2021_09_KnightMoves4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "Oq1xibzMT1Wl"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import ListedColormap\n",
    "import matplotlib.pyplot as plt\n",
    "import requests\n",
    "from bs4 import BeautifulSoup\n",
    "from scipy.ndimage import generate_binary_structure\n",
    "from copy import copy\n",
    "\n",
    "from z3 import *\n",
    "from IPython.display import Markdown, display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "ICTfvjZUT1Wr"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### September 2021 : Puzzle\n",
       "A knight was initially located in a square labeled 1. It then proceeded\n",
       "to make a series of moves, never re-visiting a square, and labeled\n",
       "the visited squares in order. When the knight was finished, the\n",
       "labeled squares in each region of connected squares\n",
       "1\n",
       "had the same sum.\n",
       "A short while later, many of the labels were erased. The remaining\n",
       "labels can be seen above.\n",
       "Complete the grid by re-entering the missing labels.\n",
       "The answer to this puzzle is the sum of the\n",
       "squares\n",
       "of the largest\n",
       "label in each row of the completed grid, as in the example."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "url='https://www.janestreet.com/puzzles/knight-moves-4-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[8]+\"\\n\"+\"\\n\".join(y[10:18])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "source": [
    "<img src=\"https://www.janestreet.com/puzzles/2021-09-01-knight-moves-4.png\" width=350>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "# Set up the regions and fixed cells\n",
    "\n",
    "regions=np.array([\n",
    "                 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "                 [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0],\n",
    "                 [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0],\n",
    "                 [ 0, 0, 1, 1, 1, 1, 3, 2, 2, 2],\n",
    "                 [ 5, 0, 1, 0, 0, 4, 3, 3, 3, 3],\n",
    "                 [ 5, 0, 0, 0, 4, 4, 4,10,10, 3],\n",
    "                 [ 5, 6, 6, 7, 4, 9, 9,10,10,11],\n",
    "                 [ 5,12, 6, 7, 7, 8, 8, 8,10,11],\n",
    "                 [ 5,12,13, 7,16,16,16,15,15,11],\n",
    "                 [12,12,13,14,14,14,14,14,15,11]\n",
    "])\n",
    "\n",
    "fixed = np.array([\n",
    "       [12, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0, 0, 0, 5, 0,23, 0],\n",
    "       [ 0, 0, 0, 0, 0, 0, 8, 0, 0, 0],\n",
    "       [ 0, 0, 0,14, 0, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [ 0, 2, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0,20, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0,33, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [ 0, 0, 0, 0, 0, 0, 0, 0, 0,28]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution is : 3,210\n",
      "[12, 23, 8, 14, 0, 2, 20, 33, 0, 28]\n",
      "[144, 529, 64, 196, 0, 4, 400, 1089, 0, 784]\n"
     ]
    }
   ],
   "source": [
    "# print in a nice format and calc the answer\n",
    "\n",
    "def output(regions,fixed):\n",
    "    fig,ax = plt.subplots(1,1,figsize=(4,4))    \n",
    "    x = np.array((fixed).astype('int').astype('str'))\n",
    "    x[x==\"0\"] =\"-\"\n",
    "    ax =sns.heatmap(regions,annot=x,cbar=False,cmap='tab20',fmt=\"\",\n",
    "                    linewidths=1,linecolor=\"k\",annot_kws={\"size\":12,\"color\":\"k\"},alpha=.4,)\n",
    "    ax.axis(\"off\")\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    print(\"Solution is : {:,.0f}\".format(sum([max(fixed[i,:])**2 for i in range(fixed.shape[1])])))\n",
    "    print([max(fixed[i,:]) for i in range(fixed.shape[1])])\n",
    "    print([max(fixed[i,:])**2 for i in range(fixed.shape[1])])\n",
    "    \n",
    "output(regions,fixed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Possible chain lengths where the total is divisible by 17 and the region totals :\n",
      "  [(33, 33), (34, 35), (50, 75), (51, 78), (67, 134), (68, 138), (84, 210), (85, 215)]\n",
      "Sum of large region given 11 & 13 must be in : 51\n",
      "Max given there are 2 regions with only 2 cells : 99 131 133\n"
     ]
    }
   ],
   "source": [
    "# The trick is to notice there are 17 regions which really limits the number of valid chain lengths. \n",
    "# You can't get to the large(chain  > 67) totals with 2 numbers and the large region already adds up to 51\n",
    "# as 13 & 11 have to be in that region,6\\ which excludes shorter chain lengths. 33 is one of the given numbrs\n",
    "# which implies the chain length is 50 or 51\n",
    "\n",
    "tot =  lambda x: x*(1+x)/2\n",
    "print(\"Possible chain lengths where the total is divisible by 17 and the region totals :\\n \",[(i,int(tot(i)/17)) for i in range(33,101) if tot(i) % 17 ==0 ])\n",
    "print(\"Sum of large region given 11 & 13 must be in :\" ,12+5+8+2+11+13)\n",
    "print(\"Max given there are 2 regions with only 2 cells :\" ,51+48,67+64,68+65)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "def moves(i,j,N):\n",
    "    moves=[(2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2), (1, -2), (2, -1)]\n",
    "    return [(i+x,j+y) for x,y in moves if i+x >=0 and i+x<N and j+y>=0 and j+y<N ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "def fill(regions,fixed,fix_y,tactic):\n",
    "    start = time.time()\n",
    "    N= regions.shape[0]\n",
    "    R =np.max(regions)\n",
    "    \n",
    "    X = np.array(IntVector('x', N*N),dtype=object).reshape((N,N))\n",
    "    Y = fix_y*(1+fix_y)/2/(R+1)\n",
    "    print(\"Total for each region : \",Y)\n",
    "            \n",
    "    s = Tactic(tactic).solver()\n",
    "    if R ==16:\n",
    "        s+= Or(And(X[1,2]==11,X[2,1]==13),And(X[1,2]==13,X[2,1]==11))\n",
    "        s+= Or(And(X[7,8]==27,X[8,7]==29),And(X[7,8]==29,X[8,7]==27))\n",
    "      \n",
    "    s += [And(e >= 0  ,e <= fix_y) for (i,j),e in np.ndenumerate(X)]\n",
    "    s += [X[i,j] == int(e) for (i,j),e in np.ndenumerate(fixed) if e !=0]\n",
    "    s += [Sum([e for (i,j),e in np.ndenumerate(X) if regions[i,j]==n])==Y for n in range(R+1)]\n",
    "    s += [Or(e==0,e==1,PbEq([(X[k,l]==e-1,1) for k,l in moves(i,j,N)],1)) for (i,j),e in np.ndenumerate(X)] \n",
    "    s += [PbEq([(e==n,1) for (i,j),e in np.ndenumerate(X)],1) for n in range(1,fix_y+1)]    \n",
    "    \n",
    "    if s.check() == sat:\n",
    "        m = s.model()\n",
    "        eval = np.vectorize(lambda x:m.evaluate(x).as_long())\n",
    "        result =  eval(X)\n",
    "        output(regions,result)\n",
    "        print(\"Took {:.4f} seconds\".format(time.time()-start))\n",
    "        return result\n",
    "    else:\n",
    "        print(\"{} failed in {:.4f} seconds\".format(fix_y,time.time()-start))       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total for each region :  75.0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution is : 14,820\n",
      "[12, 23, 17, 24, 50, 48, 49, 45, 46, 44]\n",
      "[144, 529, 289, 576, 2500, 2304, 2401, 2025, 2116, 1936]\n",
      "Took 8.5429 seconds\n"
     ]
    }
   ],
   "source": [
    "out =fill(regions,fixed,50,'pqffd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### September 2021 : Solution\n",
       "The above image shows the reconstructed path of the knight. The move\n",
       "count of 50 (and region sum of 75) can be deduced using three\n",
       "observations:\n",
       "the sum of all numbers must be a triangular number,\n",
       "the sum of all numbers must be divisible by the number of regions (17), and\n",
       "the regions of size 2 must have an odd sum by parity arguments of\n",
       "knight moves.\n",
       "Once this is known the path of the knight can be deduced by hand or\n",
       "with the aid of a program (we saw both solution methods). The sum of\n",
       "the squares of the maxima of each row comes to\n",
       "14820\n",
       ".\n",
       "Congrats to this month’s solvers who successfully deduced the\n",
       "knight’s path!"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "url='https://www.janestreet.com/puzzles/knight-moves-4-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[10:18])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://www.janestreet.com/puzzles/2021-09-01-knight-moves-4-solution.png\" width=350>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "regions1 =np.array([[0, 0, 0, 0, 0],\n",
    "                   [0, 0, 0, 0, 0],\n",
    "                   [0, 1, 0, 0, 0],\n",
    "                   [1, 1, 1, 1, 0],\n",
    "                   [1, 2, 2, 0, 0]])\n",
    "\n",
    "fixed1 =np.array([[1, 0, 0, 0, 0],\n",
    "                 [0, 0, 0, 0, 4],\n",
    "                 [0, 0, 0, 0, 0],\n",
    "                 [0, 0, 0, 0, 0],\n",
    "                 [0, 6, 0, 0, 0]])\n",
    "\n",
    "soln1 =np.array([[1, 0, 3, 0, 0],\n",
    "                 [0, 0, 0, 0, 4],\n",
    "                 [0, 2, 7, 0, 0],\n",
    "                 [8, 0, 0, 5, 0],\n",
    "                 [0, 6, 9, 0, 0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total for each region :  15.0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution is : 219\n",
      "[3, 4, 7, 8, 9]\n",
      "[9, 16, 49, 64, 81]\n",
      "Took 0.1556 seconds\n"
     ]
    }
   ],
   "source": [
    "out2 =fill(regions1,fixed1,9,'pqffd')"
   ]
  },
  {
   "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
}