2018_03_ItsSymmetric.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "Oq1xibzMT1Wl"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import requests\n",
    "from bs4 import BeautifulSoup\n",
    "import itertools\n",
    "from copy import deepcopy as dcopy,copy\n",
    "from IPython.display import Markdown, display\n",
    "\n",
    "from z3 import *\n",
    "import grilops\n",
    "import grilops.regions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "ICTfvjZUT1Wr"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### It’s Symmetric!\n",
       "The grid below can be partitioned into several regions, each of which is\n",
       "symmetric in some way (be it rotation or reflection). A cell with a number\n",
       "indicates the length of the shortest walk, within that region, to an “opposite”\n",
       "cell in the region. (I.e., a cell that could potentially be moved to the\n",
       "location of the numbered cell under a non-trivial rotation or reflection of the\n",
       "plane.)\n",
       "(A few examples: In a 1-by-N region, all cells could be labeled 0, since a\n",
       "reflection across the longer mid-line takes every cell to itself. In the\n",
       "“S”-shaped Tetris piece, the cells could be labeled 3, 1, 1, 3.)\n",
       "The answer to this puzzle is the\n",
       "sum of the cubes of the areas"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Back to the first problem. Redoing withh Z3\n",
    "url='https://www.janestreet.com/puzzles/it-s-symmetric-index/'\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "y =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "#display([(i,j) for i,j in enumerate(y)])\n",
    "display(Markdown(\"### \"+y[7]+\"\\n\"+\"\\n\".join(y[10:14])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "U9Yh1D3HT1Ws"
   },
   "source": [
    "\n",
    "<img src=\"https://www.janestreet.com/puzzles/20180301_symmetric.png\" width=\"350\" >\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "givens = np.array([[-1, -1, -1, 14, -1, -1, -1,  6, -1, -1, -1],\n",
    "                   [ 3, -1, 21, -1,  4, -1,  0, -1,  4, -1, -1],\n",
    "                   [ 7, -1, -1,  8, -1, 12, -1,  8, -1,  8,  4],\n",
    "                   [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1,  6],\n",
    "                   [ 1,  1, -1,  1, -1, -1, -1,  5, -1, -1, -1],\n",
    "                   [-1,  5, -1, -1, -1,  1, -1, -1, -1,  2, -1],\n",
    "                   [-1, -1, -1,  7, -1, -1, -1,  8, -1, 19, 12],\n",
    "                   [ 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1],\n",
    "                   [ 4,  7, -1,  1, -1,  5, -1, 15, -1, -1,  6],\n",
    "                   [-1, -1,  3, -1,  0, -1,  1, -1,  4, -1,  4],\n",
    "                   [-1, -1, -1,  3, -1, -1, -1,  3, -1, -1, -1]])\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "x = np.array((givens).astype('int').astype('str'))\n",
    "x[x==\"-1\"] =\"\"\n",
    "ax =sns.heatmap(givens!=-1,annot=x,cbar=False,center=3,cmap=\"Greys\",fmt=\"\",linewidths=1,linecolor=\"grey\",annot_kws={\"size\":12})\n",
    "ax.axis(\"off\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "givens=np.array([[-1,-1, 4, 9],\n",
    "                 [-1,-1, 0,-1],\n",
    "                 [-1, 2,-1,-1],\n",
    "                 [ 3, 1,-1,-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3ODs7Y8yYMZJyjUYjEhISoFKpcO3aNVy8eBEtLS3Yvn27oJ7/f5ydneHj44NBgwbhV7/6FTZt2oTz58//zDkklR9++AHLly9Henq60LfElvxIbW1tkv1I1GtA7S2i7j+V10lYgSksLCTbvVjCzs7O4tsZqSxatAinT59GeXk5Zs+eDYPBIPktwOPHj/HgwQMsXrwYcrkcw4cPR0xMDL755htBve4b09tVkXOl1WqxbNkyJCYmCl9zDw8PVFdXm1+3t7fj7t27kv1I1GtA7S2i7n93r1NISAg+//xznD59GlFRUZJyhRSYK1euoKGhgezTo9bWVpSWlkKn00Gv1+PYsWOoqqrqoVZ4FfR6PXQ6XQ/Pkulnt27dQldXF+7fv4/NmzcjLi4Ow4YNk9R/Nzc3KBQK5OfnQ6/Xo7W1FQUFBT2eNYgaw7fffos7d+7AaDTi0aNH+PjjjxEUFPSztx3W5jc0NGDp0qX48MMPsXDhQuH9V6lUqKmpwalTp6DT6ZCdnQ1PT0/JileKNeiNyVvU3NyMlpYWod4i6v4vWLAAxcXF0Gg00Gg0iI2NRXh4OA4ePCgpV4jZUaPRQKVSwcXFRUTcz9Dr9di9ezfu3LkDBwcHTJgwAdnZ2ZgwYYJVeX15lpYuXYq1a9fi3r17cHZ2RnR0NFJSUoSMYe/evdi2bRv2798Pe3t7TJkyBenp6Vbn9TWG8ePHY+fOnXj48CFcXFwwbdo07Ny5U1i+nZ0d7t27h+zs7B5/X3P16lUh+UlJScjKyoJarca6devg6+trVf8tIXoNekPtLaLsP5XXSUiBUavVImL6xM3NDX/729+E5fXnWTp+/LiwdrozceJE5OXlCcvrbwy/+93vSPNXr15Nmj9t2jScPHlSchu9Eb0GvaH2FlH3vzuivE78VQGGYcjgAsMwDBlcYBiGIYMLDMMwZHCBYRiGDC4wDMOQwV4khmEkw14khmFsDnuROJ/XgPOFtGEJ3sEwDEMGFxiGYcjgAsMwDBlcYBiGIYMLDMMwZAgpMI8fP8aqVavg5+cHpVJJcuRBWloaQkND4e/vjzlz5uDIkSNWZ/Xl5Dl27FgPn5Cvry88PT1x/fp1YW1Qe4tu376N6OhoTJ48GZMnT0Z8fLxVB2b3ld/R0YHk5GTMnDkTnp6eQg9fr62tRVxcHAICAqBSqVBcXCws21b+LkCsV8hER0cH0tPToVQqMWnSJMyfP1/4kbEmRLqdhJ0HI5PJUFZWhps3b2LFihXw8vISetr8ihUrsG3bNsjlcvOFOHHiRHh7e79ylsnJYzolz8TcuXMxd+5c8+uvv/4aOTk5+M1vfiOsDROVlZUYNMj66e8rf9SoUdizZw/c3d1hNBpx6NAhrFmz5pWLfn/99/f3R1xcHFJTU63uf2/0ej0SExMRGxuL3NxcVFRUYOXKlSgoKMD48eMl53c/EKu9vR0hISFkJzCK9AqZ0Ov1GDt2LPLy8vDmm2/i3LlzSE1NxfHjx6FQKIS1Y3I77dq1C++//z5++uknSXmSdzDt7e04ffo0UlJS4OzsjMDAQMycOROFhYVSo3tgchUBz8+ZtbOzs9oq8LJOISkaltflLXrjjTegUCjMZxY7ODhYNU995cvlcsTHxyMwMBD29uLeYd+5cweNjY2Ij4+Hg4MDgoOD4e/vL/w6Amj9XaK9QiacnJyQlJQEhUIBe3t7KJVKKBQK3LhxQ2g7ot1Okq+Quro62Nvb9/gt4+XlJVwIBQAZGRnw9fVFZGQkRo4ciRkzZghvw4RWq0VVVRXmzZtHkk/tLQoMDMT777+PrVu3YsWKFcLzRWPpKytdXV2oqakR3haVv4vCK9QXTU1NqKurk3wYenco3E5CdjC9D5QeOnSoEI9NbzIyMsxKTpVKZd7RUKDRaBAYGChcw2Irb1FVVRWqqqqwadMmvPfee8LzRTNhwgS4ubnhwIED6OzsxPnz51FZWSlUXAbQ+rsovEKW6OzsRFpaGqKioiQfht4dCreT5AJjyWPz5MkTyR6bvnBwcEBgYCB+/PFH5Ofnk7QB0GlYbOUtAp6vzcKFC7FhwwY0NzcLzxeJTCZDdnY2zp07h9DQUOTm5iIiIkKoehWg83dReYV6YzQasX79eshkMmzatEloNoXbSfJD3nHjxsFgMKCurg7jxo0D8Nz4J3LrZgmDwSDc7Gji8uXLaGxsxJw5c0jyu0PhLeqO0Wg0q0ZHjBhB0oYovLy88OWXX5pfx8bGCi/yhYWFWL58udBMoKdXCHi+szcYDIiKikJBQYGQNrq6uvDRRx+hqakJ+/fvh0wmE5JrgsLtJGQHo1KpsGfPHrS3t+Py5csoKSkR+uyiubkZRUVFaGtrg8FgQGlpKYqKijB16lSr8vpy8pjQaDSYPXu2JA3L6/IWlZWV4bvvvoPBYMCTJ0/wH//xH3jjjTdeeSvd3xx1dHSYP1nq7OyETqcTUiCrq6uh0+nw9OlTHDx4EI2NjYiOjpaca4LS30XlFerOli1bUFtbi88++8y82xCNaLeTkI+pt2zZgvT0dEybNg2urq7IyMgQ+hG1nZ0d8vPzsWXLFhiNRri7uyM9Pd1qL29/Th6dTocTJ04gKytLUp9fl7fo3XffxdatW9HQ0ABHR0f4+PjgwIEDcHR0FJKflJSEiIgIaLVaAEBCQgIAoKSkRPLHpYWFhTh69Cj0ej0CAgKQm5sr9Dkbpb+LyitkQqvV4quvvoJcLu8hHMzMzOzxpxVSEe12ElJgXF1dkZOTIyLKIm5ubj22zlLpz8nj6Ogo6Q+LXqYNam9RZGQkaf6ZM2ck51tiw4YN2LBhA0k2QO/v6o4or5AJd3d3fP/990IzLSHa7cRfFWAYhgwuMAzDkMEFhmEYMrjAMAxDBhcYhmHI4ALDMAwZ7EViGEYy7EViGMbmsBeJ83kNOF9IG5bgHQzDMGRwgWEYhgwuMAzDkMEFhmEYMrjAMAxDBhcYhmHIEFJg+pJ0iUJ0fn95R44cgUqlwqRJk5CQkICGhgbS9kQhUkxniSVLlsDHx8csLqM4TpRa4Ec5BluI3WwhOKyvr8fy5csxefJkhISEQK1W9zjt8VURcuDUiyRj/2z5feVVVFRg586d+Mtf/oJf//rX+NOf/oS1a9dKPuyKen4AsWK6vti8eTN+//vfC8vrjS0EflRjsIXYzRbzk5mZiREjRuD8+fNobW3Fv/7rv+Lw4cOIi4uzKk/IDuZ1ScZE5509exYRERFmyVtiYiIqKyslHy5OPT+AWDHd68BWAj9bQCF2s9X81NfXIzIyEo6Ojhg5ciRCQ0MlOc74GUw3urq6LB5efevWrdfQm1eHWkz36aefYsqUKYiNjRXqpAZsJ/CjHIMJCrGbreYnLi4ORUVFZhNFaWkppk+fbnUeF5huzJgxAydOnEB1dTWePXuG7Oxs2NnZCZd/UUEppktLS8M//vEPlJaWYsGCBfjDH/4gdIdkC4Ef9RgAOrGbrQSHQUFBuH37NgICAhAWFgZvb2+rD9cHuMD0IDg4GMnJyUhOToZSqYS7uzucnZ0xZsyY1921l4ZKTOfr6wsXFxfI5XJERUXB399fkpCrN7YQ+FGPAaATu9lifoxGIxISEqBSqXDt2jVcvHgRLS0t2L59u9WZXGB6sWjRIpw+fRrl5eWYPXs2DAaD0IdotoJSTAc8f84jUhbXXeBnglrgJ3oMAJ0R1Bbz8/jxYzx48ACLFy+GXC7H8OHDERMTg2+++cbqTCEF5kUis3+2/L7ydDodbt26ha6uLty/fx+bN29GXFwchg0b9k/V/96IFtP1prW11fwJmF6vx7Fjx1BVVdXDzyMVaoGfLcZAKXazheDQzc0NCoUC+fn50Ov1aG1tRUFBATw9Pa3OFPIxdX+Srn/G/L7yli5dirVr1+LevXtwdnZGdHQ0UlJS/un63xvRYrre6PV67N69G3fu3IGDgwMmTJiA7OxsTJgwQUi+CUqBny3GQCl2A+gFhwCwd+9ebNu2Dfv374e9vT2mTJmC9PR0q/OEFJj+JF3/jPn95VH88RL1/IgW01nK/9vf/kaWb4JS4GeLMVCL3agFhwAwceJE5OXlCcvjZzAMw5DBBYZhGDK4wDAMQwYXGIZhyOACwzAMGexFYhhGMuxFYhjG5rAXifN5DThfSBuW4B0MwzBkcIFhGIYMLjAMw5DBBYZhGDK4wDAMQwYXGIZhyBBSYKidPAC9l4dyDL8EL9JAc19ZwhbXKfD8gG4fHx+kpaUJy+zo6EB6ejqUSiUmTZqE+fPnSz7us785Ly8vR0REBHx9fbFkyRJotVqr2hByHowtnDwArZeHcgy/BC/SQHNfWcJW16larYaPj4/QTL1ej7FjxyIvLw9vvvkmzp07h9TUVBw/fhwKhcKqzL7m/OHDh1i9ejU+/vhjzJw5E7t378aaNWvwX//1X6/chpAdzEB38gC0Y/gleJEGmvvKEra4TouKijB06FAEBwcLzXVyckJSUhIUCgXs7e2hVCqhUChw48YNqzP7mvPi4mJ4eHiY/UhJSUmorq5GbW3tK7ch7BkMtZMHoHfa2GIMlAz0/tsCyjl68uQJ9uzZQ/YWrztNTU2oq6sjORS9pqamxzm8Tk5OePvtt61yMAktMFROHsA2ThvqMVAz0PtvCyjnaPfu3YiJicHYsWOFZVqis7MTaWlpiIqKwjvvvCM835KDycXFxSoHk9BPkaicPIBtnDYA7RhswUDvvy2gmKObN2+ivLwc8fHxQvL6wmg0Yv369ZDJZNi0aRNJG5YcTG1tbVY5mIQ85O0NtZMHoHHadMcWY6BkoPffFoico0uXLkGr1UKpVAJ4vgswGAyIiopCQUGBkDa6urrw0UcfoampCfv374dMJhOS2xsPD48efW5vb8fdu3etejsmeQdD7eQB6J021GMY6F4kYOC5r3pDPUcLFixAcXExNBoNNBoNYmNjER4ejoMHDwrJB55/I7q2thafffYZBg8eLDmvrzlXqVSoqanBqVOnoNPpkJ2dDU9PT6vejknewVA7eQB6pw31GAa6FwkYeO6r3lDP0ZAhQzBkyBDzaycnJ8jlcri5uQnJ12q1+OqrryCXy3v8Ys3MzMTcuXOtyuxvzrOysqBWq7Fu3Tr4+vpi586dVrUhucBQO3lMbVA6bajHMNC9SMDAc1/1xhZz1B3RY3F3d8f3338vNLO/OZ82bRpOnjwpuQ3+qgDDMGRwgWEYhgwuMAzDkMEFhmEYMrjAMAxDBhcYhmHIYPEawzCSYfEawzA2h8VrnM9rwPlC2rAE72AYhiGDCwzDMGRwgWEYhgwuMAzDkMEFhmEYMoQUGGpnkSnX9N/EiROxdetWoW08fvwYq1atgp+fH5RKJY4fPy4s2xb9F70GfTlzrl27hmXLliEoKAhTp05FcnIyGhsbheUD4pw8vamvr8fy5csxefJkhISEQK1WCz3UCnhuFYiMjISfnx9mzZqFqqoqq7P6m6MjR45ApVJh0qRJSEhIQENDg7B8UWsMCNzBbN68GVevXsXVq1dx6tQpUbEAYM69evUqysrKMHjwYERERAhtQ61WQyaToaysDNu3b0dGRgZqamqEZNui/4DYNTA5c2JiYnr8vKWlBR988AHOnDmDs2fPwtnZGRs3bhSWb3LypKSkoKKiAt7e3lizZo2ksZjIzMzEiBEjcP78eWg0GlRWVuLw4cNCsgGgrKwMO3bswCeffGI+WPytt96yOq+vOaqoqMDOnTuRk5ODS5cuQaFQYO3atcLyRa0xQHQmLyWnTp2Cm5sbAgMDhWW2t7fj9OnTOH78OJydnREYGIiZM2eisLBQqJ0PoOk/BbNnzwYA/M///E+P3469NR+LFy/G4sWLheV3d/IAzw9Fmjp1KmprayWfoF9fX4/FixfD0dERI0eORGhoqFUqjr7IyspCYmIi/Pz8AACjR4+WlNfXHJ09exYRERHw8PAAACQmJiIsLAx3797F22+/LTlf1BoDAncw1M4iEwUFBZg/fz7s7Cz+ZbJV1NXVwd7eHuPHjzf/zMvLS+jFZ4Ki/yZstQbdqaysNF/oIhDp5OlNXFwcioqK8PTpUzQ0NKC0tBTTp0+XnAs8P0D8+vXrePToEVQqFcLCwqBWq/Hs2TMh+d3p6uqyeOD9rVu3hLcFSFtjYW5qamcRANy/fx+VlZWYP3++0FxLHpihQ4da5YHpD6r+A7Zbg+5UV1cjJycH69evF5Yp0snTm6CgINy+fRsBAQEICwuDt7e3sDN5m5qa0NnZiZMnT+LQoUPQaDT47rvvsG/fPiH53ZkxYwZOnDiB6upqPHv2DNnZ2bCzsyMpZlLXWEiBsZWzSKPRICAgQNL7WktY8sA8efLEKg9Mf1D1H7DdGpj44YcfsHz5cqSnpwt9uyfSydMdo9GIhIQEqFQqXLt2DRcvXkRLSwu2b98uKdeE6ZT/JUuWYNSoUXBzc8OyZctI1iA4OBjJyclITk6GUqmEu7s7nJ2dMWbMGKHtiFhjko+pqZxFhYWFJL/9x40bB4PBgLq6OvPPqqurhWs5qfpvCUpvlFarxbJly5CYmCh8PB4eHqiurja/luLk6c7jx4/x4MEDLF68GHK5HMOHD0dMTAy++eYbqV0GAAwbNgxjxowheetriUWLFuH06dMoLy/H7NmzYTAYhL5VFbXGkgsMtbPIxJUrV9DQ0EDy6YuTkxNUKhX27NmD9vZ2XL58GSUlJZg3b56wNij7T7EGfTlzGhoasHTpUnz44YdYuHCh8HyRTp7uuLm5QaFQID8/H3q9Hq2trSgoKOjxvEcq0dHRyMvLQ3NzM1paWvDFF18gPDzc6ry+5kin0+HWrVvo6urC/fv3sXnzZsTFxWHYsGFC8kWtMSDgUyRqZ5EJjUYDlUoFFxcXobkmtmzZgvT0dEybNg2urq7IyMgQ+huBsv8Ua9CXM8fOzg737t1DdnY2srOzzf9+9epVIfkinTy92bt3L7Zt24b9+/fD3t4eU6ZMQXp6upBs4PmnOY8ePcKcOXPg6OiIyMhIrFy50uq8vuZo6dKlWLt2Le7duwdnZ2dER0cjJSVFWL6oNQYEeZEonUUm1Go1ab6rqytycnLI8in7T7EG/TlzVq9eTZovysnTm4kTJyIvL094rgmZTIaMjAxkZGQIyetvjkT8ISj1GgP8VQGGYQjhAsMwDBlcYBiGIYMLDMMwZHCBYRiGDC4wDMOQwV4khmEkw14khmFsDnuROJ/XgPOFtGEJ3sEwDEMGFxiGYcjgAsMwDBlcYBiGIYMLDMMwZAgpMLW1tYiLi0NAQABUKhWKi4tFxJoZiF6h3qSlpSE0NBT+/v6YM2cOjhw5IizbFvMjeo37cvJ0dHQgOTkZM2fOhKenp6TDy/tq4/bt24iOjsbkyZMxefJkxMfHW3WoeF/59fX18PT07LEm3c9VkZp/7NixHtm+vr7w9PTE9evXheR3Z+/evfD09MSFCxdeuf+AoAOnEhMTERsbi9zcXFRUVGDlypUoKCjocUq/FLofdNPe3o6QkBAyr9Dvf/974bkAsGLFCmzbtg1yudx8s06cOBHe3t6Ss6nnh2KNTU4e00l83fH390dcXBxSU1Ml9buvNkaNGoU9e/bA3d0dRqMRhw4dwpo1a175jJX+xgA8P41/0CDrb7G+8ufOnYu5c+eaX3/99dfIycnBb37zG6H9v3v3Lk6dOoWRI0daPQbJO5g7d+6gsbER8fHxcHBwQHBwMPz9/VFYWCg12iIDxSvUGw8PD8jlcgDPz8u1s7MjOfWfYn4o1nj27NmYNWsWXF1de/xcLpcjPj4egYGBsLeXdnn21cYbb7wBhUJhPrfYwcHBqrXoK18UL5tvrQrnRflqtRppaWnm69YaJO9gLH3VoKurS5gVsTfUXqEdO3Zg/PjxWLNmDaZMmSI0PyMjAwUFBXj27Bnee++9nwmuREAxP7ZeY1sRGBiI9vZ2GI1GJCcnC89XKpWws7NDSEgI1q1bBzc3N+FtaLVaVFVVYdu2bUJzT5w4AZlMJvkalbyDmTBhAtzc3HDgwAF0dnbi/PnzqKysJHG0DHSvUEZGhlkpqlKpJP1msATV/NhyjW1JVVUVqqqqsGnTJrz33nvCcocPH46jR4/i7Nmz+Prrr9HW1oZ169YJy++ORqNBYGCgUBVOW1sbdu3aJeS8YskFRiaTITs7G+fOnUNoaChyc3MREREhWZtpiV+CV8jBwQGBgYH48ccfkZ+fLzSban5suca2xsnJCQsXLsSGDRvQ3NwsJNPZ2Rk+Pj4YNGgQfvWrX2HTpk04f/78z3xPIqBQ4WRlZWHu3LlCriMhbmovLy98+eWX5texsbEku4zCwkIsX75ceK4lKL1CwHPVqOgdEuX82GqNXwdGo9Gskx0xYoTwfNPbVdHX0+XLl9HY2Cj8E8/y8vIevwAfPnyI1NRU/Nu//Rv+/d///ZWyhBSY6upqjB8/HkajEYcPH0ZjYyOio6NFRJuh9gp9++23CAoKgoODA/7+97+jqqpKmNKiubkZFy9eRHh4OAYPHowLFy6gqKgIO3bsEJIP0M4PIH6N9Xo9DAZDDyePg4MDBg0ahI6ODvPN2NnZCZ1OB7lc/srPlfpq49KlSxg+fDg8PT3x9OlT7N69G2+88cYru5f6yr9x4waGDh2KcePGoaWlBR9//DGCgoJ+psS1Nt/0yZRGo8Hs2bOtVuH0lf/nP/8Zer3e/L/7l3/5F/zxj39EWFjYK7chpMAUFhbi6NGj0Ov1CAgIQG5urvDnCwPNK9QdOzs75OfnY8uWLTAajXB3d0d6erowLzJA740Svcb9eZEiIiKg1WoBAAkJCQCAkpISKBQKIW28++672Lp1KxoaGuDo6AgfHx8cOHAAjo6OQvLHjx+PnTt34uHDh3BxccG0adOscjv1N0c6nQ4nTpxAVlbWK+e+TH53HBwcMGzYMKv0vUIKzIYNG7BhwwYRUX0y0LxCvfO7v72ggNobJXqN+3PynDlzhryNyMhI0vzf/e53pPmOjo6oqqoiy++OlPXgrwowDEMGFxiGYcjgAsMwDBlcYBiGIYMLDMMwZHCBYRiGDPYiMQwjGfYiMQxjc9iLxPm8BpwvpA1L8A6GYRgyuMAwDEMGFxiGYcjgAsMwDBlcYBiGIYMLDMMwZAgtMHV1dfDx8UFaWprIWJuIxR4/foxVq1bBz88PSqXylR05/fEygiupUIrdAHoxHSB+DNRiNEsUFRUhMjISfn5+mDVrlqQzW/q7bo4cOQKVSoVJkyYhISEBDQ0NUrtuRuQYhBw4ZUKtVsPHx0dkJADbiNfUajVkMhnKyspw8+ZNrFixAl5eXvDw8JCc/SLBlQgoxW4mKMV0gPgxUIvRelNWVoYdO3Zg165deP/99/HTTz9Jyuur/xUVFdi5cyf+8pe/4Ne//jX+9Kc/Ye3atUIONRM9BmE7mKKiIgwdOhTBwcGiIi1CIRZrb2/H6dOnkZKSAmdnZwQGBmLmzJnC5HHUgi7AdmI3SkSPwRbz3p2srCwkJibCz88P9vb2GD16tCTzQl/9P3v2LCIiIszzlZiYiMrKSiHrLXoMQgrMkydPsGfPHrLtf3coxGJ1dXWwt7fvoUH18vKyylf8OsnIyICvry8iIyMxcuRI4WK3Tz/9FFOmTEFsbKwkZ3R/UI+hO0qlEmFhYdi4cSMePnwoKctgMOD69et49OgRVCoVwsLCoFarSdxRXV1dFg0Ft27dkpRLMQYhBWb37t2IiYnB2LFjRcT1CZVYrL29/Wcnvg8dOhRtbW1C26GGUuxmCzEdQC+nA2jEaE1NTejs7MTJkydx6NAhaDQafPfdd9i3b5+gXv9/ZsyYgRMnTqC6uhrPnj1DdnY27OzsJBczijFILjA3b95EeXk54uPjpUa9ECqxmJOT08+kWE+ePLHqFPXXDZXYzVZiOoBWTgfQiNEGDx4M4PnD8FGjRsHNzQ3Lli0jmaPg4GAkJycjOTkZSqUS7u7ucHZ2xpgxYyTlUoxB8hOuS5cuQavVQqlUAni+GzAYDIiKikJBQYHU+B5QicXGjRsHg8GAuro6jBs3DsBzD9C7774rvC1bQSF26w61mA6gH4MJEWK0YcOGYcyYMSTOdEssWrQIixYtAgD87//+L/bt2yf5AwmKMUjewSxYsADFxcXQaDTQaDSIjY1FeHg4Dh48KKJ/ZijFYk5OTlCpVNizZw/a29tx+fJllJSUYN68eULy9Xo9dDpdD8FVd7GVVJqbm1FUVIS2tjYYDAaUlpaiqKgIU6dOFZLf2tpq/iRDr9fj2LFjqKqqQmhoqJB8gGYMfc37t99+izt37sBoNOLRo0dWi9F6Ex0djby8PDQ3N6OlpQVffPEFwsPDhfdfp9Ph1q1b6Orqwv3797F582bExcVh2LBhkvpPMQbJO5ghQ4ZgyJAh5tdOTk6Qy+Vwc3OTGt0DarHYli1bkJ6ejmnTpsHV1RUZGRlCPqIGXl5wZS3UYjdqMR1AMwZqMVpvEhMT8ejRI8yZMweOjo6IjIzEypUrhfd/6dKlWLt2Le7duwdnZ2dER0cjJSVFcv8B8WMQ+ncwAITdNL2hFou5uroiJyeHJPtlBVfWQi12oxbTmdoQPQZqMVpvZDIZMjIykJGRISSvv/6L/EPQ7ogeA39VgGEYMrjAMAxDBhcYhmHI4ALDMAwZXGAYhiGDvUgMw0iGvUgMw9gc9iJxPq8B5wtpwxK8g2EYhgwuMAzDkMEFhmEYMrjAMAxDBhcYhmHI4ALDMAwZkgtMR0cH0tPToVQqMWnSJMyfP5/kmEBqLw+lV8gWXiRKrxNA76ainiNbrIEJUX6w/u6tjo4OJCcnY+bMmfD09BR6CLtIv5nk82D0ej3Gjh2LvLw8vPnmmzh37hxSU1Nx/PhxKBQKyR3sDqWXh9IrZAsvEqXXCaB3U1HPkS3WwIQoP1h/99aoUaPg7++PuLg4pKamSu90N0T6zSTvYJycnJCUlASFQgF7e3solUooFArcuHFDRP9sBqVXiNrPQ+116g2Fm4p6jmzlSBLpB+vv3pLL5YiPj0dgYCDs7cU96RDtNxP+DKapqQl1dXUkB2ZTe3ls6eQRia29ThRuql8C1H4wynsLoOm/0ALT2dmJtLQ0REVF4Z133hEZbRMvjy2cPBTY0utE5ab6JUDpB6O8t0xQ9F9YgTEajVi/fj1kMhk2bdokKtaMrbw81E4eCmzpdaJyUw10KP1g1PcWQNd/IYd+d3V14aOPPkJTUxP2798PmUwmIrZfqL08tnLyiMCWXicqN9VAh8oPZqt7i6r/QgrMli1bUFtbi9zcXLMdTiStra349ttvERQUBAcHB/z9739HVVUV0tPTheQ3Nzfj4sWLCA8Px+DBg3HhwgUUFRVhx44dQvL1ej0MBkMPv42DgwMGDRIjdejudfr4449x8+ZNlJSU4K9//auQfBOUbirqOaLOX7BgAX7729+aX3/++efQarWST+fv797q6Ogw/5Lt7OyETqeDXC636tkYVf8lz65Wq8VXX30FuVzeQ8SVmZmJuXPnSo0HQO/lofYKUXuRAFqvkwlKNxX1HFHnU/jBXnRvRUREQKvVAgASEhIAACUlJVb9eQiV30xygXF3d8f3338vNaZfqL081F4hai8SQOt1MkHppqKeI1usQe/2pPKie+vMmTOS2+gLUXPFXxVgGIYMLjAMw5DBBYZhGDK4wDAMQwYXGIZhyOACwzAMGSxeYxhGMixeYxjG5rB4jfN5DThfSBuW4B0MwzBkcIFhGIYMLjAMw5DBBYZhGDK4wDAMQ4aQAkPt5LGVe0mkD6Y3lN4lgN4bRe1FAmDWxQQEBEClUqG4uFhoPuUa2OIaHYj3mZDjvKidPLZyL4n0wfSG0rtkgtIbRe1F0uv1SExMRGxsLHJzc1FRUYGVK1eioKCghy1BCpRrYItrdCDeZ5J3MLZw8tjCvSTaB9MbSu+SraHwIt25cweNjY2Ij4+Hg4MDgoOD4e/vL/Q6olwD6mt0oN5nkguMrZ08gHg/DLXPxgS1d4naG2WCwotk6SsrXV1dqKmpEdYGYDv3lehrdKDeZ0J2MLZy8gA0fhhKn013KL1LtvBGAXRepAkTJsDNzQ0HDhxAZ2cnzp8/j8rKSjx79kxoO7ZwX1FcowP1PhOijrWVk4fCD0Pps7EElXfJVt4oKi+STCZDdnY2zp07h9DQUOTm5iIiIgKjR48W2g5A676ichgN1PtM8kNeWzl5qPwwVD6YF0HtXaLyRlF6kby8vHocvh4bG0tqkBS9BpQOo4F6nwnZwZicPO3t7bh8+TJKSkowb948qdE9MPlhPvvsM6HupQULFqC4uBgajQYajQaxsbEIDw/HwYMHhbXR3NyMoqIitLW1wWAwoLS0FEVFRZg6daqQ/NbWVpSWlkKn00Gv1+PYsWOoqqrqoboQAaUXCXh+w+h0Ojx9+hQHDx5EY2MjoqOjhWRTrwFAd40CA/c+EyZeo3TyULqXqHww3aH2LlF7o0xQepGA57ujo0ePQq/XIyAgALm5ucKekVCvgS38YAPxPhNSYKidPLZwL5mgcOdQe5eovVEmKL1IALBhwwZs2LCBJJt6DWxxjQ7E+4y/KsAwDBlcYBiGIYMLDMMwZHCBYRiGDC4wDMOQwQWGYRgy2IvEMIxk+vIi9VtgGIZhpMBvkRiGIYMLDMMwZHCBYRiGDC4wDMOQwQWGYRgyuMAwDEPG/wOn1hqU3NC9XAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "givens = np.array([[ 0,  1,  3, 14, 12, 10,  8,  6,  4,  2,  0],\n",
    "                   [ 3,  1, 21,  6,  4,  2,  0,  2,  4,  6,  2],\n",
    "                   [ 7,  5, 19,  8, 15, 12, 10,  8,  6,  8,  4],\n",
    "                   [ 0,  3, 17, 15, 13, 11,  9,  7,  4,  2,  6],\n",
    "                   [ 1,  1, 19,  1,  3,  5,  0,  5,  7,  0,  8],\n",
    "                   [ 3,  5,  3,  1,  3,  1,  1,  3,  4,  2, 10],\n",
    "                   [ 5,  7,  0,  7,  5, 12, 10,  8,  6, 19, 12],\n",
    "                   [ 9,  7,  5,  3,  7,  9, 11, 13, 15, 17, 14],\n",
    "                   [ 4,  7,  0,  1,  3,  5,  3, 15,  6, 19,  6],\n",
    "                   [ 2,  5,  3,  1,  0,  7,  1,  1,  4, 21,  4],\n",
    "                   [ 0,  2,  4,  3,  5,  7,  9,  3,  2,  0,  2]])\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "x = np.array((givens).astype('int').astype('str'))\n",
    "x[x==\"-1\"] =\"\"\n",
    "ax =sns.heatmap(givens!=-1,annot=x,cbar=False,center=3,cmap=\"Greys\",fmt=\"\",linewidths=1,linecolor=\"grey\",annot_kws={\"size\":12})\n",
    "ax.axis(\"off\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "N= givens.shape[0]\n",
    "\n",
    "\n",
    "def neigbours(grid, i, j):     \n",
    "    l = []\n",
    "    (rows,cols) = grid.shape\n",
    "    if i-1 >= 0:\n",
    "            l.append((i-1,j))\n",
    "    if i+1 < rows:\n",
    "            l.append((i+1,j))\n",
    "    if j-1 >= 0:\n",
    "            l.append((i,j-1))\n",
    "    if j+1 < cols:\n",
    "            l.append((i,j+1))\n",
    "    return l\n",
    "\n",
    "s = Solver()\n",
    "\n",
    "X = [[Int(\"x_%s_%s\" % (i+1, j+1)) for j in range(N)] for i in range(N)]\n",
    "size = [[Int(\"s%d%d\" % (i,j)) for j in range (N) ] for i in range (N) ]\n",
    "\n",
    "# Variables for the root of each tree\n",
    "root = [[Int(\"r%d%d\" % (i,j)) for j in range (N) ] for i in range (N) ]\n",
    "\n",
    "edge = {}\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        for (k,l) in neigbours(givens,i,j) :\n",
    "            edge[(i,j,k,l)] = Int(\"e%d%d%d%d\" % (i,j,k,l))\n",
    "            s += Or(edge[(i,j,k,l)] ==0,edge[(i,j,k,l)]==1) \n",
    "\n",
    "s += [X[i][j] >=0 for j in range(N) for i in range(N)]     \n",
    "\n",
    "s += [X[i][j] == int(givens[i,j]) for j in range(N) for i in range(N) if givens[i,j] != -1]  \n",
    "\n",
    "# Define a variable to determine if there is an edge between 2 cells\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        for (k,l) in neigbours(givens,i,j):\n",
    "            s += (edge[(i,j,k,l)] + edge[(k,l,i,j)]) <= 1\n",
    "    \n",
    "# Make edges one way to form a tree\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        s += Sum([edge[(k,l,i,j)] for (k,l) in neigbours(givens,i,j) ]) <=1  \n",
    "        \n",
    "# Calculate size of cell as 1 + the cells it feeds into\n",
    "for i in range(N):\n",
    "    for j in range(N):   \n",
    "        s +=  size[i][j] == Sum([If(edge[(i,j,k,l)]==1,size[k][l],0) for (k,l) in neigbours(givens,i,j)])+1\n",
    "\n",
    "# put the root cell number in the root\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        s+= Implies(Sum([edge[(k,l,i,j)] for (k,l) in neigbours(givens,i,j)]) == 0 ,root[i][j]==i*N+j)              \n",
    "\n",
    "# root size must be number +1\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        s+= Implies(Sum([edge[(k,l,i,j)] for (k,l) in neigbours(givens,i,j)]) == 0 ,size[i][j]>X[i][j])      \n",
    "        \n",
    "# shared edges have the same root and are either 1:1 or x:x+2\n",
    "for i in range(N):\n",
    "    for j in range(N):  \n",
    "        for (k,l) in neigbours(givens,i,j):\n",
    "            s+= Implies(edge[(k,l,i,j)]  == 1 ,root[i][j] == root[k][l])\n",
    "            s+= Implies(edge[(k,l,i,j)]  == 1 ,Or(X[i][j]+2 == X[k][l],X[i][j] == X[k][l]+2,And(X[i][j] == 1, X[k][l]== 1)))\n",
    "\n",
    "# each number apart from 0 appears twice\n",
    "for i in range(N):\n",
    "    for j in range(N):              \n",
    "        s+=Implies(X[i][j] != 0,\n",
    "                   PbGe(\n",
    "                       [(And(root[i][j]==root[k][l],X[i][j]==X[k][l]),1) for k in range(N) for l in range(N)]\n",
    "                       ,2))\n",
    "        \n",
    "start = time.time()\n",
    "if s.check() == sat:\n",
    "    m = s.model()\n",
    "    r = np.array([ [ m.evaluate(X[i][j]).as_long() for j in range(N) ] for i in range(N) ])\n",
    "    roots = np.array([ [ m.evaluate(root[i][j]).as_long() for j in range(N) ] for i in range(N) ])\n",
    "    print(\"Solved in {} seconds\".format(time.time()-start))\n",
    "    fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "    ax = sns.heatmap(roots,annot=r,cbar=False,cmap=\"tab20\",fmt=\"\",linewidths=1)\n",
    "    ax.axis(\"off\")\n",
    "    plt.tight_layout()\n",
    "\n",
    "else:\n",
    "    print(\"Failed in {} seconds\".format(time.time()-start))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "url= \"https://www.janestreet.com/puzzles/it-s-symmetric-solution/\"\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "y =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "#display([(i,j) for i,j in enumerate(y)])\n",
    "display(Markdown(\"### \"+y[8]+\"\\n\"+\"\\n\".join(y[10:13])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ld_NFUIfT1W9"
   },
   "source": [
    "### Solution\n",
    "<img src=\"https://www.janestreet.com/puzzles/Mar18_solution.png\" width=\"400\">\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "givens = np.array([[ 0,  1,  3, 14, 12, 10,  8,  6,  4,  2,  0],\n",
    "                   [ 3,  1, 21,  6,  4,  2,  0,  2,  4,  6,  2],\n",
    "                   [ 7,  5, 19,  8, 15, 12, 10,  8,  6,  8,  4],\n",
    "                   [ 0,  3, 17, 15, 13, 11,  9,  7,  4,  2,  6],\n",
    "                   [ 1,  1, 19,  1,  3,  5,  0,  5,  7,  0,  8],\n",
    "                   [ 3,  5,  3,  1,  3,  1,  1,  3,  4,  2, 10],\n",
    "                   [ 5,  7,  0,  7,  5, 12, 10,  8,  6, 19, 12],\n",
    "                   [ 9,  7,  5,  3,  7,  9, 11, 13, 15, 17, 14],\n",
    "                   [ 4,  7,  0,  1,  3,  5,  3, 15,  6, 19,  6],\n",
    "                   [ 2,  5,  3,  1,  0,  7,  1,  1,  4, 21,  4],\n",
    "                   [ 0,  2,  4,  3,  5,  7,  9,  3,  2,  0,  2]])\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "x = np.array((givens).astype('int').astype('str'))\n",
    "x[x==\"-1\"] =\"\"\n",
    "ax =sns.heatmap(givens!=-1,annot=x,cbar=False,center=3,cmap=\"Greys\",fmt=\"\",linewidths=1,linecolor=\"grey\",annot_kws={\"size\":12})\n",
    "ax.axis(\"off\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  3, 14, 12, 10,  8,  6,  4,  2,  0],\n",
       "       [ 3,  1, 21,  6,  4,  2,  0,  2,  4,  6,  2],\n",
       "       [ 7,  5, 19,  8, 15, 12, 10,  8,  6,  8,  4],\n",
       "       [ 0,  3, 17, 15, 13, 11,  9,  7,  4,  2,  6],\n",
       "       [ 1,  1, 19,  1,  3,  5,  0,  5,  7,  0,  8],\n",
       "       [ 3,  5,  3,  1,  3,  1,  1,  3,  4,  2, 10],\n",
       "       [ 5,  7,  0,  7,  5, 12, 10,  8,  6, 19, 12],\n",
       "       [ 9,  7,  5,  3,  7,  9, 11, 13, 15, 17, 14],\n",
       "       [ 4,  7,  0,  1,  3,  5,  3, 15,  6, 19,  6],\n",
       "       [ 2,  5,  3,  1,  0,  7,  1,  1,  4, 21,  4],\n",
       "       [ 0,  2,  4,  3,  5,  7,  9,  3,  2,  0,  2]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "givens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "include_colab_link": true,
   "name": "JaneSt-Feb18.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}