Partitions-Bell-Number.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PW_explorer.load_worlds import load_worlds\n",
    "from PW_explorer.run_clingo import run_clingo\n",
    "from PW_explorer.visualize import PWEVisualization\n",
    "from PW_explorer.helper import pw_slicer, rel_slicer, rel_name_remapper\n",
    "from PW_explorer.export import PWEExport"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os.path\n",
    "from nxpd import draw\n",
    "from nxpd import nxpdParams\n",
    "nxpdParams['show'] = 'ipynb'\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper Python Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_edge_facts(pw, edge_rel_idx):\n",
    "    \"\"\"\n",
    "    Converts the tog/2 into e/2 edges and exports the PW as a string containing ASP Facts.\n",
    "    \"\"\"\n",
    "    pw_objs = [pw]\n",
    "    _,_,pw_objs = rel_slicer(None, None, pw_objs, rels_to_use=['tog_2'])\n",
    "    _, pw_objs, _ = rel_name_remapper(None, pw_objs, None, \n",
    "                                      rel_name_map={'tog_2': 'tog{}_2'.format(str(edge_rel_idx))})\n",
    "    return PWEExport.export_as_asp_facts(pw_objs, include_pw_ids=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Refinement Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_refinement_rels(objs, refinement_check_func):\n",
    "    \"\"\"\n",
    "    This function finds the set of all refinement relations between all the PWs\n",
    "    \"\"\"\n",
    "    refinement_rels = []\n",
    "    for i, pw_1 in enumerate(objs):\n",
    "        for j, pw_2 in enumerate(objs):\n",
    "            if i == j:\n",
    "                continue\n",
    "            if refinement_check_func(pw_1, pw_2):\n",
    "                refinement_rels.append((pw_1.pw_id, pw_2.pw_id))\n",
    "    return refinement_rels\n",
    "\n",
    "\n",
    "def refinement_check(pw1, pw2, refinement_check_encoding):\n",
    "    \"\"\"\n",
    "    This function checks if PW1 is a refinement of PW2 using a given encoding of \n",
    "    the refinement relation to use.\n",
    "    \"\"\"\n",
    "    pw1_edge_facts = get_edge_facts(pw1, 1)\n",
    "    pw2_edge_facts = get_edge_facts(pw2, 2)\n",
    "    # print(pw1_edge_facts, pw2_edge_facts)\n",
    "    asp_out, _ = run_clingo(refinement_check_encoding.split('\\n')+pw1_edge_facts+pw2_edge_facts, num_solutions=1)\n",
    "    # print(asp_out)\n",
    "    _,_,eq_check_pws = load_worlds(asp_out, silent=True)\n",
    "    \n",
    "    return len(eq_check_pws) >= 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Efficient Grouping Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_equivalent_sets(objs, match_func):\n",
    "    \"\"\"\n",
    "    This function efficiently computes the disjoint sets of equivalent \n",
    "    PWs using the given match_func\n",
    "    \"\"\"\n",
    "    sets = []\n",
    "    curr_iter_set = list(range(len(objs)))\n",
    "    while len(curr_iter_set) > 0:\n",
    "        next_iter_set = []\n",
    "        seed = curr_iter_set[0]\n",
    "        curr_set = {objs[seed]}\n",
    "        for c in curr_iter_set[1:]:\n",
    "            if match_func(objs[seed], objs[c]):\n",
    "                curr_set.add(objs[c])\n",
    "            else:\n",
    "                next_iter_set.append(c)\n",
    "        sets.append(curr_set)\n",
    "        curr_iter_set = next_iter_set\n",
    "    return sets\n",
    "\n",
    "\n",
    "def are_equivalent_patterns(pw1, pw2, eq_check_encoding):\n",
    "    \"\"\"\n",
    "    This function checks if PW1 and PW2 are equivalent based on the equivalence \n",
    "    function defined by eq_check_encoding\n",
    "    \"\"\"    \n",
    "    pw1_edge_facts = get_edge_facts(pw1, 1)\n",
    "    pw2_edge_facts = get_edge_facts(pw2, 2)\n",
    "    # print(pw1_edge_facts, pw2_edge_facts)\n",
    "    asp_out, _ = run_clingo(eq_check_encoding.split('\\n')+pw1_edge_facts+pw2_edge_facts, num_solutions=1)\n",
    "    # print(asp_out)\n",
    "    _,_,eq_check_pws = load_worlds(asp_out, silent=True)\n",
    "    \n",
    "    return len(eq_check_pws) >= 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partitions Encoding\n",
    "\n",
    "We can encode partitions of n (named) objects in Datalog as follows (here n=4):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
    },
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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\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">2</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">3</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">4</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">5</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">6</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">13 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">7</span>\n",
       "<span class=\"lineno\">14 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">8</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">17 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">9</span>\n",
       "<span class=\"lineno\">18 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">19 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">10</span>\n",
       "<span class=\"lineno\">20 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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\">tog</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\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">21 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">11</span>\n",
       "<span class=\"lineno\">22 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">23 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">12</span>\n",
       "<span class=\"lineno\">24 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">25 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">13</span>\n",
       "<span class=\"lineno\">26 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">27 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">14</span>\n",
       "<span class=\"lineno\">28 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">29 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">15</span>\n",
       "<span class=\"lineno\">30 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">31 </span><span class=\"nv\">SATISFIABLE</span>\n",
       "<span class=\"lineno\">32 </span>\n",
       "<span class=\"lineno\">33 </span><span class=\"nv\">Models</span>       <span class=\"s s-Atom\">:</span> <span class=\"mi\">15</span>\n",
       "<span class=\"lineno\">34 </span><span class=\"nv\">Calls</span>        <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">35 </span><span class=\"nv\">Time</span>         <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.001</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\">36 </span><span class=\"nv\">CPU</span> <span class=\"nv\">Time</span>     <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.001</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\nobj(1) obj(2) obj(3) obj(4)\\nAnswer: 2\\nobj(1) obj(2) obj(3) obj(4) tog(4,2) tog(2,4)\\nAnswer: 3\\nobj(1) obj(2) obj(3) obj(4) tog(4,3) tog(3,4)\\nAnswer: 4\\nobj(1) obj(2) obj(3) obj(4) tog(3,2) tog(2,3)\\nAnswer: 5\\nobj(1) obj(2) obj(3) obj(4) tog(3,2) tog(4,2) tog(2,3) tog(4,3) tog(2,4) tog(3,4)\\nAnswer: 6\\nobj(1) obj(2) obj(3) obj(4) tog(4,1) tog(1,4)\\nAnswer: 7\\nobj(1) obj(2) obj(3) obj(4) tog(4,1) tog(3,2) tog(2,3) tog(1,4)\\nAnswer: 8\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(1,3)\\nAnswer: 9\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(4,2) tog(1,3) tog(2,4)\\nAnswer: 10\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(4,1) tog(1,3) tog(4,3) tog(1,4) tog(3,4)\\nAnswer: 11\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(1,2)\\nAnswer: 12\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(1,2) tog(4,3) tog(3,4)\\nAnswer: 13\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(3,1) tog(1,2) tog(3,2) tog(1,3) tog(2,3)\\nAnswer: 14\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(4,1) tog(1,2) tog(4,2) tog(1,4) tog(2,4)\\nAnswer: 15\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(3,1) tog(4,1) tog(1,2) tog(3,2) tog(4,2) tog(1,3) tog(2,3) tog(4,3) tog(1,4) tog(2,4) tog(3,4)\\nSATISFIABLE\\n\\nModels       : 15\\nCalls        : 1\\nTime         : 0.001s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.001s'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%clingo --donot-display_input\n",
    "\n",
    "% Define the n objects.\n",
    "obj(1..4).\n",
    "\n",
    "% Generate \"equivalence\" between objects\n",
    "tog(A,B) ; not tog(A,B) :- obj(A), obj(B), A!=B.\n",
    "\n",
    "% Define symmetric property between equivalent objects\n",
    "tog(A,B) :- tog(B,A).\n",
    "\n",
    "% Define transitivity property between the equivalent objects\n",
    "tog(A,B) :- tog(A,C), tog(C,B), A!=B, B!=C, A!=C."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An equivalent way to encode this shown below. Note that the encoding above uses the \"Generate-Define\" protocol while the one below uses a \"Generate-Test\" approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       ".highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".highlight .nv { color: #19177C } /* Name.Variable */\n",
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "output_type": "display_data"
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    {
     "data": {
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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\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">2</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">3</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">4</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">5</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">6</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">13 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">7</span>\n",
       "<span class=\"lineno\">14 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">8</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">17 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">9</span>\n",
       "<span class=\"lineno\">18 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">19 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">10</span>\n",
       "<span class=\"lineno\">20 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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\">tog</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\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">21 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">11</span>\n",
       "<span class=\"lineno\">22 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">23 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">12</span>\n",
       "<span class=\"lineno\">24 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">25 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">13</span>\n",
       "<span class=\"lineno\">26 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">27 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">14</span>\n",
       "<span class=\"lineno\">28 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">29 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">15</span>\n",
       "<span class=\"lineno\">30 </span><span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">obj</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</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=\"nf\">tog</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\">tog</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=\"nf\">tog</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=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">tog</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">31 </span><span class=\"nv\">SATISFIABLE</span>\n",
       "<span class=\"lineno\">32 </span>\n",
       "<span class=\"lineno\">33 </span><span class=\"nv\">Models</span>       <span class=\"s s-Atom\">:</span> <span class=\"mi\">15</span>\n",
       "<span class=\"lineno\">34 </span><span class=\"nv\">Calls</span>        <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">35 </span><span class=\"nv\">Time</span>         <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.001</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\">36 </span><span class=\"nv\">CPU</span> <span class=\"nv\">Time</span>     <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.001</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\nobj(1) obj(2) obj(3) obj(4)\\nAnswer: 2\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(1,3)\\nAnswer: 3\\nobj(1) obj(2) obj(3) obj(4) tog(3,2) tog(2,3)\\nAnswer: 4\\nobj(1) obj(2) obj(3) obj(4) tog(4,1) tog(1,4)\\nAnswer: 5\\nobj(1) obj(2) obj(3) obj(4) tog(4,1) tog(3,2) tog(2,3) tog(1,4)\\nAnswer: 6\\nobj(1) obj(2) obj(3) obj(4) tog(4,2) tog(2,4)\\nAnswer: 7\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(4,2) tog(1,3) tog(2,4)\\nAnswer: 8\\nobj(1) obj(2) obj(3) obj(4) tog(4,3) tog(3,4)\\nAnswer: 9\\nobj(1) obj(2) obj(3) obj(4) tog(3,2) tog(4,2) tog(2,3) tog(4,3) tog(2,4) tog(3,4)\\nAnswer: 10\\nobj(1) obj(2) obj(3) obj(4) tog(3,1) tog(4,1) tog(1,3) tog(4,3) tog(1,4) tog(3,4)\\nAnswer: 11\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(1,2)\\nAnswer: 12\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(4,1) tog(1,2) tog(4,2) tog(1,4) tog(2,4)\\nAnswer: 13\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(1,2) tog(4,3) tog(3,4)\\nAnswer: 14\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(3,1) tog(1,2) tog(3,2) tog(1,3) tog(2,3)\\nAnswer: 15\\nobj(1) obj(2) obj(3) obj(4) tog(2,1) tog(3,1) tog(4,1) tog(1,2) tog(3,2) tog(4,2) tog(1,3) tog(2,3) tog(4,3) tog(1,4) tog(2,4) tog(3,4)\\nSATISFIABLE\\n\\nModels       : 15\\nCalls        : 1\\nTime         : 0.001s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.001s'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%clingo --donot-display_input -exp partitions\n",
    "\n",
    "% Define the n objects.\n",
    "obj(1..4).\n",
    "\n",
    "% Generate \"equivalence\" between objects\n",
    "tog(A,B) ; not tog(A,B) :- obj(A), obj(B), A!=B.\n",
    "\n",
    "% Test that the symmetric property between equivalent objects holds\n",
    ":- tog(A,B), not tog(B,A).\n",
    "\n",
    "% Test that the transitivity property between the equivalent objects holds\n",
    ":- not tog(A,B), tog(A,C), tog(C,B), A!=B, B!=C, A!=C.\n",
    "\n",
    "% Define some graphviz annotation for quick visualizations\n",
    "\n",
    "%graphviz graph graph_type=undirected rankdir=TB\n",
    "%graphviz edge tog(HEAD, TAIL)\n",
    "%graphviz node obj(N) colorscheme=pastel28 color=$1 style=filled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 15\n"
     ]
    }
   ],
   "source": [
    "partitions['pw_rel_dfs'], partitions['rel_schema'], partitions['pw_objs'] = load_worlds(partitions['asp_soln'],\n",
    "                                                                                        partitions['meta_data'])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize these partitions very simply using PWE's built-in visualization function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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Q5cpMFejPVooAmXSKg3uKFAfiX3hpS9q73JnpU/RtK0UE0gPIgXcgxYm4q9kaY/CuV/EuL7d/258fACuTIn1oGPvuxgfvLkxWNL2AK7NVFkp1MILph6huzx/ZOzHA5Ei+v0fqvTpm+iXMwiVA+iRU2vNH9rwVmTjS1zN9TTOgeWUZf77Wusj3x+kPKcHZO9h63ubuPwDRhMkKtxlwda7KfKm1G12SktrQbr0ZsG2LPeMDTIzksO6sSZdMbgVz7TRm4SKJDBVZ+QdII7ve0gqRPujSbFbo+njTZfz5euuFBJ3/wOqNKLFtnD2FVohEd/5HGyYrPD9kbqnO7EKNph/GunIbsHr8Yj7N5GiO4eI2f+bIc1uDtLNnwavHu3KbALSOL4UJmDjSut3bxy2R2zFeiD9XxZupYJphvAu3Sft/xmAX06QmC6RGuvLMUXfC5EaVWpPFZZeFZRfPD9pjPe0rVJeItLtaBgZyDqODWYYHM2Sc7XMV3BwDlXnM0hXM4uXW/sUrJ1E3/9lXw0tgYLg1i3d4H6S3dqtxOwjKTYLFOv5CDeOFN52bXXNDetkDaezRHKmRHJLp6vnf/TC5Ud31KVebVGoey1UXv73/xkorYeulyA3vm0EEMo7NYCFDMe9QyKdjmwafSPVlTGUWKrOt/XpX9uhZbSWYrYVMe3IToWl9rwhkCkhxsvXUc2EitmnwSRTWPYJyk7DsEiy7GL/dWpT2w4TmDkJGpP09ZnUw1R7MYBUz2MXMpqbBR6S3YXIrPwipN3zqro/bDPD8ENcL8P2AIDSERjh/9gzffOYp/t7HfrL19KIFtiU4jk3asUmnLLKZFLlMilzG3t7dl6j5TUy9BI1lcCut7lGz2mrBhH4rJIzfOsnFboWObbcGTp08pHPg5CBbRLKDrRXQtnH3JWrGDwnrHmHdxzR8jBdgmj7GC1sbXZn2HjXGtM5rS8ACsSwkk0LSFpK2sbIprJyDlUvF+chFvGGyGV/+8pf58Ic/nKjBXKXUGuuvAauUUlulYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKhYaKUioSGiVIqEhomSqlIaJgopSKRiruAGxkMbuDjBh6+CTAGTN7h/gffzky9hCUWlgiOlSJrp3CsRJWv1I4mxhjT64MGJqTUrLHs1Sl7dUrNOlXfxQ8DDJsvR8Qia6UopLMMOjmKqRxD6TxFJ9vF6pVS6zjRk0u7AZaaVWbqJebcMkvNGsYYBGl//c7yzJiQetCkUW8yXy9jxGAMOGIzmi0ykS2yKzdEzk5H+LdRSq2nqy2TBbfCldoiV2uLNEMfEaHbDSEDSPs/2scrOjn25UeYGhgjaztdPb5SO9SJyMPENyGXq/OcL89S9RtYCOEdtjyitNIKmswNcqgwwUR2MOaKlNpWogsT34RcqsxxZvkaXhi0X40/RG610joqprK8aWgPe/IjcZek1HZw92FigIuVWU6XpvFN2PVuTFSEVu1DTp77Rg8wnM7HXZJS/ezuwqTUrPHC4gVKXj2JjZBNkXasHCiM85ahfTiWHXdJSvWjOw+Ts+XrvFyaRsyd341JEhEhY6V4aOwII5mBuMtRqt9sPUy8MODk/Dnm3HLftkY6aY2nwPHhvRwt7oq7HKX6ydbmmdSDJs/NvErdb3aroFit5OrLS9PU/CZvG5lavQuklNrYpp/Nqfouf3jtNDW/mYhbvd1luFiZ4+T8uW3RhVOqFzYVJm7g8dzMqzS3ON29nxkM12vLvLBwMe5SlOoLtw2TwIQ8N/MqbujtmCBZYTBcqs1zpnQ17lKUSrzbhsmppctUApewT+aPRM7Aq8tXmXfLcVeiVKJtGCbX6yUuVOb6ZiJa1wicnDt/w8xepdStOoZJaAwvLV7SuxmAMa1b4q8tX4u7FKUSq2OYXKjM0gjiHydZnJ3nxW+djLUGaI2fnKvMbNvb4krdrXXDxACvLV+PNUhK84t87lOP8bH3fIhvPfVMbHXcSAy8XpmNuwylEmndMJlrLOOGXq9rucnM5Wne/zc+SLPhxlrHjUIMl6rzOoak1DrWnQE7XVtEkFhbJvc8cC++F2+gracZ+sy5ZV0PRalbdGiZlGMfK0kqS4QFtxp3GUolzpowaYY+9UAHGTsJjWFB55wotcaaMNG7FbdX0/dIqTXWbZmojXn6Him1xpowCUwYRx19JdDxJKXWWBMmq7vk6eelo5To0o5K3WpNmKRX1kDVWfQdpXWdWKXWWBMmA6ksIslIkkqpddfEc5Mz4CkIQ7qSvVJrrJm0ZokwmMpR8mpx1LPq5Df+iK9/5f8A8K3f/yb3PHAv7/yR9zEyMRZrXQAjaV1wWqlbrbug9CulaV5bvqbDJh08svs4RScXdxlKJcmJdWfA7h8Y0yBZhwCDTk6DRKl1rBsm+VSG0cyArmWyhnCoMBF3EUolUsf1TN4ytE+fz7mBIGTsFFMD8Y/ZKJVEHcNkNFNgMjeIlZA7O3EzwPHhffp+KNXBhmvA3jdyQD88gIUwni2wLz8adylKJdaGYZKz09w/crBXtSSUkLJsHhw9FHchSiXabbe62Jsf4XBxkp3aQBGBh8ePkLGduEtRKtE2taPfW4en2JMb3XF3dwThobHDjGYKcZeiVOJtKkwEeHD0ILvzwzsiTgRBRHj72EF254bjLkepvrDpjctFhHeMHeZwcbKb9cRORLAs4V3jx3TAVaktWHdB6U6EVpen6OR4cfEimNaK7duFAHk7zcPjRyk62bjLUaqvbClMVuwfGGMkPcDJuXNUfLfvJ7eJCMYY9hfGuXd4Cls23WBTSrWt+6DfZhnT2uXuTGka06etFEEYcNLcN3KAsUwx7nKU6lcn7ipMVjQCj9Olaa5UFxD6I1QEcMTmnqE9HCpMJGYNF6X6VDRhsqLqu7y2fI3LtQUwJK770+rOtFZKOza4i4OFCe3SKBWNaMNkhRt4XKrO83p783NLhNC0oqX31//W7BiDYSxT4FBhgl25YX1MQKlodSdMVhhg0a1wtb7EdG0RN/BWuxPd3K93JbwEGM4MsCc3wu7cMPlUumvHVGqH626Y3Krs1Zl3Kyy4FeYa5dU9ekQEMdDaZGPz5axMLjOEGNP6fT6VYSJbZCxTYDRT0GnwSvVGb8PkVs3Qp+zVKXsNqr6LG3jU/CZu4OGbEGNCAgzGGGwRBMEWm5Rlk0s5ZO00Oduh4GQppLIUnZx2X5SKR7xhopTaNtZfA1YppbZKw0QpFQkNE6VUJFLAibiLUEr1vef+P12EsN1N6fVVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 10\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 11\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 12\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 13\n"
     ]
    },
    {
     "data": {
      "image/png": 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5X6/wveXL5O1qPw7CbSENWR9Kj/Oq3AFMrSeTlY5Qqdm8PFOkYtmD2/8NUU+MJJmazKDrsvmLmrN9MV8s3uSl/Ayidh6N6AdEhLhm8PDYMUbiQ0Gbsymzi2Wuz5WA7k+qe4EIGLrO8akc6dS2Rumti9n2XE4tTrNgFQd2NGiF70/DyeH9HM/sCdqcpriux4VreYrletCmdAFBRHFgMs3esS0PKE9uKbpddes8N3eeqhPGjrwVb31pZYaKU+c1I1NrUZB+oG67nLu8jGV7QZvSJfx1gus3S1h1l0P7slvq/baDfmXH4m9mz1Bx6n0RausuiiulBU4tTveNC2XVXV66tIxVd0PhVmyEAhaWq1y8lt9SWLEtMVuuzXNz56lvcbl5kFEoblYKfG/pStCmYDseZy8v4/RxyK3TKBT5Yo3LNwptv2ZTMbvK47m581ievWuEvIpCcbWyyLn8jcBs8DzFucvL2M7ghD07gz9/WVipMjNfausVm4r59Mo1Sq6Ft6s68jYUnC/cYNEqBtL81ZtFqrvAtdiImflyWxPeDcV8s5rncmlhV3ckAAKnFi7dtrLZG1aKFvPL1f5Yjw4UYfp6AdfduB9aitlTiheXr/bVbD4olPJDkhcKsz1sU3Flthj1PgAKx/G4sVDe8FktxXy5NE/NDd5PXp5f5IVvngrUBvD95+nSXM/CknPLVWzbDaz3i8U8f/rZP+D3fusDPPd//xrP7e1d6W4UiptLFep2azuailkBFwo3AxVyfnGZT3/4cd79xrfzza98LTA7bkcUvFya70lbswuVwHq/kF/hZ/75D3P+7Gkunj/DL//bn+bn3vW2gKy5k7mlasvHmop5oVbA8uyuGdQOc9dmeMtPvo16zQrUjtvxUFwtL3Z9DlEo1bGd4EbCp7/yv/jjz3+Fx37rCX7/01/k53/x1/n7F77Nd7/9t4HZBL7rtbBSbTmFaCrmmcpy4L7yPQ/cy9SJI4Ha0Iy65/hL+V1kqVALrPdt2+YNb/yHZHPDa9f+yY//CwCGhjIBWXULx/VaRjZajMzFwH3lfkUTYcnaeCKyUwplK7DeN02T/VOH7rh24dxp3vzoD3HiFScDsuoWmkCx2lzM6/Zm1D2HqhvOvRedwFOKJasI7OvK+zuuR71P9l4opXjmq3/BJ3//I3zsU58P2hwAPAWlsg0T6x9bNzKHdRNRJ6l0sY82mq33kmq1wn/94Ht57Dd+mUsXz/FT//QHOf3id4I2CwDLdppeXyfmutf8iRG3sLvYR47TH+5dMpniNx77CN/4fxd5z/s/RLlS4rc/9L6gzQKg1dx4nZhd1R+3uH6mm9Hffts2oGka7/yZf8Nb3vpjnH3pRer14O/craJJ68S8liWov/q0rzCke0erdnBsqKu8/vsfJZsbJhYLPgdJq0RK6y7HVs/A9Wef9gWxLp4T7LeUV6tcPH+GN//gPw7aDKB1H627OmQk1jLdBE0p78dzbSv4W9sqgpDr4knuREwPtP+tWo1P/7ePcvH8mbVr+ZVlzr70Au95/4cCs+sWQirR/IzgutCcJkLWSJK3K103ayNOff3/8MwX/xKAb371r7nngXt53VvfzMjEWKB2AYzEunfgVURIxQ3KtWBWYD3l8bWnv8QnnvgdTt77AN//preQGxnlo5/4HKlU8Ad9RWh54LXpgdaz+RkuFGYjt7kFj+49ScZMdu39r8+VmF2sBLr1tljMY5oxEonufc7tcu/xsWbJGZ9s6nwcHBqLhNwEAT/baBeFDDA+nAx8D3kmk+tLIacSZssso03FnDLijMaHAt+f0X8IR9JNlp46TDymk07G6JOpS98g+MliWtFy6vyq3IFof8ZtCEJcN5ga6o3PfmDPUHTA5DYEMA2N8eHWuelaink0nmYymUWLhgfAD7ufHD7Qs/7IpGLk0vG+iSz1A1N7Mhv2x4ZBzftGDkViBjSE8USaA6nRnrZ7eN/Gv7zdggikh2KM5jbOGLqhmJN6jPtHDnfUsMFDMDSdh0aP9LzlmKlzZH/we4iDRAR0TePYgdymz910uWl/aoSjmcldOxkRgUfGjxEPKOP+aDbBntEUu3dJVjhxMNdWxv221k5fPTzFvuTorotuCMLDY0cZjacDtePg3gxjufgu633/6+tnBW1vP0hbiRMFeGj0MArFbGU59DEOv2QBPDh6mL3J4c1f0AOO7M+hFCwVLEK/C0z838HR/VmGM/G2X9b2rhYR4bVjRzmamdyWfYOCiKBpwuvHT/R8wrcRInBsKseesf5byOgkIv6E+55Dw5tO+Na9djvJxq+WF3lh+QooQpURVPAXjB4ZP97XtQQXVqpcni2CUuGKRYuQMDWOHxzeTi3B7WfOL9k1Ti1MU3KsgV9cWS3acyg9zr3DU+jSn9swb6dmOVy8lqdmOQPe+6wVmJkYSXJwb2a74eCd1TRRys/ycy4/gxrQUVoQhswY940cYiw+WGEwpeDmUpnrc2VWE3UPGgLEYwaH92XI7KycWmdKp9VcmzP5Ga6XlxAGQ9SCX8n1ntw+jqQnBnpxom67XJ8vs5SvgpLBuFM24sf7J4aYHEl1IvTb2aKWZcfiQmGWa5Ul6MPCPas1S2KazonsHg6nJwbCpWgXq+5yY6HMYr4GdKaMcKdQ+DkvUKDrGvvGh5gYSaJpHRtEulNu2HJtrpYXebmRfFETwVNqrRRwb1ktjqYYi6c5kp5gT3I41Mv0tuOxsFJlfqlC3fF6UuZ5I9YKiaZiTI4mGc50Zc9Jd2tnK2DZKnGjusJMZRnLtTtafLwVq18eAYbjQ+xLjrA3OUzKCP4wZq8pVeosFyyWCha24za+2KslPbuDSMPVUTCUNBnNJhjOxol3tyB8d8V8N0W7yqJVYskqsVArruXoEBFEgZ/koH1zBGl0nIdS/v9TRpyJRIaxeJrReDqwZeh+pGo5FMt1ShWbQtnCaSTv3v4AI7fV5vYLzcdNnWw6TiZlkk7Fuln4/W56K+a7qXsORbtK0a5Rdiws16bi1LFcu1G62MNFoZRCF0EQdNExNJ2kYZLQYyR1k7SZIG0kyJjJULsPncZxPao1h6rlYNVdbMfDsl0cx8X1FJ7y3QOllD/giKBroGuCaerETJ2YoZGIGyTjBsl4oIdxgxVzREQHaX4GMCJiEInEHBEaIjFHhAYDeDJoIyIiOsBz/x+7trch5x+jfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 14\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PW: 15\n"
     ]
    },
    {
     "data": {
      "image/png": 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HYCk9Jz0KgIogRDS109gUpRS1HgfqvS7kNJTCyOiRaolDWmS8IsKcMGECnnnmGbAs2+EJZMhFxsLCQvTs2RNfffUVJk6cKJvdSncD8u2VqHA1ABBPcIHANEbgaH0EekYnIS0yAXqZuvLc3Fz069cP3377LUaNGtWhz6hjkCEiGzZsQFxcnGxVZ6vcNnxbdgIHK3NR4W4AbfyfGmgaCtg4N47XnsX/SrLxa30pOIGX3Hbfvn3Rp08f7Nixo8OfCTkxZmVl4Y477oDRaJTUTp3XgT1lJ3CgMgcNrBsAZKt97Q8UACvwyGkow/9Kj6PAXiX5V+bGG28MXzHm5eXhxx9/xJ133imZDVbgkV1biH3lp2BrEqFKImFHoKC+36GuEHvLTqLe65TM1oQJE3DkyJEOn48JKTFu3boVsbGxGDNmjCTt13js2F36Cwod1aJORBSBAg2cC99WnEKeTfwiTgDO/R327dvXofeHnBhvuukmSbb/chvKsL8iBx7Kqbo77gyUUoBSnKgvxoHKHLAijyWtVisGDRoUfmJsaGjA3r17ccstt4jaLgXFT7WFOFlf6puahIgQz4MC1W4b9pWfgpsX94q2UaNGhZ8Yt2/fDp7nRb2YnILicNVpnLVXA8HcJXcACsDJe7C37CScnHiVaUeOHIkjR47A7Xa3+96QEePWrVsxatQoJCQkiNbmsZpCVLjqg3ts2AkESuEROHxXkQOPSBFy5MiR8Hg8OHz4cLvvDQkxCoKA7du3i5q3eKq+BMXO6jCR4W9QUHh4FgcrcyF0Ys+8NXr16oW0tDTs3bu33feGhBh//PFHVFVV4cYbbxSlvSq3DbkNZQjF4WFHoKCwcW78UidOubtrrrkGBw8ebPd9ISHG//3vf0hOTsbgwYMDbosVePxQfQYI87LKlNLG7c36gNsaPnx4hy40Chkxjhs3TpS63DkNZWAFPjRnzZ2EAMiuPRvwsxg2bBgKCgpQW1vb5vuCXoxerxd79+7FDTfcEHBbTs6LM/YKUdK7AqG2shrZ+48o6gPgm2G7eBYFjsAqjA0bNgyU0nYP+Ae9GL/77js4HA5RxJhvr1A0h7q+uharXlqK6SNvwf7t3yjoSXOob/wcQAtpaWlITk5ut6sOejF+88036N27N3r16hVQO5RSnLVXQ1Cwe64oKsG4KZPhdUtzA5W/uHkW1W7/DuY3MXTo0NCPjHv27BFlL7rK48vEVpJ+Qy9Fet+eivrQEgQEJc6agNoYNmxYaEdGlmVx6NAhjBw5MuC2qj12MGE+g24NCooqtz2gNi677DKcPHkSgtD62mVQi/GHH36A0+kURYy1HruiXbTacfIeeAXO78/369cPbrcbZ8+ebfU9QS3Gffv2ITExEQMGDAi4LQfnFcGj0MYVwDNq+hv9+uuvrb4n6MV47bXXirK+yFL/v/XhQiCRMT4+HgkJCTh16lSr7wlqMX733XeidNEAtC66A/AB7lX3798fOTk5rb4etGIsLCxEaWkprrnmGlHa0wfvo5ANIxPYyeYBAwaEZjd96NAhMAwj2o2oRl1IHiEXFUOAYuzXr19oivHIkSO45JJLRLtcKMZoUcWd0/Z63+Iy61HXhIoQgki9KaA2evTogaKiolaXd4JWjIcPH8YVV1whWnvxxkjFk7mP7NyHlQt91+bu37EL/9n4OWorq5V1qpFYgyXgddj09HR4vV5UVFS0+HpQ9k2UUhw9elTU8y6JEdGKZ3Rffv1IXH79SGS+8zdF/bgQhhAkR8QE3E5TRbKioiKkpKRcbCdgCwpw+vRpVFdXixoZow2+il4aFyNQivTI+IDbSUtLAyGk1VtYg1KMR48ehU6nw9ChQ0Vtt0dUouprH8oNIQQJpihYAhwvAkBERAQSExNDS4zZ2dno168fLBaLqO12j0wIimKcckIpxYBY8e7PSU9PR3Fxy8cZglaMYhwxuBCGMLjEmqb0PEY1MISgizkG8aYo0dpMTU1FSUlJy/ZEsyIjUokRANIs8UgyR6timUdpGBBcau0uapuJiYmt1t4JOjE6nU6cOXMGl112mWQ2hsX1gAFM2B/KGhrfAxa9uNXcEhISUF3d8nJV0Inx559/hiAIkkVGADDpDLg8qXfYjhwJAfpEd0FXS5zobYeUGLOzs2GxWNC7d29J7SSYojEioVfYTWYIfEOVS6xpkrSfmJgYOmI8deoUBg4cCIaR3vWuZiuGJfQACAmLHpsQoKslDkPjekhmIyEhAXV1deC4i9PRgk6MTbWi5SLNEo+rE/uAARPyk5reUV18vYGEv2dCQoKvGH4LZ6iDUoxy35CaFBGDUV0GIFJvDLlum4CAIQRD43tI1jU3x2q1AgDq6uouei2oxEgpRV5eHvr06SO77WiDGaO7XIJukb4qZ6EhSYIovQnXNfu9pKZpo8LpvLh8c1AlSpSUlMDhcCh2d7SOMBgS3x1pkXH4qaYQTs6reHKFPxBCwIBgQGxX9IpKlnX4ERnpu5PG4XBc9FpQiTE3NxcAFL/IPMEUjbEpg3DGXoncBt9VFoEXj5OepiFGuiUeA2JTEaGT/7bZJjEGfWTMzc1FZGRki+lHckMIQe/oZPSISkS+vRK5DeVgBR5EhbHSF/gI0i3x6BeTIkrSg780ddNBHxnz8vLQt29fVc1qdYRBn+gu6BWVjDJXHfJtlajx2kFAGkUprzQpfONZhhAIlCJCZ0TPqER0i0yASYFIeCFGoxEGgyH4xajETLqjMIQg1RKHVEscnJwXZa5abNn+JYpKinH97ZPOXZ0mFU2XWoJSROgMSLXEIcVsRZwpSnWTrcjISNjtF1eoCDoxillAXioseiO6MFFYPu8lXHnVlRgxYzZqPHZUum1wch5QUBACEDCgtLPXuxEwACj57UYuI6NHYkQ04k1RSDBFqT5J2GAwgGUvrhkedGJ89NFHlXajQzzzzDOor6/HW2++hS6NERMABCrAxrph59yws264eBZuzgsXz4ITePCUBwUFTymK8wpQnHsGI28aDz1hYNIZYNEbYdIZEKk3NWanRwR8hFRudDodeP7iIltB81uUlZXBZrOptptuzvfff4933nkHH374Ibp06XLeawxhEGu0INbYfmLw8s/34YOX/44Xpv9FKlcVgWGYFk8IBs2id15eHgDll3Xag+M4zJw5E6NHj8bUqVMDastqtbZbejgYCfrIWFhYCL1ej9RU8VLgpeCVV17BqVOn8NNPPwU867darfB4PHC73Ypc5C4VrYkxaCJjSUkJunbtKku2jr/8+uuvWLx4MZ5//nlRInhb+7jBTNCLsbS0VNVRkVKKWbNmoX///njyySdFaTPcxBg03XRxcbGqxbhy5Urs3r0bBw8eFO1W11AVI8dx0Osvll7QRMaSkhLVirGsrAzz58/HX/7yF1x++eWitRuqYmRZtsUvbFCJsWvXrkq70SKPPfYYYmNjsXDhQlHbjYqKgl6vDxsxBk03XVpairQ06ZM/O8sXX3yBzZs3Y8eOHecyUsSCEILY2NiQE6PX6w3eyFhXVweHw6G6brqhoQGzZs3C1KlTRbtE80KsVmvIiZFlWRiNFx+BDQoxNlUgUJsYMzMz4Xa78fe//10yG1arFfX1gV8mqSaCuptuqs2iJjHu378fH3zwAdatW4ekpCTJ7IRqZAzabrqkpAQRERGIixP/ULk/eDweTJ8+HRMmTEBGRoaktkJNjG63GzzPtzi+DorI2LSso5ak2sWLFyM/Px9ffPGF5LasVmurVbuCkaY8xqioi4tJBUVkrKiouCj7RSmOHz+OV199FS+//HLAl2d2hFCLjEEvxurqaiQkyHOUsi0EQcDMmTMxbNgwzJ49Wxaboba005YYg6Kbrq2tRXx84GV8A+Xtt9/G999/j0OHDkGn08liU4uMKqOmpkbxyUthYSGeffZZPP300xg2bJhsdkMtp7HpIFbQirG2tlZxMT7++OPo2rUrFixYIKvd5jmNoYDN5rvnpqX7e4Kim66pqVG0m/7444+xdetW/Pe//5U9ybV5soQazosHSlVVFWJiYoJ3nbGurk6xyFhTU4M///nPmDFjBsaNGye7/VDL3GlrMqp6MTocDng8HsUi49y5c0EIwSuvvKKI/XASo+q76abBuxJi3LVrF9auXYtPP/1UscgcTmJUfWSsqakBANnF4HK5MGPGDEyaNAm33367rLabE2o5jTU1NVpk7CwLFy5ERUUFdu7cKavdCwm1nMbq6upzdwheiOrF2BQZm7orOTh27BiWLVuG5cuXt/rg5CSUFr4rKyuRmJjY4muq76YbGhpgsVhEO+TUHjzPY9q0abjiiiswY8YMWWy2RyjlNLZ1lkn1kdHhcIiezt8Wb7zxBo4fP46jR4+q5ox2qERGp9OJhoaGVs8yqeNpt4HT6RT9wsrWyM/Px6JFi7BgwQIMGjRIFpsdIVTEWFpaCgDBK0Y5I+PMmTPRrVs3ZGZmymKvo4SLGFXfTcsVGdesWYP//ve/2LNnD0wm5coMt4TVasXPP/+stBsBU1paCoZhkJyc3OLrqo+McoixqqoKmZmZmD17NkaOHCmpLX8IlaWd0tJSJCYmtlhNAggCMcrRTT/xxBMwm8146aWXJLXjL6HSTZ89exbdunVr9fWw76a3bduGjRs3YsuWLS2mNamBUMlpzM/PR8+ePVt9PSgio1RidDgceOyxx3DPPffg1ltvlcSGGIRKTmNBQQF69Gj9kkzVi9HpdErWTTfV3V62bJkk7YtFqCRLBL0YpYqMTXW3lyxZopqTh60RCmJ0uVyorKwM7m7a4/GInl0tZt1tOQgFMRYUFIBS2mZkVP0EprVSGIEgZt1tOQgFMebn5wNAcIuR4zhRj4U21d1etGiR6m9OaCIUchpzc3ORmJjYZvaV6rtpMcXYVHd7wIABotXdloNQyGnMyclBv3792nxPUETG1lbsO4sUdbflItgXvjsiRtVHRp7nRRGjVHW35SLYcxpzcnLaHRapXoxiRUap6m7LRTBHRo7jUFBQoHXTgLR1t+UimMV45swZsCwb/N10oGKUo+62HASzGE+ePAlCSHBFRgqA4wSwnACe910VzrIcvCxFvd0DQggYQqDTERj0DPS69r9LctTdloNgzmnMzs5G9+7dERMT0+b7FBGjQCkcLhYuNweXh4PTzcHj5c8JsDkbNn8Da1w8cgovjgqEEBj0BBFGAyxmPcwmPSwRvv8C8tXdloNgXtrJzs7GkCFD2n2fbGK0u1jU2zxocHjhdHOglJ7b/Wi6Ub4lUtO7t/oapRRelsLLemB3eiBQAoBCxzCIsujw0J+m4UYZ6m7LQTB309nZ2bjtttvafZ+kYrQ7WVTXu1Db4AbHUxACNNddWyLsLAIF0BhXeUFAg13AM8+/gfjEZPxyugbxMSYkWM0w6FU/TG6RYM1p9Hq9yMnJweDBg9t9r+hiFASKqnoXKqqdcHv58wQoovbahQIYNHg4AMDp9g0JiivtiI0yITnegpjIiy/FUTPBevf0yZMn4fV65RWjIFBU1rlQWuk4b+wnpwDbgoICFKi3e1Bn8yDCpEdaUiTiYoLjDxusdRqzs7NhNBrbnUkDIomxstaFonI7BOHiCYjaaPpyeLwc8orqYYlwokfXaESa1b09GMxiHDhwYIvXs11IQGJ0ulnkl9jg9LBQvQovoEmULg+LE2dqkBRnRnpyNHQ6daaUBWsa2fHjxzvURQMBLHqXVTtw4kwNXB4u6ITYnCZRVtW5cDyvGnYnq6xDrRCsYszOzpZOjDwv4FRBLYrK7aBU3BmxklAKsJyAUwU1KKt2KO3ORQRjTmN9fT3Onj3bYTF2qpv2sjx+LaiFhxX8ck79UFAKFJfb4fHy6N41BmrptIMxp/H48eOglIovRo+Xx8n8WnAcH8y9coegAKpqXWB5ij5psVDLyYRgW/jOzs5GbGxsh2tcdqib9nVfteBa2K4LVSgo6m1uFJQ2KO3KOYItp/HYsWMYMmRIh88ZtStGQaD4taAWLCeEzJlRgPYAABP9SURBVPiwYxBQ6pvYlFTalXYGQPBFxgMHDuCqq67q8PvbFePZchtcXj7MhHg+JZUO2Bxepd0IKjE6nU4cP34cV199dYc/06YY62weVNa61LONohgEp4sbwPPKPodgEuPhw4fBcZw4YqSUorDMpprZpLJQcJyA0ipll3yCSYwHDx5ESkoKundvPevqQlqdTVfUusCyys2cbbZ6bNm0AeWlxRg5Zjyuuno0GJmu1W0JCoryGieS480wGpTxI5iWdg4ePIhrrrmmU59pNTKWVTkVE2JDfR3+eOcE5Jz6BXk5JzFn5r34032TFfLmfCpqXIrZDrbI2JkuGmglMjbYvWA5XhSn/OHr7VuwNms7YmJ9W2AfvvcG3l/+Go798D2GDu/47ExsKKWoqnMhLTlKkbXHYMlpLCkpQVFRUafF2GJkrGlwKzZWZFkWvxt5/TkhAsCkW+8CAERGKl/Mk+MFxWbWwVKn8cCBA2AYptPn01sUY4PDo1gXbTAYLjpqkPvrLxg95v+hb/9LFPLqNxgC2FzKiRFQf7LEwYMHMWjQoHYPYF3IRd00xwvwqmTvmVKK/+3YipXvvo63P8hS2h0AvuMNdgcLKHC+K1hyGv0ZLwItREYvq9xYsTkulxMvP/8UFi2YgzN5v+Ke28bil+M/Ku0WAMDDcorYDYbIyPM8jhw5Io4YOU4dC9xmswULFr2O3Yfy8Jd5L8DhtOOVF9RxWZBSc7tgEOPx48dht9s7vawDtCBGQWW7LQzDIOOPD2Pc+Jtx6sRxeL3Kb8sptTUaDDmN3333HaKjo/267u4iMao17f7qa8cgJtbaobMUUtOBQhaSEAw5jbt27cLo0aP9qql50WPtSMkQJcjLOYnRY9VRK0fJZ6TmhW9KKXbv3o2xY8f69fmLnmqEUadonWuP241V7y9DXs7Jcz+rr6vFqRPZ+Mu8FxTz6zcILBHKnSRUc07jiRMnUF5e7rcYL1raIYTAYtLD4VbmYJJABXzz9Zd4b/mruOTSobh21DjExsVj2XsbYLEoX86OECDKoqwY1RoZd+7ciejoaAwfPtyvz7e4HRgTZYTTwykyUDebLVj36dew2ephMBgREWGW3Ye2oJQiWsFqFGoW4+7du3Hdddf5XcKwxcFPotWseDJtdHSs6oQIAJYIw7kqZ0qgVjFSSrFnzx6/u2igFTGajDpEmY2qOYikFgiApDhlvyBqFePPP/8c0HgRaCOFLK1LpJbg3QwCwKBnkGhVtjaPWpd2du3ahdjYWL/Hi0AbYoy2GBEbZQqKG6TkIr1LtOLPQ62RMZD1xSbaXDDr0VX5h68GCAGiIo2Ij1W+Ypkacxoppfj2228D6qKBdsRoNOjQM1X5HEIlIQTQMQx6p8Uq7QoAdeY0Hj9+HBUVFdKKEQDiYyLQJd4ChO3RLIK+3WJVU/FWjckSO3fuhNVqxbBhwwJqp0NPuFtKNBJiTWEnRwKgT3osoizK74c3oUYxbt++HTfccEPAdzx2+OveMzW2scprGEiS+HaieqXFwhptUtqb81CbGN1uN3bv3o2bbrop4LY6LEZCgN7pseiSoL6FaDEhBGBA0K+7VRUTlgtRmxh37doFp9MpyoVPnd5K6NYlGmaTHgVlNoDS0FqLJAQmA4M+3ayK7rK0hdpyGrdv347BgwejW7duAbfl1xNPtJoRZTYgr6gebg8X/JXJfNfHIMkagW4p0WBUvJyltpzGbdu24fe//70obfn99Y8w6TGodwLKaxwornCgqdBmsEEAmAx69OgarWgCRGdQy8L3mTNn8Ouvv2LixImitBdQX0QIkJIQifiYCBRXOlBT7wIo8V1zoXYa1w9TkyKRHGcJqn14teQ0btu2DVFRUbj22mtFaU+UgZHRoEOv1BikJkaitMqB6nrfgqzSmT/NofCdeQYFdDoGXRMjkRRnBsMEkQobUUtk3LZtG8aPHw+TSZwVB1FXck1GHXqmxmBIv0SkJkXC2LhQrPSWIiEEtTVViDIb0Ts9FkP7J6JLgiUohQioQ4xerxe7du0SrYsGJLpv2qD3RZ4h/ZMwsGcckuPMMOh9C6Kk2f9LBSHknIlIswEnfvwWd066FtRdjriYCMW/HIGiBjHu2bMHdrtd1Du8JV+/iLIYEWUxoltKNFweDjaHF3YniwaHB1xj8c2O3K7aMqTZ3YS+izJNBh1iokyIthgQZTHCoGfQN/1WrHj7Mtxxxx04ePAgIiOVP74QCGq4e3rbtm245JJL0KtXL9HalHUxzWzy3QWdHO/7N8cL5+6c9nh5sJwAD8uD43jwAoVACSil564DJoRAxwA6hsBg0MFo0MGoZxDR2K7Z1PJhMoPBgI8//hgjRozAjBkzsGHDBjl/bdFRw9LOtm3bRNl1aY6iK7t6HYPoSKMsSyrdunXD2rVrccstt2Ds2LF4+OGHJbcpFUp30zk5OThx4gRWrFgharvqSEWRiZtvvhlPP/00nnjiCRw5ckRpd/xG6ZzGTZs2ISEhASNHjhS13bASIwC8+OKLuO666zBlyhTU1NQo7Y5fKJ3TuGXLFtx2221+nwJsjbATI8MwWLduHTiOw9SpU1W1FtpRlEyWKC8vx/fff4/bbrtN9LbDTowAkJycjE8++QQ7duzAkiVLlHan0ygpxs8++wwREREYP3686G2HpRgB4He/+x1efPFFzJ8/H99++63S7nQKJcW4ZcsWTJw4ERaLRfS2w1aMAJCZmYlbbrkFd911F0pLS5V2p8MoJUabzYadO3dK0kUDYS5GQghWrVoFi8WC++67Dzyvjqq97aFUTuOXX34JjuNw8803S9J+WIsR8EWZzZs348CBA1i0aJHS7nQIpXIat2zZgjFjxiAxMVGS9sNejAAwdOhQLFmyBIsXL8a2bduUdqdDyL3wzbIstm/fLloibUtoYmxk1qxZuP/++3H//fcjPz9faXfaRe6cxm+++Qb19fW49dZbJbOhibEZ7777LlJSUnD33XeronZ4W8gdGbOysnDllVeiR48ektnQxNiMyMhIfPbZZzh58iQyM9Vxs0JryClGr9eLLVu24O6775bUjibGC+jfvz9WrlyJN998E+vXr1fanVaRU4w7duxAbW0tpkyZIqkdTYwtcPfdd2PWrFl45JFHcOLECaXdaRE5xZiVlYWRI0dK2kUDmhhbZenSpRg4cCDuuusuOJ1Opd25CLmWdtxuN7Zu3Sp5Fw1oYmwVk8mETZs2obS0VJW5j3JFxi+//BJ2ux2333675LY0MbZB9+7dsXbtWmzYsAGrVq1S2p3zkCunMSsrC2PHjkVqaqrktjQxtsOkSZOQmZmJxx57DEePHlXanXPIkdPocDjw1VdfydJFA5oYO8TixYsxatQo3H333ao4PA/IkyyxZcsWeDweSXddmqOJsQPodDqsW7cODocDf/zjH1WRkCuHGLOysjB+/HgkJydLZqM5mhg7SJcuXbBhwwZ89dVXWLZsmdLuSC7G2tpa7NixQ7YuGtDE2CnGjh2LRYsWITMzE3v37lXUF6nFmJWVBYZh8Ic//EGS9ltCE2MnmT9/PiZNmoSMjAxUVlYq5ofUOY0fffQR/vCHPyA2Vr7C+poYOwkhBKtXr4bBYMA999yjWEKulDmNubm52L9/Px544AHR224LTYx+EBcXh6ysLOzbtw8vvfSSYn5ItfD90UcfITk5WZJDV22hidFPrrzySrz++ut44YUXsGPHDkV8kCKnkVKKdevW4YEHHhD9XHR7aGIMgNmzZ+Pee+/Fvffei4KCAtntSxEZ9+7di9OnT8veRQOaGANmxYoVSElJwT333CN7Qq4UYvzoo49w2WWXYciQIaK22xE0MQZIVFQU/vWvfyE7Oxvz58+X1bbYYnS73fjkk0/w4IMPitZmZ9DEKAKXXnopPvjgAyxduhSbNm2Sza7YYtyyZQtsNhvuvfde0drsDJoYRSIjIwPTp0/HQw89hFOnTsliU+ylnTVr1uDGG29E165dRWuzM2hiFJG33noL/fv3ly0hV8zIWFRUhK+//hrTpk0TpT1/0MQoIhEREdi0aROKioowZ84cye2JmdP4j3/8A3FxcZg8ebIo7fmDJkaR6dGjB9auXYt//OMfWLNmjaS2xMppFAQBq1evxkMPPSTaNRr+oIlRAiZPnoy5c+di1qxZ+OGHHySzI1ayxNdff42CggI89NBDYrjlN4SqITkvBOE4DuPGjUNZWRkOHz6MmJgY0W1kZ2djyJAhOHHiBAYOHOh3O3fddRfKysqwZ88eEb3rPFpklAi9Xo9//etfsNvtmDFjhiQ2xIiM1dXV+Pe//63oxKUJTYwSkpKSgvXr12PTpk1Yvny56O2LIca1a9ciIiICd955p1hu+Y0mRom5/vrr8dxzz2Hu3LnYt2+fqG2LkdO4atUqZGRkSFKJtrNoYpSBZ599FuPHj0dGRgaqqqpEazfQnMa9e/fi559/lmwY0Vk0McpA0w0LOp0OGRkZoibkBrLw/e677+Kqq67CiBEjRPMnEDQxykR8fDyysrKwZ88e/O1vfxOtXX9zGisrK7F582bMmjVLNF8CRROjjFx11VV47bXXsHDhQnz99deitOlvZPzwww9hNptx1113ieKHGGhilJk5c+ZgypQpuP/++1FcXBxwe/6IURAEfPDBB/jTn/6kiolLE5oYFWDVqlWIj4/HnXfeCZZlA2rLHzF+9dVXyM/Px8yZMwOyLTaaGBWgKSH32LFjePbZZzv9ecoJEFwseLsXsZZo1FbVgKtxga91gW/wgG/wQHCyoCwPtLC/tmLFCowfPx79+/cX4bcRD207UEHWr1+PBx54AJs2bWrxsLzgYiE4Wd9/HRyom4XACk23vQMA8ksK4fa4MbBXK8IiANExYEx6kEgDimvK0O+KS/GvrCxMueMOqX41v9DEqDDTpk3D5s2bceTIEfRK7wGuzu2LbA0eUF7wvYmQ8wToL4QQCJRiz+F9GDniGphizGBiTNDHRoCJkv7O73b908SoLM56OyZMmIDMaU9g3LBRIITIW1iqUejEwEAfZ4Y+waKYMDUxKgRf7wFbYQdf35iLqIa/AkMAgYIx66FPjoI+0QLCENnMa2KUGb7BA+/ZeghOFiBQhwhbgegY6LtEwpASBaKTfq6riVEmBIcXnvx6CE6v6kXYHEIAMAyM3WKgT4qU1pYmRmmhvADv2QZwlY5z3WBwQsBYDDD1soKxGKSxoIlROni7F57cGlBOEGU2rDSEABQExvQYGFKixG9fE6M0sKU2eIsbfP8IuSdMoIsxwdQ3TtSxpCZGsaGAp6AOXJUjBEXYDELAmHSIGJAIYtSJ06QmRhGhgDu3Bny9K7SF2AQhIHqCiEuSwJgCL5+n7U2LiCe/FnxdmAgRACgF5Sg8J6tAWSHg5jQxioS3uAFclUtpN+SHUlBWgPtUZcArBZoYRYBv8IAtsSF8QuL5UEohuHh4zwZWRVcTY4BQToAnr8a3kB3WULAVDvB1/pda0cQYIGypzZddE55B8SK8hXV+r6lqYgwA6uHBlqtjCaemvhavr3lbaTcgeHmwlf6VA9TEGABsuR2qUCKAx156Cu9+/A+l3QAowJY2+PVRTYz+Qim4KqcqtLj68w345bQ81XI7AvUK4Bs8nf6cJkY/4ZtnYitIbuFpHDt1HDeNlvcCoTYhBFxN57tqTYx+wtu8vvQqBWE5DotWvIaXHn9GWUcuhFIIWmSUD8HuUTwR55UPl2J2xnREWcTPoAkUwcP7spU6gSZGPxE8ylxg2cTeoweg0+lw9ZArFPWjLai3c89IE6O/cMqFxXpbA977ZDUy//SEYj50hM5GRnlvKgwhlEx2mrf0eVw+aCi+2vNbvZ68wjNwe934985tiI2OwZgrRirm3zn4zj0jTYx+QnQA5ZSxXVVbjW8Onl9/u95hg8vtwv+9/ldc0nuAOsSo79wMT8tn9BNXdhkEt7LjxuY8u3wxNnz5KU5vl+52hc5ivqwLGHPH4502ZvQTxmLUkiPaghAwEZ3LANfE6CdqKAeiZnQWAzq7EKt1034iuFi4jlco7YY6IQSGrlEwpnXu7hstMvoJYzZ0ajwUVlAKfWLni5BqYgwAfXKUNm68EEKgizb6dUBLE2MAGBItIHqdJsjmUApDeqxfH9XEGAgMgbGb+HcCBi0E0MVGQOfn5E4TY4DoEyzQxUSAKJ3CowIIYWDqYfX785oYRcDUywroEPbdtbGXFcTkf3UJTYwiQAw6mPomwFdAW2lvlIDAkBIFfbw5oFY0MYqELtoEU584pd2QHQJAn2CGsZt/k5bmaGIUEX2cGaZecY07D+EQIgl08RbfMEWM1rQdGPHh6z3w5FYDAlXDeS3JMKREiRIRm9DEKBGCi4Unt8aXER5Sj9g3Ljb1tPq1y9Jmy5oYJUSg8BTW+0oohwIEYCL0MPVNABMh/laoJkYZ4Bs88BbUQfBwqjhn3VkI8UVDQ1oMDF0iO52N02E7mhhlglKw5Q6wpTaAE4JCk4QQUFDoEywwpsWIVqG2VXuaGGVG8FXrUnXBqMbIp08ww5AaLUpV2g6Z1cSoEJSCq3WDq7CDt3kbBUAVE2fT9YTEqIMhORL6xEgQg7wrf5oYVQD18OBqXeBqXBAcXt8PRbq8si1+EyADfbwFujiz30kOovijiVFdUFYAb/NAsDXeG31u0tO41djZPxdB0wUu5z5LDAx00SYw0SZf7qFZmkuGOosmRrUjUAhuznfntJsD9fKgXgHUw4EKAiD43kMp9d0+wJDGO6YJiIEBMepBDDqQCD0Ysx6M2QCiV+fGmyZGDdWgzq+IRliiiVFDNWhi1FANegCfKO2EhgYA/H+Wunzk2yIUqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(1, len(partitions['pw_objs'])+1):\n",
    "    print(\"PW:\", i)\n",
    "    v = PWEVisualization.graphviz_from_meta_data(pw_slicer(partitions['pw_rel_dfs'], None, [i])[0], \n",
    "                                                 partitions['meta_data']['graphviz'])\n",
    "    draw(v, filename='Partitions-Viz/partition_{}.png'.format(i), show=False)\n",
    "    display(draw(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Named to Un-Named\n",
    "\n",
    "Above we saw that for n we get B<sub>n</sub> (Bell-Number) of PWs. If the objects were unnamed, we could group these PWs using a simple isomorphism based equivalence grouping function. The number of such disjoint groups would then be the number of integer partitions of n."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Encoding Isomorphism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-display_input -lci partition_eq_check --donot-run\n",
    "\n",
    "% e(X,Y) :- e(Y,X). --> only if undirected\n",
    "gnode1(X) :- tog1(X,_).\n",
    "gnode1(X) :- tog1(_,X).\n",
    "\n",
    "gnode2(X) :- tog2(X,_).\n",
    "gnode2(X) :- tog2(_,X).\n",
    "\n",
    "vmap(X,Y) ; not vmap(X,Y) :- gnode1(X), gnode2(Y).\n",
    ":- vmap(X1,Y1), vmap(X2,Y2), tog1(X1,X2), not tog2(Y1,Y2).\n",
    ":- vmap(X1,Y1), vmap(X2,Y2), not tog1(X1,X2), tog2(Y1,Y2).\n",
    "\n",
    ":- gnode1(X), #count {Y: vmap(X,Y)} != 1.\n",
    ":- gnode2(Y), #count {X: vmap(X,Y)} != 1.\n",
    "\n",
    "#show.\n",
    "% #show vmap/2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With those in place, we can find the disjoint sets of partitions, each of which are equivalent within themselves modulo renaming:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sets = get_equivalent_sets(partitions['pw_objs'], \n",
    "                           lambda pw1, pw2: are_equivalent_patterns(pw1, pw2, partition_eq_check))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1}\n",
      "{2, 3, 4, 6, 8, 11}\n",
      "{5, 13, 7}\n",
      "{9, 10, 12, 14}\n",
      "{15}\n"
     ]
    }
   ],
   "source": [
    "for s in sets:\n",
    "    print({pw.pw_id for pw in s})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, we found I<sub>n</sub> sets. We can see these sets below and verify the validity of the groupings ourselves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "Set: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "Set: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "Set: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "Set: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "Set: 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for i, s in enumerate(sets):\n",
    "    print('-'*60)\n",
    "    print(\"Set:\", i)\n",
    "    for pw in s:\n",
    "        display(draw(PWEVisualization.graphviz_from_meta_data(pw_slicer(partitions['pw_rel_dfs'], None, [pw.pw_id])[0], \n",
    "                                                              partitions['meta_data']['graphviz'])))\n",
    "    print('-'*60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### As discussed earlier, the number of such sets is the number of integer partitions of n, in this case that is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The number of integer partitions of n:\n",
    "len(sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Ordering of the Partitions using a Refinement Relation\n",
    "\n",
    "We can define a refinement relation to apply a partial ordering to the B<sub>n</sub> partitions. In this scenario, we use a simple refinement relation called the *finer-than* relation, which basically checks if a partition is a further fragmentation of another fragmentation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the *finer-than* relation below in ASP:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-display_input -lci finer_than_relation --donot-run\n",
    "\n",
    "% G1 >= G2\n",
    "\n",
    "% Get all the nodes\n",
    "n(X) :- tog1(X,_).\n",
    "n(X) :- tog1(_,X).\n",
    "n(X) :- tog2(X,_).\n",
    "n(X) :- tog2(_,X).\n",
    "\n",
    "% Check if all edges in G2 are also in G1\n",
    ":- not tog1(X,Y), tog2(X,Y), n(X), n(Y)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, using this refinement relation, we can find all pairs of PWs such that one is a refinement of the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pw_refinement_rels = get_refinement_rels(partitions['pw_objs'],\n",
    "                                         lambda pw1, pw2: refinement_check(pw1, pw2, finer_than_relation))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize this ordering, we can use a graph-based visualization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.DiGraph()\n",
    "G.add_edges_from(pw_refinement_rels)\n",
    "# Applying some custom Graphviz styling, along with images of the partitions in the nodes\n",
    "for pw in partitions['pw_objs']:\n",
    "    G.add_node(pw.pw_id, image=os.path.abspath('Partitions-Viz/partition_{}.png'.format(pw.pw_id)),\n",
    "               shape='box', fixedsize='true', imagescale='true', size=2, label=\" \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, there are redundant edges here, i.e. e(A,B), e(A,C), e(B,C), where e(A,B), e(B,C) would suffice. This is called transitive reduction. We can perform it very simply in Python (using the NetworkX library) as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G_trans_redcd = nx.algorithms.dag.transitive_reduction(G)\n",
    "\n",
    "# Copying over the Graphviz styling from G\n",
    "for n in G.nodes:\n",
    "    for k,v in G.nodes[n].items():\n",
    "        G_trans_redcd.nodes[n][k] = v\n",
    "draw(G_trans_redcd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also perform this transitive reduction using ASP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-display_input -lci transitive_reduction --donot-run\n",
    "\n",
    "% Add all transitive edges to the graph (that are not already there)\n",
    "e(X,Y) :- e(X,Z), e(Z,Y).\n",
    "\n",
    "% An edge e(X,Y) is redundant if there already exists e(X,Z), e(Z,Y) for some Z\n",
    "tc(X,Y) :- e(X,Z), e(Z,Y).\n",
    "\n",
    "% Only keep non-redundant edges\n",
    "new_e(X,Y) :- e(X,Y), not tc(X,Y).\n",
    "\n",
    "%graphviz graph graph_type=directed\n",
    "%graphviz edge new_e(HEAD, TAIL)\n",
    "\n",
    "#show new_e/2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To use the above encoding, we must first enlist the edges of graph G above as Datalog Facts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "refinement_rel_edges = ' '.join(['e({},{}).'.format(*e) for e in G.edges])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can get the set of edges after transitive reduction using the encoding and our list of edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
    },
    {
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       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<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\">new_e</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=\"nf\">new_e</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=\"nf\">new_e</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\">new_e</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\">new_e</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">new_e</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=\"nf\">new_e</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=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">7</span><span class=\"p\">,</span><span class=\"mi\">6</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">8</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">9</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">9</span><span class=\"p\">,</span><span class=\"mi\">6</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">9</span><span class=\"p\">,</span><span class=\"mi\">8</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">,</span><span class=\"mi\">8</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">11</span><span class=\"p\">,</span><span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">12</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">12</span><span class=\"p\">,</span><span class=\"mi\">6</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">12</span><span class=\"p\">,</span><span class=\"mi\">11</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">13</span><span class=\"p\">,</span><span class=\"mi\">8</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">13</span><span class=\"p\">,</span><span class=\"mi\">11</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">14</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">14</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">14</span><span class=\"p\">,</span><span class=\"mi\">11</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">5</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">7</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">9</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">10</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">12</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">13</span><span class=\"p\">)</span> <span class=\"nf\">new_e</span><span class=\"p\">(</span><span class=\"mi\">15</span><span class=\"p\">,</span><span class=\"mi\">14</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\">0.002</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\">0.002</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\nnew_e(2,1) new_e(3,1) new_e(4,1) new_e(5,3) new_e(5,4) new_e(6,1) new_e(7,2) new_e(7,6) new_e(8,1) new_e(9,3) new_e(9,6) new_e(9,8) new_e(10,2) new_e(10,4) new_e(10,8) new_e(11,1) new_e(12,4) new_e(12,6) new_e(12,11) new_e(13,8) new_e(13,11) new_e(14,2) new_e(14,3) new_e(14,11) new_e(15,5) new_e(15,7) new_e(15,9) new_e(15,10) new_e(15,12) new_e(15,13) new_e(15,14)\\nSATISFIABLE\\n\\nModels       : 1\\nCalls        : 1\\nTime         : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.002s'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%clingo -l refinement_rel_edges transitive_reduction --donot-display_input -exp trans_redc_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 1\n"
     ]
    }
   ],
   "source": [
    "trans_redc_edges['pw_rel_dfs'], trans_redc_edges['rel_schema'], trans_redc_edges['pw_objs'] = load_worlds(trans_redc_edges['asp_soln'], \n",
    "                                                                                                          trans_redc_edges['meta_data'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now visualize the output of performing transitive reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G_trans_redcd_asp = PWEVisualization.graphviz_from_meta_data(trans_redc_edges['pw_rel_dfs'],\n",
    "                                                             trans_redc_edges['meta_data']['graphviz'])\n",
    "# Copy over Graphviz Styling\n",
    "for n in G.nodes:\n",
    "    for k,v in G.nodes[n].items():\n",
    "        G_trans_redcd_asp.nodes[str(n)][k] = v\n",
    "draw(G_trans_redcd_asp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the output is the same as using the Python 'blackbox' version.\n",
    "\n",
    "Another interesting observation is that the different disjoint groups we found by using isomorphisms can all almost be seen distinctly on the different BFS-level of the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}