example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Roma Solver - Experimentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from roma import RomaPuzzle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Roma Puzzle Instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example usage\n",
    "n = 4\n",
    "roma_cell = (1, 1)\n",
    "arrows = {(0, 0): '↓', (0, 1): '→', (1, 3): '↑', (3, 1): '←', (3, 2): '↑', (3, 3): '↑'}\n",
    "boxes = {\n",
    "    (0, 0): 1, (1, 0): 2, (2, 0): 2, (3, 0): 2,\n",
    "    (0, 1): 3, (0, 2): 3, (1, 2): 3, (2, 2): 3,\n",
    "    (0, 3): 4, (1, 3): 4, (2, 3): 5, (3, 3): 5,\n",
    "    (3, 2): 6, (3, 1): 6, (2, 1): 6, (1, 1): 7\n",
    "}\n",
    "\n",
    "# Create the puzzle\n",
    "puzzle = RomaPuzzle(n, roma_cell, arrows, boxes)\n",
    "puzzle.display_board()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "# Retrieve adjacency matrix\n",
    "adj_matrix = puzzle.adjacency_matrix()\n",
    "print(np.array(adj_matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display graph\n",
    "puzzle.display_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "puzzle.is_solved()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instance solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "puzzle.update_arrows({(0, 2): '↓', (1, 2): '←', (2, 2): '↑', (2, 3): '←', (0, 3): '←', (3, 0): '↑', (2, 0): '→', (1, 0): '↓', (2, 1): '→'})\n",
    "puzzle.display_board()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "puzzle.display_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "puzzle.is_solved()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Search Tree Algorithm for Roma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example usage\n",
    "n = 4\n",
    "roma_cell = (1, 1)\n",
    "arrows = {(0, 0): '↓', (0, 1): '→', (1, 3): '↑', (3, 1): '←', (3, 2): '↑', (3, 3): '↑'}\n",
    "boxes = {\n",
    "    (0, 0): 1, (1, 0): 2, (2, 0): 2, (3, 0): 2,\n",
    "    (0, 1): 3, (0, 2): 3, (1, 2): 3, (2, 2): 3,\n",
    "    (0, 3): 4, (1, 3): 4, (2, 3): 5, (3, 3): 5,\n",
    "    (3, 2): 6, (3, 1): 6, (2, 1): 6, (1, 1): 7\n",
    "}\n",
    "\n",
    "# Create the puzzle\n",
    "puzzle = RomaPuzzle(n, roma_cell, arrows, boxes)\n",
    "puzzle.display_board()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No solution found.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "puzzle.solve_puzzle()\n",
    "puzzle.display_board()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "myenv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}