx, 'initial_state']\n",
    "puzzle_solution = wreath_6_6_puzzles.loc[idx, 'solution_state']\n",
    "\n",
    "print(\"Initial State:\")\n",
    "print_wreath_puzzle(puzzle_initial)\n",
    "print(f\"{'-'*45}\\nSolution State:\")\n",
    "print_wreath_puzzle(puzzle_solution)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial State list:\n",
      "['A', 'A', 'A', 'A', 'B', 'C', 'B', 'C', 'B', 'B']\n",
      "---------------------------------------------\n",
      "Initial State:\n",
      "   A   A      C   B\n",
      "A         C          B\n",
      "     l          r\n",
      "B         B          A\n",
      "   C   B     C  B\n",
      "---------------------------------------------\n",
      "After l move:\n",
      "['A', 'A', 'A', 'B', 'C', 'A', 'B', 'C', 'B', 'B']\n",
      "---------------------------------------------\n",
      "   A   A      C   B\n",
      "A         A          B\n",
      "     l          r\n",
      "C         B          B\n",
      "   A   B     C  B\n"
     ]
    }
   ],
   "source": [
    "# start turning the puzzle with a call to l\n",
    "puzzle_state = puzzle_initial.copy()\n",
    "l = Permutation(wreath_6_6_moves_dict['l'])\n",
    "r = Permutation(wreath_6_6_moves_dict['r'])\n",
    "\n",
    "print('Initial State list:')\n",
    "print(puzzle_state)\n",
    "print(f\"{'-'*45}\")\n",
    "print(\"Initial State:\")\n",
    "print_wreath_puzzle(puzzle_state)\n",
    "print(f\"{'-'*45}\")\n",
    "puzzle_state = l(puzzle_state)\n",
    "print(\"After l move:\")\n",
    "print(puzzle_state)\n",
    "print(f\"{'-'*45}\")\n",
    "print_wreath_puzzle(puzzle_state)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reassessing the Approach to the Wreath Puzzle\n",
    "\n",
    "### Decision on Visualization\n",
    "\n",
    "After considering the challenges and complexities mentioned earlier, I have decided to **abandon the attempt to create a visualization** for the wreath puzzle. The intricacies involved in accurately representing the puzzle's movements exceed the capabilities of the simplistic model initially proposed.\n",
    "\n",
    "### Exploring Heuristic Approaches for Solving the Puzzle\n",
    "\n",
    "In lieu of visualization, my focus shifts toward identifying an effective heuristic method for solving the puzzle:\n",
    "\n",
    "- **Potential Search Algorithms**:\n",
    "  - Preliminary research suggests that algorithms like **A\\* (A-Star)** or **Greedy Best-First Search** might be suitable starting points.\n",
    "\n",
    "- **Considering Heuristic Options**:\n",
    "  - Two heuristic approaches under consideration are the **Hamming distance** and the **Manhattan distance**.\n",
    "  - **Hamming Distance**: This method involves counting the number of positions in which the current state differs from the solution state. It's seemingly the more straightforward approach.\n",
    "  - **Manhattan Distance**: Calculating the Manhattan distance appears to be more challenging and potentially less feasible for this specific problem.\n",
    "\n",
    "### Moving Forward\n",
    "\n",
    "The next steps will involve a deeper exploration into these heuristic methods, assessing their suitability and efficacy in tackling the wreath puzzle's complexities.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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