2019_01_Fences.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "Oq1xibzMT1Wl"
   },
   "outputs": [],
   "source": [
    "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 skimage.morphology import label\n",
    "from collections import defaultdict\n",
    "import numba as nb\n",
    "from skimage.segmentation import clear_border"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "ICTfvjZUT1Wr"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A 17-by-17 field is divided into unit squares. Some of the squares contain “posts” at their center. Each post is represented below by a number. Construct one or more fences emanating from each post, such that the total length of fence connected to a post equals the number given. Fences have integer length and can only be constructed horizontally or vertically. Fences from different posts may not touch, nor may a fence from one post touch a different post. The goal of this puzzle is to build your fences in such a manner that it is possible to draw a closed loop through some of the remaining empty squares. The loop must enclose at least one post, and must be symmetric in some way (either via rotation or reflection). As in the example, the loop must be rectilinear, passing through the centers of adjacent empty squares. The answer to this puzzle is the product of the fence-lengths of the fences inside the loop . (Note that in the Example, the answer is 2 , not 4.)\n"
     ]
    }
   ],
   "source": [
    "# Computer assisted rather than computer solved for this one\n",
    "# The forced cells from the boundaries were easy enough to code\n",
    "# but the cells forced to be boundary to keep the path open were harder\n",
    "# got to a solution but seemed to have multiple choices on the 4 in [4,4]\n",
    "# until I noticed the symmetry condition which I then correct for\n",
    "\n",
    "\n",
    "url='https://www.janestreet.com/puzzles/fences/'\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "x =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "print(\" \".join(x[7:20]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "U9Yh1D3HT1Ws"
   },
   "source": [
    "### Puzzle details\n",
    "<img src=\"https://www.janestreet.com/puzzles/20190101_fences.png\" width=\"350\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Setup the constraints\n",
    "fixed = np.array([[0, 0, 0, 0, 0, 2, 0,  0, 0, 1, 0,  0, 0, 0, 0, 0, 5],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  3, 0, 0, 0,  0, 0, 0, 2, 0, 0],\n",
    "                  [0, 0, 0, 0, 3, 0, 0,  0, 0, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [5, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0, 22, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 4, 0, 0,  0, 0, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 0, 4, 0,  0, 0, 1, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0, 0, 0, 0,19, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 4, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 0, 2, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 9, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 3, 0, 0, 0,  2, 0, 0, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0, 4, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 8, 0,  0, 0, 0, 0,  0, 0, 0, 0, 0, 9],\n",
    "                  [0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0, 4, 0, 0, 0, 0],\n",
    "                  [0, 0, 3, 0, 0, 0, 0,  0, 0,15, 0,  0, 0, 0, 0, 0, 0],\n",
    "                  [6, 0, 0, 0, 0, 0, 0,  1, 0, 0, 0,  4, 0, 0, 0, 0, 0]],dtype=int)\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(6,6))\n",
    "x = np.array(fixed.astype('int').astype('str'))\n",
    "x[x==\"0\"] =\"-\"\n",
    "ax =sns.heatmap(fixed>0,annot=x,cbar=False,cmap=\"Reds\",center =2,fmt=\"\",linewidths=1)\n",
    "ax.axis(\"off\")\n",
    "plt.plot()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "class Matrix():\n",
    "    def __init__(self,fixed):\n",
    "        self.fixed = fixed\n",
    "        \n",
    "    #########################################\n",
    "    # force the lines \n",
    "\n",
    "    def clearance(self,grid,row,col):\n",
    "        num = grid[row,col]\n",
    "        \n",
    "        top = grid[:row,col][::-1]\n",
    "        bot = grid[row+1:,col]\n",
    "        lhs = grid[row,:col][::-1]\n",
    "        rhs = grid[row,col+1:]\n",
    "        bounds = [top,bot,lhs,rhs]\n",
    "        \n",
    "        allowed = [-num,0]\n",
    "        clearance = []\n",
    "        \n",
    "        for i in range(4):\n",
    "\n",
    "            for n in range(len(bounds[i])):\n",
    "                if bounds[i][n] not in allowed:\n",
    "                    n -=1\n",
    "                    break                        \n",
    "            if len(bounds[i])==0:\n",
    "                n=-1\n",
    "            clearance.append(n+1)\n",
    "        \n",
    "        return clearance\n",
    "    \n",
    "    def forced_by_clearance(self,grid):\n",
    "        for row,col in itertools.product(range(17),range(17)):\n",
    "            num = grid[row,col]\n",
    "            if num >0:\n",
    "                bounds = self.clearance(grid,row,col)\n",
    "                forced = [max(0,num-np.sum(bounds)+bounds[i]) for i in range(4)]\n",
    "                [top,bot,lhs,rhs] =forced\n",
    "                grid[row-top:row,col] = -num\n",
    "                grid[row+1:row+1+bot,col] = -num\n",
    "                grid[row,col-lhs:col] = -num\n",
    "                grid[row,col+1:col+1+rhs] = -num\n",
    "        return grid\n",
    "   \n",
    "    ##############################################\n",
    "    # Turn the grid moves into a nice format\n",
    "    def sol_print(self,grid):\n",
    "        fig,ax =plt.subplots(1,1,figsize=(5,5))\n",
    "        \n",
    "        y= dcopy(grid)\n",
    "        y[y>0] = 2\n",
    "        y[y==-99] = 1\n",
    "        y[y<0] = 0\n",
    "                \n",
    "        x = np.array(grid.astype('int').astype('str'))\n",
    "        x[x==\"0\"] =\"-\"\n",
    "        x[x==\"-99\"] =\"\"\n",
    "        ax =sns.heatmap(y,annot=x,cbar=False,cmap=\"Reds\",center =3,fmt=\"\",linewidths=1,ax=ax)\n",
    "        ax.axis(\"off\") \n",
    "        plt.tight_layout()\n",
    "        plt.plot\n",
    "                                         \n",
    "    ###############################################\n",
    "    # Main solver.  \n",
    "    def solve(self):\n",
    "        start = time.time()\n",
    "        grid=dcopy(fixed)\n",
    "        \n",
    "        # loop through and find the cells forced by the lengths of \n",
    "        # the fences. The 22 and 15 narrow things down a lot !\n",
    "        changed = True\n",
    "        while changed:\n",
    "            changed = False\n",
    "            copy_grid = dcopy(grid)\n",
    "            grid = self.forced_by_clearance(grid)\n",
    "            if np.any(copy_grid !=grid):\n",
    "                changed=True   \n",
    "        #self.sol_print(grid)\n",
    "        \n",
    "        # then iterate round the boundary making sure the path\n",
    "        # is clear. Did this manually\n",
    "        grid[6:9,0] = -99\n",
    "        grid[2:7,1] =-99\n",
    "        grid[0,10:13] = -99\n",
    "        grid[13,10:14] = -99\n",
    "        grid[2:5,14] = -99\n",
    "        grid[1,1:7] = -99\n",
    "        grid[2,6:11] =-99\n",
    "        grid[1,10] =-99\n",
    "        grid[1:3,12] =-99\n",
    "        grid[2,13 ]=-99\n",
    "        grid[4,12:14] =-99\n",
    "        grid[5:9,12]=-99\n",
    "        grid[11:14,14]=-99\n",
    "        grid[11,9]=-99\n",
    "        grid[11:15,8]=-99\n",
    "        grid[8:12,13]=-99\n",
    "        grid[11:13,10]=-99\n",
    "        grid[14,7]=-99\n",
    "        grid[8:15,6]=-99\n",
    "        grid[8,1:6]=-99\n",
    "        \n",
    "        #forced numbers\n",
    "        grid[15,0]=-3\n",
    "        grid[0,6]=-2\n",
    "        \n",
    "        #fix the symmetry to solve the 4\n",
    "        grid[0,1:4]=-99\n",
    "        grid[1,2]= 0\n",
    "        grid[4,1:4]=-99\n",
    "        grid[6,1:4]=-99\n",
    "        grid[5,3]=-99\n",
    "        grid[5,1]= 0\n",
    "        # fill in the rest\n",
    "        changed = True\n",
    "        while changed:\n",
    "            changed = False\n",
    "            copy_grid = dcopy(grid)\n",
    "            grid = self.forced_by_clearance(grid)\n",
    "            if np.any(copy_grid !=grid):\n",
    "                changed=True   \n",
    "        \n",
    "        self.sol_print(grid)\n",
    "        counts = np.unique(fixed,return_counts=True)\n",
    "        \n",
    "        for i in range(len(counts[0])):\n",
    "            num = counts[0][i]\n",
    "            count = counts[1][i] \n",
    "            if num ==0:\n",
    "                continue\n",
    "            print(\"Number of {}'s : {} (Should be {}) Status:{}\".format(num,np.sum(grid==-num),count*num,np.sum(grid==-num)==count*num))\n",
    "\n",
    "        print(\"\\nSolution is {:,.0f}\".format((2*1)*(2*2)*(2*2*9*9)*(2*2)*(1*1*1*1)*(3*3*3*6)*2*(1*1)*(3*1))) # legs for the 3,4,22,4,4,15,2,2,4 \n",
    "        print(\"\\n***Solved in {:.4f} seconds***\\n\".format(time.time() - start))    \n",
    "      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 374
    },
    "id": "zexQ8t1kT1W3",
    "outputId": "7c2aec4e-d2fb-45d8-fc7e-679051faafed"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of 1's : 3 (Should be 3) Status:True\n",
      "Number of 2's : 8 (Should be 8) Status:True\n",
      "Number of 3's : 12 (Should be 12) Status:True\n",
      "Number of 4's : 24 (Should be 24) Status:True\n",
      "Number of 5's : 10 (Should be 10) Status:True\n",
      "Number of 6's : 6 (Should be 6) Status:True\n",
      "Number of 8's : 8 (Should be 8) Status:True\n",
      "Number of 9's : 18 (Should be 18) Status:True\n",
      "Number of 15's : 30 (Should be 30) Status:True\n",
      "Number of 19's : 19 (Should be 19) Status:True\n",
      "Number of 22's : 22 (Should be 22) Status:True\n",
      "\n",
      "Solution is 10,077,696\n",
      "\n",
      "***Solved in 0.2364 seconds***\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = Matrix(fixed)\n",
    "test.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The unique configuration that works is shown to the left. The product of the lengths of the fences inside the loop is 10,077,696 . Nicely done, solvers!\n"
     ]
    }
   ],
   "source": [
    "url='https://www.janestreet.com/puzzles/solutions/january-2019-solution/'\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "x =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "print(\" \".join(x[7:10]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://www.janestreet.com/puzzles/20190130_fences_solved.png\" width=\"500\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "        "
   ]
  }
 ],
 "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
}