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QuantumnQueenProblem.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0ad2e6ba-25c6-4046-9383-aa0a97c61d4d",
+   "metadata": {},
+   "source": [
+    "# Quantum Game Theory - 8 Queen Problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "df808299-0a82-47ce-8d26-dcbd7dffd5cf",
+   "metadata": {},
+   "source": [
+    "The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques.\n",
+    "\n",
+    "The eight queens puzzle is a special case of the more general n queens problem of placing n non-attacking queens on an n×n chessboard. Solutions exist for all natural numbers n with the exception of n = 2 and n = 3. Although the exact number of solutions is only known for n ≤ 27, the asymptotic growth rate of the number of solutions is approximately (0.143 n)n. \n",
+    "\n",
+    "Chess composer Max Bezzel published the eight queens puzzle in 1848. Franz Nauck published the first solutions in 1850. Nauck also extended the puzzle to the n queens problem, with n queens on a chessboard of n×n squares\n",
+    "\n",
+    "https://en.wikipedia.org/wiki/Eight_queens_puzzle"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76c16453-0a46-4d2b-b969-c2d387a913d1",
+   "metadata": {},
+   "source": [
+    "Coded by Y3TI & Sam Rahmeh"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c6e19829-aecc-40f4-8cdc-5ad52734638c",
+   "metadata": {},
+   "source": [
+    "### Import Libraries"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "d5a90bf0-b803-459e-b582-fd5cd3120669",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (2050042617.py, line 1)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  Cell \u001b[0;32mIn[3], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m    from 'nqueen/util.py' import constraint, displayBoard\u001b[0m\n\u001b[0m         ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+     ]
+    }
+   ],
+   "source": [
+    "from util import constraint, displayBoard\n",
+    "from sympy import *\n",
+    "from IPython.display import display\n",
+    "import dimod\n",
+    "import dynex\n",
+    "from util import constraint, displayBoard\n",
+    "import matplotlib.pyplot as plt\n",
+    "import matplotlib.colors as mcolors\n",
+    "import numpy as np\n",
+    "import matplotlib.image as mpimg\n",
+    "import matplotlib.offsetbox as offsetbox\n",
+    "init_printing()\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5357a17c-acda-40d8-977b-a46ca4538d47",
+   "metadata": {},
+   "source": [
+    "### Compute on DYNEX"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ed2be420-e965-4b1b-8336-bec94f6fdd42",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def NQueen2BQM(n):\n",
+    "    bqm = dimod.BinaryQuadraticModel('BINARY')\n",
+    "    for row in range(n):\n",
+    "        bqm.add_linear_equality_constraint(\n",
+    "            [(row * n + col, 1.0) for col in range(n)],\n",
+    "            constant=-1.0,\n",
+    "            lagrange_multiplier=n)\n",
+    "    for i in range(n):\n",
+    "        for j in range(n):\n",
+    "            if i < j:\n",
+    "                for k in range(n):\n",
+    "                    bqm.add_interaction(i * n + k, j * n + k, 2 * n)\n",
+    "                    if k + (j - i) < n:\n",
+    "                        bqm.add_interaction(i * n + k, j * n + (k + (j - i)), 2 * n)\n",
+    "                    if k - (j - i) >= 0:\n",
+    "                        bqm.add_interaction(i * n + k, j * n + (k - (j - i)), 2 * n)\n",
+    "    return bqm\n",
+    "\n",
+    "def Visualize(board):\n",
+    "    n = len(board)\n",
+    "    cmap = mcolors.ListedColormap(['#f5ecce', '#614532'])\n",
+    "    img = mpimg.imread('queen.png')\n",
+    "    fig, ax = plt.subplots()\n",
+    "    ax.matshow(np.add.outer(range(n), range(n)) % 2 == 0, cmap=cmap)\n",
+    "    plt.axis(\"off\")  \n",
+    "    ax_width = ax.get_window_extent().width / ax.figure.dpi * fig.dpi\n",
+    "    ax_height = ax.get_window_extent().height / ax.figure.dpi * fig.dpi\n",
+    "    cell_size = min(ax_width, ax_height) / n\n",
+    "    img_height, img_width = img.shape[:2]\n",
+    "    scale_width = cell_size / img_width\n",
+    "    scale_height = cell_size / img_height\n",
+    "    scale = min(scale_width, scale_height)\n",
+    "    for r in range(n):\n",
+    "        for c in range(n):\n",
+    "            if board[r][c] == 'Q':\n",
+    "                box = offsetbox.OffsetImage(img, zoom=scale)\n",
+    "                ab = offsetbox.AnnotationBbox(box, (c, r), frameon=False)\n",
+    "                ax.add_artist(ab)\n",
+    "    scale_factor = 1.1  \n",
+    "    fig.set_size_inches(n * scale_factor, n * scale_factor)\n",
+    "    plt.show()\n",
+    "    return fig\n",
+    "\n",
+    "def SolveNQueens(n):\n",
+    "    bqm = NQueen2BQM(n)\n",
+    "    model = dynex.BQM(bqm)\n",
+    "    sampler = dynex.DynexSampler(model, mainnet=False, description='Quantum 8 Queen Problem')\n",
+    "    sampleset = sampler.sample(num_reads=10000, annealing_time=500, debugging=False, alpha=10, beta=1)\n",
+    "    solution = sampleset.first.sample\n",
+    "    board = [['.' for _ in range(n)] for _ in range(n)]\n",
+    "    for i in range(n):\n",
+    "        for j in range(n):\n",
+    "            if solution[i * n + j] == 1:\n",
+    "                board[i][j] = 'Q'\n",
+    "    Visualize(board)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c2724afe-c279-4643-8954-a1d25750cd05",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print(\"[DYNEX] 8 Queen Problem Solver\")\n",
+    "n = 8\n",
+    "SolveNQueens(n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "341db188-999b-4262-b8e3-70177e5efe89",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}