{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unattacked Queens\n",
    "===\n",
    "The properties of chess pieces play a part in many challenges, including in a group of problems about unattacked queens. Imagine three white queens and five black queens on a 5 × 5 chessboard. Can you arrange them so that no queen of one color can attack a queen of the other color? There is only one solution, excluding reflections and rotations.\n",
    "http://www.scientificamerican.com/article/martin-gardner-fans-try-these-mathematical-games/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcdfdd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.table import Table\n",
    "from copy import deepcopy\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb38b6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "min_val, max_val, diff = 0., 10., 1.\n",
    "\n",
    "#imshow portion\n",
    "N_points = (max_val - min_val) / diff\n",
    "imshow_data = np.random.rand(N_points, N_points)\n",
    "ax.imshow(imshow_data, interpolation='nearest')\n",
    "\n",
    "#text portion\n",
    "ind_array = np.arange(min_val, max_val, diff)\n",
    "x, y = np.meshgrid(ind_array, ind_array)\n",
    "\n",
    "for x_val, y_val in zip(x.flatten(), y.flatten()):\n",
    "    c = 'x' if (x_val + y_val)%2 else 'o'\n",
    "    ax.text(x_val, y_val, c, va='center', ha='center')\n",
    "\n",
    "#set tick marks for grid\n",
    "ax.set_xticks(np.arange(min_val-diff/2, max_val-diff/2))\n",
    "ax.set_yticks(np.arange(min_val-diff/2, max_val-diff/2))\n",
    "ax.set_xticklabels([])\n",
    "ax.set_yticklabels([])\n",
    "ax.set_xlim(min_val-diff/2, max_val-diff/2)\n",
    "ax.set_ylim(min_val-diff/2, max_val-diff/2)\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcf3e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5\n",
    "#board = [[(i*N+j)%2 for j in range(N)] for i in range(N)]\n",
    "board = [[0 for j in range(N)] for i in range(N)]\n",
    "temp_board = deepcopy(board)\n",
    "plt.matshow(board, interpolation='nearest', cmap=plt.get_cmap(\"gray\"))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def addQueen(board, pos, val=-2):\n",
    "    x, y = pos\n",
    "    board[x][y] = val\n",
    "    val = (abs(val)+1)*val/abs(val)\n",
    "    for i in range(1,N):\n",
    "        board[(x+i)%N][y] = val\n",
    "        board[x][(y+i)%N] = val\n",
    "        for j in [1, -1]:\n",
    "            for k in [1,-1]:\n",
    "                if (x+i*j) >= 0 and (x+i*j) < N and (y+i*k) >= 0 and (y+i*k) < N:\n",
    "                    board[(x+i*j)][(y+i*k)] = val\n",
    "    plt.matshow(board, interpolation='nearest', cmap=plt.get_cmap(\"Set3\"), vmin=-3,vmax=3)\n",
    "    plt.grid()\n",
    "    plt.show()\n",
    "    return board"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0xda3d748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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       "+qCZ3SLp1+4+Z2bb3+7zdt91j65av1aStGLVSq3fMnv+7qKDvW6b7c3brlvUv3+77QOv//7OnIM9\n",
       "VortG65fl3S9EtuD9+Vaf7C3GtylM9X2QK71a82764E59Y4saGbTao0y8uSZmX1T0mckvSlphaTV\n",
       "kn7o7p8d+hxOnuGSOHmWX6uTZ+7+dXff6O7vkXSbpD3DQ50bHTu/iJnp2M0mvY7NWXEgAJ4rjmw4\n",
       "FM+P54oDS0jVg03Hzi9iZjp2s6oHG0A7dGxkQ8fOj44NLCFVDzYdO7+ImenYzaoebADt0LGRDR07\n",
       "Pzo2sIRUPdh07PwiZqZjN6t6sAG0Q8dGNnTs/OjYwBJS9WDTsfOLmJmO3azqwT717PGuI0zk2PGX\n",
       "uo4wsYiZe/MLXUeYSBd5qx7s1199resIE3n1tf/rOsLEImb+7Sv/23WEiXSRt+rBBtBO1YP98qkX\n",
       "uo4wkVOnX+06wsQiZn7ul690HWEiXeRNcrkrURYALVzqcteiBxtAfao+FAfQDoMNTCEGG5hCDDYw\n",
       "hRhsYAr9PzeUeki2MQMZAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xda3d4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[[-2, 3, -3, -3, 3],\n",
       " [-3, -3, 3, 0, 3],\n",
       " [-3, 0, -3, 3, 3],\n",
       " [3, 3, 3, 3, 2],\n",
       " [-3, 0, 0, 3, 3]]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "board = deepcopy(temp_board)\n",
    "addQueen(board, (0,0))\n",
    "addQueen(board, (N-2,N-1), val = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0xd2f6b00>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
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       "+kTSS5Lu7nuWBr29DfUyhv2GpNtt77O9R9L9kl7seaY43nz3uSckbVTV7/qep4ntm2x/aXL7Bknf\n",
       "l3Sy36mmq6pfV9VqVX1Z0k8lvVJVP+/i7166sKvqvKSHJB3T5pXEP1fVqX6nms72EUmvS7rD9mnb\n",
       "D/Y9UwvflvQzbV5dPjn5s8xX9m+R9MrkOfYJSUer6uWeZ9qqzp5m8l9KgUBLt2MDmB1hA4EIGwhE\n",
       "2EAgwgYCETYQiLCBQIQNBPofgHpWOr1agY4AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd2fe320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(temp_board, interpolation='nearest', cmap=plt.get_cmap(\"gray\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}