Towers-of-Hanoi-States-based-Search.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing PWE and other essentials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PW_explorer.run_clingo import run_clingo\n",
    "from PW_explorer.load_worlds import load_worlds\n",
    "from PW_explorer.pwe_helper import rel_slicer\n",
    "from PW_explorer.time_series import PWETimeSeriesModule\n",
    "from PW_explorer.pwe_nb_helper import ASPRules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.CodeCell.options_default.highlight_modes['prolog'] = {'reg':[/^%%(clingo|dlv)/]};"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%load_ext PWE_NB_Extension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulating the Towers of Hanoi Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the towers of Hanoi instance with 3 pegs and 3 disks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-run -lci toh_instance --donot-display_input\n",
    "\n",
    "#const num_disks=3.\n",
    "% schema peg(PEG)\n",
    "peg(a;b;c).              % Define the 3 pegs a,b,c\n",
    "% schema disk(DISK)\n",
    "disk(1..num_disks).      % Define the three disks.\n",
    "% schema init_on(DISK, PEG)\n",
    "init_on(1..num_disks,a). % Define the initial position of the disks\n",
    "% schema goal_on(DISK, PEG)\n",
    "goal_on(1..num_disks,c). % Define the desired final position of the disks\n",
    "moves(7).                % Define the maximum number of moves allowed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the encoding of the rules of the game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-run -lci toh_encoding --donot-display_input\n",
    "\n",
    "% schema move(TIME, DISK, PEG)\n",
    "% temporal move(T,_,_)\n",
    "% Generate a move at each time-step\n",
    "{ move(T,D,P) : disk(D), peg(P) } = 1 :- moves(M),  T = 1..M.\n",
    "\n",
    "% schema move(TIME, DISK)\n",
    "% temporal move(T,_)\n",
    "move(T,D)   :- move(T,D,_).\n",
    "\n",
    "% schema on(TIME, DISK, PEG)\n",
    "% temporal on(T,_,_)\n",
    "on(0,D,P)   :- init_on(D,P).\n",
    "\n",
    "% Update state\n",
    "% Update location of moved disk\n",
    "on(T,D,P)   :- move(T,D,P).\n",
    "% Maintain disk D’s position at time-step T+1 if not moved\n",
    "on(T+1,D,P) :- on(T,D,P), not move(T+1,D), not moves(T).\n",
    "\n",
    "% schema blocked(TIME, DISK, PEG)\n",
    "% temporal blocked(T,_,_)\n",
    "\n",
    "% If disk D is on peg P at time-step T, then at time-step T+1\n",
    "% disk D-1 cannot be moved to peg P\n",
    "blocked(T+1,D-1,P) :- on(T,D,P), not moves(T).\n",
    "% If disk D cannot be moved to peg P at time-step T,\n",
    "% then neither can disk D-1 (and so on..)\n",
    "blocked(T,D-1,P)   :- blocked(T,D,P), disk(D).\n",
    "\n",
    "% Test the validity of move at time-step T\n",
    ":- move(T,D,P), blocked(T,D-1,P).\n",
    ":- move(T,D), on(T-1,D,P), blocked(T,D,P).\n",
    "\n",
    "% Test the validity of the sequence of moves:\n",
    "% Series of steps doesn’t achieve goal\n",
    ":- goal_on(D,P), not on(M,D,P), moves(M).\n",
    "% Disk is not on exactly one peg at any time-step\n",
    ":- { on(T,D,P) } != 1, disk(D), moves(M), T = 1..M.\n",
    "\n",
    "%% % Display\n",
    "%% #show move/3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "clingo_rules = toh_encoding.splitlines()+toh_instance.splitlines()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running this carefully constructed to yield exactly one PW example with clingo "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\">1 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">2 </span><span class=\"nf\">disk</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">disk</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">disk</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">peg</span><span class=\"p\">(</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">peg</span><span class=\"p\">(</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">peg</span><span class=\"p\">(</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">moves</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">)</span> <span class=\"nf\">init_on</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">init_on</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">init_on</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">goal_on</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">goal_on</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">goal_on</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">on</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">move</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">b</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">6</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">0</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"s s-Atom\">c</span><span class=\"p\">)</span> <span class=\"nf\">blocked</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"s s-Atom\">a</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">3 </span><span class=\"nv\">SATISFIABLE</span>\n",
       "<span class=\"lineno\">4 </span>\n",
       "<span class=\"lineno\">5 </span><span class=\"nv\">Models</span>       <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">6 </span><span class=\"nv\">Calls</span>        <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">7 </span><span class=\"nv\">Time</span>         <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.005</span><span class=\"nf\">s</span> <span class=\"p\">(</span><span class=\"nv\">Solving</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"mi\">1</span><span class=\"s s-Atom\">st</span> <span class=\"nv\">Model</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"nv\">Unsat</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">8 </span><span class=\"nv\">CPU</span> <span class=\"nv\">Time</span>     <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.004</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\ndisk(1) disk(2) disk(3) peg(a) peg(b) peg(c) moves(7) init_on(1,a) init_on(2,a) init_on(3,a) on(0,1,a) on(0,2,a) on(0,3,a) blocked(1,0,a) blocked(1,1,a) blocked(1,2,a) goal_on(1,c) goal_on(2,c) goal_on(3,c) on(1,1,a) on(1,2,a) blocked(2,0,a) blocked(2,1,a) on(1,3,c) move(1,3,c) on(2,1,a) on(2,2,b) move(2,2,b) on(2,3,c) on(3,1,a) on(3,2,b) on(3,3,b) move(3,3,b) on(4,1,c) move(4,1,c) on(4,2,b) on(4,3,b) on(5,1,c) on(5,2,b) on(5,3,a) move(5,3,a) on(6,1,c) on(6,2,c) move(6,2,c) on(6,3,a) on(7,1,c) on(7,2,c) on(7,3,c) move(7,3,c) move(1,3) move(2,2) move(3,3) move(4,1) move(5,3) move(6,2) move(7,3) blocked(2,0,c) blocked(2,1,c) blocked(2,2,c) blocked(3,0,a) blocked(3,0,b) blocked(3,0,c) blocked(3,1,b) blocked(3,1,c) blocked(3,2,c) blocked(4,0,a) blocked(4,0,b) blocked(4,1,b) blocked(4,2,b) blocked(5,0,b) blocked(5,0,c) blocked(5,1,b) blocked(5,2,b) blocked(6,0,a) blocked(6,0,b) blocked(6,0,c) blocked(6,1,a) blocked(6,1,b) blocked(6,2,a) blocked(7,0,a) blocked(7,0,c) blocked(7,1,a) blocked(7,1,c) blocked(7,2,a)\\nSATISFIABLE\\n\\nModels       : 1\\nCalls        : 1\\nTime         : 0.005s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.004s'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clingo_soln, meta_data = run_clingo(clingo_rules=clingo_rules)\n",
    "ASPRules('\\n'.join(clingo_soln))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the extracted meta data for the ASP formulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'temporal_dec': {'move_3': [0], 'move_2': [0], 'on_3': [0], 'blocked_3': [0]},\n",
       " 'attr_def': {'move_3': ['TIME', 'DISK', 'PEG'],\n",
       "  'move_2': ['TIME', 'DISK'],\n",
       "  'on_3': ['TIME', 'DISK', 'PEG'],\n",
       "  'blocked_3': ['TIME', 'DISK', 'PEG'],\n",
       "  'peg_1': ['PEG'],\n",
       "  'disk_1': ['DISK'],\n",
       "  'init_on_2': ['DISK', 'PEG'],\n",
       "  'goal_on_2': ['DISK', 'PEG']},\n",
       " 'graphviz': {'graph': {'graph_type': 'undirected', 'styles': []},\n",
       "  'node': {},\n",
       "  'edge': {}}}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meta_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we load the solution using PWE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 1\n"
     ]
    }
   ],
   "source": [
    "pw_rels_dfs, rel_schemas, pw_objs = load_worlds(asp_output=clingo_soln, meta_data=meta_data, reasoner='clingo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'relation_name': 'disk_1',\n",
       "  'arity': 1,\n",
       "  'r_id': 0,\n",
       "  'meta_data': {'attr_def': ['DISK']}},\n",
       " {'relation_name': 'peg_1',\n",
       "  'arity': 1,\n",
       "  'r_id': 1,\n",
       "  'meta_data': {'attr_def': ['PEG']}},\n",
       " {'relation_name': 'moves_1', 'arity': 1, 'r_id': 2, 'meta_data': {}},\n",
       " {'relation_name': 'init_on_2',\n",
       "  'arity': 2,\n",
       "  'r_id': 3,\n",
       "  'meta_data': {'attr_def': ['DISK', 'PEG']}},\n",
       " {'relation_name': 'on_3',\n",
       "  'arity': 3,\n",
       "  'r_id': 4,\n",
       "  'meta_data': {'attr_def': ['TIME', 'DISK', 'PEG'], 'temporal_dec': [0]}},\n",
       " {'relation_name': 'blocked_3',\n",
       "  'arity': 3,\n",
       "  'r_id': 5,\n",
       "  'meta_data': {'attr_def': ['TIME', 'DISK', 'PEG'], 'temporal_dec': [0]}},\n",
       " {'relation_name': 'goal_on_2',\n",
       "  'arity': 2,\n",
       "  'r_id': 6,\n",
       "  'meta_data': {'attr_def': ['DISK', 'PEG']}},\n",
       " {'relation_name': 'move_3',\n",
       "  'arity': 3,\n",
       "  'r_id': 7,\n",
       "  'meta_data': {'attr_def': ['TIME', 'DISK', 'PEG'], 'temporal_dec': [0]}},\n",
       " {'relation_name': 'move_2',\n",
       "  'arity': 2,\n",
       "  'r_id': 8,\n",
       "  'meta_data': {'attr_def': ['TIME', 'DISK'], 'temporal_dec': [0]}}]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(lambda x: x.__dict__, rel_schemas))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have parsed the following relations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['disk_1', 'peg_1', 'moves_1', 'init_on_2', 'on_3', 'blocked_3', 'goal_on_2', 'move_3', 'move_2'])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pw_rels_dfs.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And they are each stored in a Pandas Dataframe which looks like this:\n",
    "\n",
    "(Also notice that the column names were inferred from the meta_data we parsed earlier)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pw</th>\n",
       "      <th>TIME</th>\n",
       "      <th>DISK</th>\n",
       "      <th>PEG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    pw  TIME DISK PEG\n",
       "0    1     0    1   a\n",
       "1    1     0    2   a\n",
       "2    1     0    3   a\n",
       "3    1     1    1   a\n",
       "4    1     1    2   a\n",
       "5    1     1    3   c\n",
       "6    1     2    1   a\n",
       "7    1     2    2   b\n",
       "8    1     2    3   c\n",
       "9    1     3    1   a\n",
       "10   1     3    2   b\n",
       "11   1     3    3   b\n",
       "12   1     4    1   c\n",
       "13   1     4    2   b\n",
       "14   1     4    3   b\n",
       "15   1     5    1   c\n",
       "16   1     5    2   b\n",
       "17   1     5    3   a\n",
       "18   1     6    1   c\n",
       "19   1     6    2   c\n",
       "20   1     6    3   a\n",
       "21   1     7    1   c\n",
       "22   1     7    2   c\n",
       "23   1     7    3   c"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pw_rels_dfs['on_3']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### All these are hard to make sense of, especially since there's time states involved.\n",
    "##### A simple groupby on the temporal columns would go a long way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sliced_dfs, sliced_rels, _ = rel_slicer(pw_rels_dfs, rel_schemas, None, ['move_3', 'on_3', \n",
    "                                                                         'init_on_2', 'peg_1', \n",
    "                                                                         'goal_on_2', 'disk_1',])\n",
    "timestep_state_map = PWETimeSeriesModule.group_by_time(sliced_dfs, sliced_rels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'constant': {'init_on_2':    pw DISK PEG\n",
       "  0   1    1   a\n",
       "  1   1    2   a\n",
       "  2   1    3   a, 'disk_1':    pw DISK\n",
       "  0   1    1\n",
       "  1   1    2\n",
       "  2   1    3, 'goal_on_2':    pw DISK PEG\n",
       "  0   1    1   c\n",
       "  1   1    2   c\n",
       "  2   1    3   c, 'peg_1':    pw PEG\n",
       "  0   1   a\n",
       "  1   1   b\n",
       "  2   1   c}, 0: {'on_3':    pw DISK PEG\n",
       "  0   1    1   a\n",
       "  1   1    2   a\n",
       "  2   1    3   a}, 1: {'on_3':    pw DISK PEG\n",
       "  3   1    1   a\n",
       "  4   1    2   a\n",
       "  5   1    3   c, 'move_3':    pw DISK PEG\n",
       "  0   1    3   c}, 2: {'on_3':    pw DISK PEG\n",
       "  6   1    1   a\n",
       "  7   1    2   b\n",
       "  8   1    3   c, 'move_3':    pw DISK PEG\n",
       "  1   1    2   b}, 3: {'on_3':     pw DISK PEG\n",
       "  9    1    1   a\n",
       "  10   1    2   b\n",
       "  11   1    3   b, 'move_3':    pw DISK PEG\n",
       "  2   1    3   b}, 4: {'on_3':     pw DISK PEG\n",
       "  12   1    1   c\n",
       "  13   1    2   b\n",
       "  14   1    3   b, 'move_3':    pw DISK PEG\n",
       "  3   1    1   c}, 5: {'on_3':     pw DISK PEG\n",
       "  15   1    1   c\n",
       "  16   1    2   b\n",
       "  17   1    3   a, 'move_3':    pw DISK PEG\n",
       "  4   1    3   a}, 6: {'on_3':     pw DISK PEG\n",
       "  18   1    1   c\n",
       "  19   1    2   c\n",
       "  20   1    3   a, 'move_3':    pw DISK PEG\n",
       "  5   1    2   c}, 7: {'on_3':     pw DISK PEG\n",
       "  21   1    1   c\n",
       "  22   1    2   c\n",
       "  23   1    3   c, 'move_3':    pw DISK PEG\n",
       "  6   1    3   c}}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timestep_state_map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not very fun to look at either"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### So we can use this built-in text-based visualization for a clearer understanding of the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constants:\n",
      "\n",
      "init_on_2:\n"
     ]
    },
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       "   pw DISK PEG\n",
       "0   1    1   a\n",
       "1   1    2   a\n",
       "2   1    3   a"
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      "\n",
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       "   pw DISK\n",
       "0   1    1\n",
       "1   1    2\n",
       "2   1    3"
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       "   pw DISK PEG\n",
       "0   1    1   c\n",
       "1   1    2   c\n",
       "2   1    3   c"
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      "peg_1:\n"
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       "   pw PEG\n",
       "0   1   a\n",
       "1   1   b\n",
       "2   1   c"
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 0:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
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       "   pw DISK PEG\n",
       "0   1    1   a\n",
       "1   1    2   a\n",
       "2   1    3   a"
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 1:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
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       "   pw DISK PEG\n",
       "3   1    1   a\n",
       "4   1    2   a\n",
       "5   1    3   c"
      ]
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      "\n",
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       "   pw DISK PEG\n",
       "0   1    3   c"
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 2:\n",
      "---------------\n",
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      "text/plain": [
       "   pw DISK PEG\n",
       "1   1    2   b"
      ]
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    {
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     "text": [
      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 3:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
     ]
    },
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       "    pw DISK PEG\n",
       "9    1    1   a\n",
       "10   1    2   b\n",
       "11   1    3   b"
      ]
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      "\n",
      "\n",
      "move_3:\n"
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       "   pw DISK PEG\n",
       "2   1    3   b"
      ]
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 4:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
     ]
    },
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      "text/plain": [
       "    pw DISK PEG\n",
       "12   1    1   c\n",
       "13   1    2   b\n",
       "14   1    3   b"
      ]
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      "\n",
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      "move_3:\n"
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       "   pw DISK PEG\n",
       "3   1    1   c"
      ]
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 5:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
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       "    pw DISK PEG\n",
       "15   1    1   c\n",
       "16   1    2   b\n",
       "17   1    3   a"
      ]
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       "   pw DISK PEG\n",
       "4   1    3   a"
      ]
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 6:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
     ]
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       "    pw DISK PEG\n",
       "18   1    1   c\n",
       "19   1    2   c\n",
       "20   1    3   a"
      ]
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       "   pw DISK PEG\n",
       "5   1    2   c"
      ]
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      "\n",
      "\n",
      "\n",
      "---------------\n",
      "Timestep 7:\n",
      "---------------\n",
      "\n",
      "on_3:\n"
     ]
    },
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       "    pw DISK PEG\n",
       "21   1    1   c\n",
       "22   1    2   c\n",
       "23   1    3   c"
      ]
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      "\n",
      "\n",
      "move_3:\n"
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      "text/plain": [
       "   pw DISK PEG\n",
       "6   1    3   c"
      ]
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     "text": [
      "\n",
      "END\n"
     ]
    }
   ],
   "source": [
    "PWETimeSeriesModule.simple_timeseries_text_visualization(timestep_state_map, jupyter=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building a Custom Visualization for the TOH problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# More informative custom visualization (still a WIP)\n",
    "# Inspired by: https://stackoverflow.com/questions/49391076/illustrate-tower-of-hanoi-with-ascii\n",
    "def toh_viz(timestep_state_map):\n",
    "    \n",
    "    NUM_DISKS = len(timestep_state_map['constant']['disk_1'])\n",
    "    NUM_PEGS = len(timestep_state_map['constant']['peg_1'])\n",
    "    PEG_SIZE = NUM_DISKS + 2\n",
    "    \n",
    "    def get_state(state_df):\n",
    "        pegs = [[] for _ in range(NUM_PEGS)]\n",
    "        for i, row in state_df.iterrows():\n",
    "            pegs[ord(row['PEG']) - ord('a')].append(NUM_DISKS+1-int(row['DISK']))\n",
    "        pegs = [sorted(peg) for peg in pegs]\n",
    "        return pegs\n",
    "    \n",
    "    def render_ring(ring):\n",
    "        result = '*' * ring  # the character * repeated ring times.\n",
    "        return result.center(PEG_SIZE) # add the spaces required\n",
    "    def render_tower(tower, tower_id):\n",
    "        result = [render_ring(0) for _ in range(NUM_DISKS-len(tower))] #[]\n",
    "        for ring in tower:\n",
    "            result.append(render_ring(ring))\n",
    "        result.append(str(tower_id).center(PEG_SIZE))\n",
    "        return result\n",
    "    def render_final(towers): \n",
    "        tower_results = []\n",
    "        for i, tower in enumerate(towers):\n",
    "            tower_results.append(render_tower(tower, chr(ord('a')+i)))\n",
    "        result = []\n",
    "        for all_rows in zip(*tower_results):\n",
    "            result.append(''.join(all_rows)) \n",
    "        return result\n",
    "    \n",
    "    print(\"Initial State:\")\n",
    "    print('\\n'.join(render_final(get_state(timestep_state_map['constant']['init_on_2']))))\n",
    "    print(\"\")\n",
    "    print(\"Goal:\")\n",
    "    print('\\n'.join(render_final(get_state(timestep_state_map['constant']['goal_on_2']))))\n",
    "    print(\"\")\n",
    "    for t in sorted(set(timestep_state_map.keys()) - set(['constant'])):\n",
    "        print(\"Timestep: {}\".format(t))\n",
    "        print(\"\")\n",
    "        if 'move_3' in timestep_state_map[t]:\n",
    "            for i, row in timestep_state_map[t]['move_3'].iterrows():\n",
    "                print(\"Move {} to peg {}.\".format('*'*(NUM_DISKS+1-int(row['DISK'])), row['PEG']))\n",
    "        print('\\n'.join(render_final(get_state(timestep_state_map[t]['on_3']))))\n",
    "        print(\"\")\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Now let's use the above user-defined visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial State:\n",
      "  *            \n",
      "  **           \n",
      " ***           \n",
      "  a    b    c  \n",
      "\n",
      "Goal:\n",
      "            *  \n",
      "            ** \n",
      "           *** \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 0\n",
      "\n",
      "  *            \n",
      "  **           \n",
      " ***           \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 1\n",
      "\n",
      "Move * to peg c.\n",
      "               \n",
      "  **           \n",
      " ***        *  \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 2\n",
      "\n",
      "Move ** to peg b.\n",
      "               \n",
      "               \n",
      " ***   **   *  \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 3\n",
      "\n",
      "Move * to peg b.\n",
      "               \n",
      "       *       \n",
      " ***   **      \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 4\n",
      "\n",
      "Move *** to peg c.\n",
      "               \n",
      "       *       \n",
      "       **  *** \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 5\n",
      "\n",
      "Move * to peg a.\n",
      "               \n",
      "               \n",
      "  *    **  *** \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 6\n",
      "\n",
      "Move ** to peg c.\n",
      "               \n",
      "            ** \n",
      "  *        *** \n",
      "  a    b    c  \n",
      "\n",
      "Timestep: 7\n",
      "\n",
      "Move * to peg c.\n",
      "            *  \n",
      "            ** \n",
      "           *** \n",
      "  a    b    c  \n",
      "\n"
     ]
    }
   ],
   "source": [
    "toh_viz(timestep_state_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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