csp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CONSTRAINT SATISFACTION PROBLEMS\n",
    "\n",
    "This IPy notebook acts as supporting material for topics covered in **Chapter 6 Constraint Satisfaction Problems** of the book* Artificial Intelligence: A Modern Approach*. We make use of the implementations in **csp.py** module. Even though this notebook includes a brief summary of the main topics, familiarity with the material present in the book is expected. We will look at some visualizations and solve some of the CSP problems described in the book. Let us import everything from the csp module to get started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from csp import *\n",
    "from notebook import psource, pseudocode, plot_NQueens\n",
    "%matplotlib inline\n",
    "\n",
    "# Hide warnings in the matplotlib sections\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CONTENTS\n",
    "\n",
    "* Overview\n",
    "* Graph Coloring\n",
    "* N-Queens\n",
    "* Backtracking Search\n",
    "* Tree CSP Solver\n",
    "* Graph Coloring Visualization\n",
    "* N-Queens Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OVERVIEW\n",
    "\n",
    "CSPs are a special kind of search problems. Here we don't treat the space as a black box but the state has a particular form and we use that to our advantage to tweak our algorithms to be more suited to the problems. A CSP State is defined by a set of variables which can take values from corresponding domains. These variables can take only certain values in their domains to satisfy the constraints. A set of assignments which satisfies all constraints passes the goal test. Let us start by exploring the CSP class which we will use to model our CSPs. You can keep the popup open and read the main page to get a better idea of the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(CSP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The __ _ _init_ _ __ method parameters specify the CSP. Variable can be passed as a list of strings or integers. Domains are passed as dict where key specify the variables and value specify the domains. The variables are passed as an empty list. Variables are extracted from the keys of the domain dictionary. Neighbor is a dict of variables that essentially describes the constraint graph. Here each variable key has a list its value which are the variables that are constraint along with it. The constraint parameter should be a function **f(A, a, B, b**) that **returns true** if neighbors A, B **satisfy the constraint** when they have values **A=a, B=b**. We have additional parameters like nassings which is incremented each time an assignment is made when calling the assign method. You can read more about the methods and parameters in the class doc string. We will talk more about them as we encounter their use. Let us jump to an example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GRAPH COLORING\n",
    "\n",
    "We use the graph coloring problem as our running example for demonstrating the different algorithms in the **csp module**. The idea of map coloring problem is that the adjacent nodes (those connected by edges) should not have the same color throughout the graph. The graph can be colored using a fixed number of colors. Here each node is a variable and the values are the colors that can be assigned to them. Given that the domain will be the same for all our nodes we use a custom dict defined by the **UniversalDict** class. The **UniversalDict** Class takes in a parameter which it returns as value for all the keys of the dict. It is very similar to **defaultdict** in Python except that it does not support item assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['R', 'G', 'B']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = UniversalDict(['R','G','B'])\n",
    "s[5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our CSP we also need to define a constraint function **f(A, a, B, b)**. In this what we need is that the neighbors must not have the same color. This is defined in the function **different_values_constraint** of the module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(different_values_constraint)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CSP class takes neighbors in the form of a Dict. The module specifies a simple helper function named **parse_neighbors** which allows us to take input in the form of strings and return a Dict of a form compatible with the **CSP Class**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%pdoc parse_neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **MapColoringCSP** function creates and returns a CSP with the above constraint function and states. The variables are the keys of the neighbors dict and the constraint is the one specified by the **different_values_constratint** function. **australia**, **usa** and **france** are three CSPs that have been created using **MapColoringCSP**. **australia** corresponds to ** Figure 6.1 ** in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(MapColoringCSP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<csp.CSP at 0x22a22ebc9e8>,\n",
       " <csp.CSP at 0x22a230355f8>,\n",
       " <csp.CSP at 0x22a23036b00>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "australia, usa, france"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## N-QUEENS\n",
    "\n",
    "The N-queens puzzle is the problem of placing N chess queens on an N×N chessboard so that no two queens threaten each other. Here N is a natural number. Like the graph coloring problem, NQueens is also implemented in the csp module. The **NQueensCSP** class inherits from the **CSP** class. It makes some modifications in the methods to suit the particular problem. The queens are assumed to be placed one per column, from left to right. That means position (x, y) represents (var, val) in the CSP. The constraint that needs to be passed on the CSP is defined in the **queen_constraint** function. The constraint is satisfied (true) if A, B are really the same variable, or if they are not in the same row, down diagonal, or up diagonal. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
       "   \"http://www.w3.org/TR/html4/strict.dtd\">\n",
       "\n",
       "<html>\n",
       "<head>\n",
       "  <title></title>\n",
       "  <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
       "  <style type=\"text/css\">\n",
       "td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
       "span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
       "pre { line-height: 125%; }\n",
       "body .hll { background-color: #ffffcc }\n",
       "body  { background: #f8f8f8; }\n",
       "body .c { color: #408080; font-style: italic } /* Comment */\n",
       "body .err { border: 1px solid #FF0000 } /* Error */\n",
       "body .k { color: #008000; font-weight: bold } /* Keyword */\n",
       "body .o { color: #666666 } /* Operator */\n",
       "body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       "body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       "body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       "body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       "body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       "body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       "body .gd { color: #A00000 } /* Generic.Deleted */\n",
       "body .ge { font-style: italic } /* Generic.Emph */\n",
       "body .gr { color: #FF0000 } /* Generic.Error */\n",
       "body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       "body .gi { color: #00A000 } /* Generic.Inserted */\n",
       "body .go { color: #888888 } /* Generic.Output */\n",
       "body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       "body .gs { font-weight: bold } /* Generic.Strong */\n",
       "body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       "body .gt { color: #0044DD } /* Generic.Traceback */\n",
       "body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       "body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       "body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       "body .kp { color: #008000 } /* Keyword.Pseudo */\n",
       "body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       "body .kt { color: #B00040 } /* Keyword.Type */\n",
       "body .m { color: #666666 } /* Literal.Number */\n",
       "body .s { color: #BA2121 } /* Literal.String */\n",
       "body .na { color: #7D9029 } /* Name.Attribute */\n",
       "body .nb { color: #008000 } /* Name.Builtin */\n",
       "body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       "body .no { color: #880000 } /* Name.Constant */\n",
       "body .nd { color: #AA22FF } /* Name.Decorator */\n",
       "body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       "body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       "body .nf { color: #0000FF } /* Name.Function */\n",
       "body .nl { color: #A0A000 } /* Name.Label */\n",
       "body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       "body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       "body .nv { color: #19177C } /* Name.Variable */\n",
       "body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       "body .w { color: #bbbbbb } /* Text.Whitespace */\n",
       "body .mb { color: #666666 } /* Literal.Number.Bin */\n",
       "body .mf { color: #666666 } /* Literal.Number.Float */\n",
       "body .mh { color: #666666 } /* Literal.Number.Hex */\n",
       "body .mi { color: #666666 } /* Literal.Number.Integer */\n",
       "body .mo { color: #666666 } /* Literal.Number.Oct */\n",
       "body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       "body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       "body .sc { color: #BA2121 } /* Literal.String.Char */\n",
       "body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       "body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       "body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       "body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       "body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       "body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       "body .sx { color: #008000 } /* Literal.String.Other */\n",
       "body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       "body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       "body .ss { color: #19177C } /* Literal.String.Symbol */\n",
       "body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       "body .fm { color: #0000FF } /* Name.Function.Magic */\n",
       "body .vc { color: #19177C } /* Name.Variable.Class */\n",
       "body .vg { color: #19177C } /* Name.Variable.Global */\n",
       "body .vi { color: #19177C } /* Name.Variable.Instance */\n",
       "body .vm { color: #19177C } /* Name.Variable.Magic */\n",
       "body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "\n",
       "  </style>\n",
       "</head>\n",
       "<body>\n",
       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">queen_constraint</span><span class=\"p\">(</span><span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">B</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;Constraint is satisfied (true) if A, B are really the same variable,</span>\n",
       "<span class=\"sd\">    or if they are not in the same row, down diagonal, or up diagonal.&quot;&quot;&quot;</span>\n",
       "    <span class=\"k\">return</span> <span class=\"n\">A</span> <span class=\"o\">==</span> <span class=\"n\">B</span> <span class=\"ow\">or</span> <span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"o\">!=</span> <span class=\"n\">b</span> <span class=\"ow\">and</span> <span class=\"n\">A</span> <span class=\"o\">+</span> <span class=\"n\">a</span> <span class=\"o\">!=</span> <span class=\"n\">B</span> <span class=\"o\">+</span> <span class=\"n\">b</span> <span class=\"ow\">and</span> <span class=\"n\">A</span> <span class=\"o\">-</span> <span class=\"n\">a</span> <span class=\"o\">!=</span> <span class=\"n\">B</span> <span class=\"o\">-</span> <span class=\"n\">b</span><span class=\"p\">)</span>\n",
       "</pre></div>\n",
       "</body>\n",
       "</html>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psource(queen_constraint)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **NQueensCSP** method implements methods that support solving the problem via **min_conflicts** which is one of the techniques for solving CSPs. Because **min_conflicts** hill climbs the number of conflicts to solve, the CSP **assign** and **unassign** are modified to record conflicts. More details about the structures **rows**, **downs**, **ups** which help in recording conflicts are explained in the docstring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
       "   \"http://www.w3.org/TR/html4/strict.dtd\">\n",
       "\n",
       "<html>\n",
       "<head>\n",
       "  <title></title>\n",
       "  <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
       "  <style type=\"text/css\">\n",
       "td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
       "span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
       "pre { line-height: 125%; }\n",
       "body .hll { background-color: #ffffcc }\n",
       "body  { background: #f8f8f8; }\n",
       "body .c { color: #408080; font-style: italic } /* Comment */\n",
       "body .err { border: 1px solid #FF0000 } /* Error */\n",
       "body .k { color: #008000; font-weight: bold } /* Keyword */\n",
       "body .o { color: #666666 } /* Operator */\n",
       "body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       "body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       "body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       "body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       "body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       "body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       "body .gd { color: #A00000 } /* Generic.Deleted */\n",
       "body .ge { font-style: italic } /* Generic.Emph */\n",
       "body .gr { color: #FF0000 } /* Generic.Error */\n",
       "body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       "body .gi { color: #00A000 } /* Generic.Inserted */\n",
       "body .go { color: #888888 } /* Generic.Output */\n",
       "body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       "body .gs { font-weight: bold } /* Generic.Strong */\n",
       "body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       "body .gt { color: #0044DD } /* Generic.Traceback */\n",
       "body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       "body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       "body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       "body .kp { color: #008000 } /* Keyword.Pseudo */\n",
       "body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       "body .kt { color: #B00040 } /* Keyword.Type */\n",
       "body .m { color: #666666 } /* Literal.Number */\n",
       "body .s { color: #BA2121 } /* Literal.String */\n",
       "body .na { color: #7D9029 } /* Name.Attribute */\n",
       "body .nb { color: #008000 } /* Name.Builtin */\n",
       "body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       "body .no { color: #880000 } /* Name.Constant */\n",
       "body .nd { color: #AA22FF } /* Name.Decorator */\n",
       "body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       "body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       "body .nf { color: #0000FF } /* Name.Function */\n",
       "body .nl { color: #A0A000 } /* Name.Label */\n",
       "body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       "body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       "body .nv { color: #19177C } /* Name.Variable */\n",
       "body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       "body .w { color: #bbbbbb } /* Text.Whitespace */\n",
       "body .mb { color: #666666 } /* Literal.Number.Bin */\n",
       "body .mf { color: #666666 } /* Literal.Number.Float */\n",
       "body .mh { color: #666666 } /* Literal.Number.Hex */\n",
       "body .mi { color: #666666 } /* Literal.Number.Integer */\n",
       "body .mo { color: #666666 } /* Literal.Number.Oct */\n",
       "body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       "body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       "body .sc { color: #BA2121 } /* Literal.String.Char */\n",
       "body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       "body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       "body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       "body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       "body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       "body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       "body .sx { color: #008000 } /* Literal.String.Other */\n",
       "body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       "body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       "body .ss { color: #19177C } /* Literal.String.Symbol */\n",
       "body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       "body .fm { color: #0000FF } /* Name.Function.Magic */\n",
       "body .vc { color: #19177C } /* Name.Variable.Class */\n",
       "body .vg { color: #19177C } /* Name.Variable.Global */\n",
       "body .vi { color: #19177C } /* Name.Variable.Instance */\n",
       "body .vm { color: #19177C } /* Name.Variable.Magic */\n",
       "body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "\n",
       "  </style>\n",
       "</head>\n",
       "<body>\n",
       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">NQueensCSP</span><span class=\"p\">(</span><span class=\"n\">CSP</span><span class=\"p\">):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;Make a CSP for the nQueens problem for search with min_conflicts.</span>\n",
       "<span class=\"sd\">    Suitable for large n, it uses only data structures of size O(n).</span>\n",
       "<span class=\"sd\">    Think of placing queens one per column, from left to right.</span>\n",
       "<span class=\"sd\">    That means position (x, y) represents (var, val) in the CSP.</span>\n",
       "<span class=\"sd\">    The main structures are three arrays to count queens that could conflict:</span>\n",
       "<span class=\"sd\">        rows[i]      Number of queens in the ith row (i.e val == i)</span>\n",
       "<span class=\"sd\">        downs[i]     Number of queens in the \\ diagonal</span>\n",
       "<span class=\"sd\">                     such that their (x, y) coordinates sum to i</span>\n",
       "<span class=\"sd\">        ups[i]       Number of queens in the / diagonal</span>\n",
       "<span class=\"sd\">                     such that their (x, y) coordinates have x-y+n-1 = i</span>\n",
       "<span class=\"sd\">    We increment/decrement these counts each time a queen is placed/moved from</span>\n",
       "<span class=\"sd\">    a row/diagonal. So moving is O(1), as is nconflicts.  But choosing</span>\n",
       "<span class=\"sd\">    a variable, and a best value for the variable, are each O(n).</span>\n",
       "<span class=\"sd\">    If you want, you can keep track of conflicted variables, then variable</span>\n",
       "<span class=\"sd\">    selection will also be O(1).</span>\n",
       "<span class=\"sd\">    &gt;&gt;&gt; len(backtracking_search(NQueensCSP(8)))</span>\n",
       "<span class=\"sd\">    8</span>\n",
       "<span class=\"sd\">    &quot;&quot;&quot;</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">n</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;Initialize data structures for n Queens.&quot;&quot;&quot;</span>\n",
       "        <span class=\"n\">CSP</span><span class=\"o\">.</span><span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">)),</span> <span class=\"n\">UniversalDict</span><span class=\"p\">(</span><span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">))),</span>\n",
       "                     <span class=\"n\">UniversalDict</span><span class=\"p\">(</span><span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">))),</span> <span class=\"n\">queen_constraint</span><span class=\"p\">)</span>\n",
       "\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">rows</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">n</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">ups</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">downs</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">nconflicts</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;The number of conflicts, as recorded with each assignment.</span>\n",
       "<span class=\"sd\">        Count conflicts in row and in up, down diagonals. If there</span>\n",
       "<span class=\"sd\">        is a queen there, it can&#39;t conflict with itself, so subtract 3.&quot;&quot;&quot;</span>\n",
       "        <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">variables</span><span class=\"p\">)</span>\n",
       "        <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">rows</span><span class=\"p\">[</span><span class=\"n\">val</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">downs</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"o\">+</span><span class=\"n\">val</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">ups</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"o\">-</span><span class=\"n\">val</span><span class=\"o\">+</span><span class=\"n\">n</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">]</span>\n",
       "        <span class=\"k\">if</span> <span class=\"n\">assignment</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"bp\">None</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"n\">val</span><span class=\"p\">:</span>\n",
       "            <span class=\"n\">c</span> <span class=\"o\">-=</span> <span class=\"mi\">3</span>\n",
       "        <span class=\"k\">return</span> <span class=\"n\">c</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">assign</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;Assign var, and keep track of conflicts.&quot;&quot;&quot;</span>\n",
       "        <span class=\"n\">oldval</span> <span class=\"o\">=</span> <span class=\"n\">assignment</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"bp\">None</span><span class=\"p\">)</span>\n",
       "        <span class=\"k\">if</span> <span class=\"n\">val</span> <span class=\"o\">!=</span> <span class=\"n\">oldval</span><span class=\"p\">:</span>\n",
       "            <span class=\"k\">if</span> <span class=\"n\">oldval</span> <span class=\"ow\">is</span> <span class=\"ow\">not</span> <span class=\"bp\">None</span><span class=\"p\">:</span>  <span class=\"c1\"># Remove old val if there was one</span>\n",
       "                <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">record_conflict</span><span class=\"p\">(</span><span class=\"n\">assignment</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">oldval</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "            <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">record_conflict</span><span class=\"p\">(</span><span class=\"n\">assignment</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "            <span class=\"n\">CSP</span><span class=\"o\">.</span><span class=\"n\">assign</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">)</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">unassign</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;Remove var from assignment (if it is there) and track conflicts.&quot;&quot;&quot;</span>\n",
       "        <span class=\"k\">if</span> <span class=\"n\">var</span> <span class=\"ow\">in</span> <span class=\"n\">assignment</span><span class=\"p\">:</span>\n",
       "            <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">record_conflict</span><span class=\"p\">(</span><span class=\"n\">assignment</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">[</span><span class=\"n\">var</span><span class=\"p\">],</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "        <span class=\"n\">CSP</span><span class=\"o\">.</span><span class=\"n\">unassign</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">)</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">record_conflict</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">delta</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;Record conflicts caused by addition or deletion of a Queen.&quot;&quot;&quot;</span>\n",
       "        <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">variables</span><span class=\"p\">)</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">rows</span><span class=\"p\">[</span><span class=\"n\">val</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">delta</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">downs</span><span class=\"p\">[</span><span class=\"n\">var</span> <span class=\"o\">+</span> <span class=\"n\">val</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">delta</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">ups</span><span class=\"p\">[</span><span class=\"n\">var</span> <span class=\"o\">-</span> <span class=\"n\">val</span> <span class=\"o\">+</span> <span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">delta</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">display</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">):</span>\n",
       "        <span class=\"sd\">&quot;&quot;&quot;Print the queens and the nconflicts values (for debugging).&quot;&quot;&quot;</span>\n",
       "        <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">variables</span><span class=\"p\">)</span>\n",
       "        <span class=\"k\">for</span> <span class=\"n\">val</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span>\n",
       "            <span class=\"k\">for</span> <span class=\"n\">var</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span>\n",
       "                <span class=\"k\">if</span> <span class=\"n\">assignment</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"s1\">&#39;&#39;</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"n\">val</span><span class=\"p\">:</span>\n",
       "                    <span class=\"n\">ch</span> <span class=\"o\">=</span> <span class=\"s1\">&#39;Q&#39;</span>\n",
       "                <span class=\"k\">elif</span> <span class=\"p\">(</span><span class=\"n\">var</span> <span class=\"o\">+</span> <span class=\"n\">val</span><span class=\"p\">)</span> <span class=\"o\">%</span> <span class=\"mi\">2</span> <span class=\"o\">==</span> <span class=\"mi\">0</span><span class=\"p\">:</span>\n",
       "                    <span class=\"n\">ch</span> <span class=\"o\">=</span> <span class=\"s1\">&#39;.&#39;</span>\n",
       "                <span class=\"k\">else</span><span class=\"p\">:</span>\n",
       "                    <span class=\"n\">ch</span> <span class=\"o\">=</span> <span class=\"s1\">&#39;-&#39;</span>\n",
       "                <span class=\"k\">print</span><span class=\"p\">(</span><span class=\"n\">ch</span><span class=\"p\">,</span> <span class=\"n\">end</span><span class=\"o\">=</span><span class=\"s1\">&#39; &#39;</span><span class=\"p\">)</span>\n",
       "            <span class=\"k\">print</span><span class=\"p\">(</span><span class=\"s1\">&#39;    &#39;</span><span class=\"p\">,</span> <span class=\"n\">end</span><span class=\"o\">=</span><span class=\"s1\">&#39; &#39;</span><span class=\"p\">)</span>\n",
       "            <span class=\"k\">for</span> <span class=\"n\">var</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span>\n",
       "                <span class=\"k\">if</span> <span class=\"n\">assignment</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"s1\">&#39;&#39;</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"n\">val</span><span class=\"p\">:</span>\n",
       "                    <span class=\"n\">ch</span> <span class=\"o\">=</span> <span class=\"s1\">&#39;*&#39;</span>\n",
       "                <span class=\"k\">else</span><span class=\"p\">:</span>\n",
       "                    <span class=\"n\">ch</span> <span class=\"o\">=</span> <span class=\"s1\">&#39; &#39;</span>\n",
       "                <span class=\"k\">print</span><span class=\"p\">(</span><span class=\"nb\">str</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">nconflicts</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">assignment</span><span class=\"p\">))</span> <span class=\"o\">+</span> <span class=\"n\">ch</span><span class=\"p\">,</span> <span class=\"n\">end</span><span class=\"o\">=</span><span class=\"s1\">&#39; &#39;</span><span class=\"p\">)</span>\n",
       "            <span class=\"k\">print</span><span class=\"p\">()</span>\n",
       "</pre></div>\n",
       "</body>\n",
       "</html>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psource(NQueensCSP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _ ___init___ _ method takes only one parameter **n** the size of the problem. To create an instance we just pass the required n into the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eight_queens = NQueensCSP(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have defined our CSP. \n",
    "We now need to solve this.\n",
    "\n",
    "### Min-conflicts\n",
    "As stated above, the `min_conflicts` algorithm is an efficient method to solve such a problem.\n",
    "<br>\n",
    "To begin with, all the variables of the CSP are _randomly_ initialized. \n",
    "<br>\n",
    "The algorithm then randomly selects a variable that has conflicts and violates some constraints of the CSP.\n",
    "<br>\n",
    "The selected variable is then assigned a value that _minimizes_ the number of conflicts.\n",
    "<br>\n",
    "This is a simple stochastic algorithm which works on a principle similar to **Hill-climbing**.\n",
    "The conflicting state is repeatedly changed into a state with fewer conflicts in an attempt to reach an approximate solution.\n",
    "<br>\n",
    "This algorithm sometimes benefits from having a good initial assignment.\n",
    "Using greedy techniques to get a good initial assignment and then using `min_conflicts` to solve the CSP can speed up the procedure dramatically, especially for CSPs with a large state space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
       "   \"http://www.w3.org/TR/html4/strict.dtd\">\n",
       "\n",
       "<html>\n",
       "<head>\n",
       "  <title></title>\n",
       "  <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
       "  <style type=\"text/css\">\n",
       "td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
       "span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
       "pre { line-height: 125%; }\n",
       "body .hll { background-color: #ffffcc }\n",
       "body  { background: #f8f8f8; }\n",
       "body .c { color: #408080; font-style: italic } /* Comment */\n",
       "body .err { border: 1px solid #FF0000 } /* Error */\n",
       "body .k { color: #008000; font-weight: bold } /* Keyword */\n",
       "body .o { color: #666666 } /* Operator */\n",
       "body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       "body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       "body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       "body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       "body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       "body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       "body .gd { color: #A00000 } /* Generic.Deleted */\n",
       "body .ge { font-style: italic } /* Generic.Emph */\n",
       "body .gr { color: #FF0000 } /* Generic.Error */\n",
       "body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       "body .gi { color: #00A000 } /* Generic.Inserted */\n",
       "body .go { color: #888888 } /* Generic.Output */\n",
       "body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       "body .gs { font-weight: bold } /* Generic.Strong */\n",
       "body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       "body .gt { color: #0044DD } /* Generic.Traceback */\n",
       "body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       "body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       "body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       "body .kp { color: #008000 } /* Keyword.Pseudo */\n",
       "body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       "body .kt { color: #B00040 } /* Keyword.Type */\n",
       "body .m { color: #666666 } /* Literal.Number */\n",
       "body .s { color: #BA2121 } /* Literal.String */\n",
       "body .na { color: #7D9029 } /* Name.Attribute */\n",
       "body .nb { color: #008000 } /* Name.Builtin */\n",
       "body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       "body .no { color: #880000 } /* Name.Constant */\n",
       "body .nd { color: #AA22FF } /* Name.Decorator */\n",
       "body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       "body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       "body .nf { color: #0000FF } /* Name.Function */\n",
       "body .nl { color: #A0A000 } /* Name.Label */\n",
       "body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       "body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       "body .nv { color: #19177C } /* Name.Variable */\n",
       "body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       "body .w { color: #bbbbbb } /* Text.Whitespace */\n",
       "body .mb { color: #666666 } /* Literal.Number.Bin */\n",
       "body .mf { color: #666666 } /* Literal.Number.Float */\n",
       "body .mh { color: #666666 } /* Literal.Number.Hex */\n",
       "body .mi { color: #666666 } /* Literal.Number.Integer */\n",
       "body .mo { color: #666666 } /* Literal.Number.Oct */\n",
       "body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       "body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       "body .sc { color: #BA2121 } /* Literal.String.Char */\n",
       "body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       "body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       "body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       "body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       "body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       "body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       "body .sx { color: #008000 } /* Literal.String.Other */\n",
       "body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       "body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       "body .ss { color: #19177C } /* Literal.String.Symbol */\n",
       "body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       "body .fm { color: #0000FF } /* Name.Function.Magic */\n",
       "body .vc { color: #19177C } /* Name.Variable.Class */\n",
       "body .vg { color: #19177C } /* Name.Variable.Global */\n",
       "body .vi { color: #19177C } /* Name.Variable.Instance */\n",
       "body .vm { color: #19177C } /* Name.Variable.Magic */\n",
       "body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "\n",
       "  </style>\n",
       "</head>\n",
       "<body>\n",
       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">min_conflicts</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">max_steps</span><span class=\"o\">=</span><span class=\"mi\">100000</span><span class=\"p\">):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;Solve a CSP by stochastic hillclimbing on the number of conflicts.&quot;&quot;&quot;</span>\n",
       "    <span class=\"c1\"># Generate a complete assignment for all variables (probably with conflicts)</span>\n",
       "    <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n",
       "    <span class=\"k\">for</span> <span class=\"n\">var</span> <span class=\"ow\">in</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">variables</span><span class=\"p\">:</span>\n",
       "        <span class=\"n\">val</span> <span class=\"o\">=</span> <span class=\"n\">min_conflicts_value</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">current</span><span class=\"p\">)</span>\n",
       "        <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">assign</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">current</span><span class=\"p\">)</span>\n",
       "    <span class=\"c1\"># Now repeatedly choose a random conflicted variable and change it</span>\n",
       "    <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">max_steps</span><span class=\"p\">):</span>\n",
       "        <span class=\"n\">conflicted</span> <span class=\"o\">=</span> <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">conflicted_vars</span><span class=\"p\">(</span><span class=\"n\">current</span><span class=\"p\">)</span>\n",
       "        <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">conflicted</span><span class=\"p\">:</span>\n",
       "            <span class=\"k\">return</span> <span class=\"n\">current</span>\n",
       "        <span class=\"n\">var</span> <span class=\"o\">=</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">choice</span><span class=\"p\">(</span><span class=\"n\">conflicted</span><span class=\"p\">)</span>\n",
       "        <span class=\"n\">val</span> <span class=\"o\">=</span> <span class=\"n\">min_conflicts_value</span><span class=\"p\">(</span><span class=\"n\">csp</span><span class=\"p\">,</span> <span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">current</span><span class=\"p\">)</span>\n",
       "        <span class=\"n\">csp</span><span class=\"o\">.</span><span class=\"n\">assign</span><span class=\"p\">(</span><span class=\"n\">var</span><span class=\"p\">,</span> <span class=\"n\">val</span><span class=\"p\">,</span> <span class=\"n\">current</span><span class=\"p\">)</span>\n",
       "    <span class=\"k\">return</span> <span class=\"bp\">None</span>\n",
       "</pre></div>\n",
       "</body>\n",
       "</html>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psource(min_conflicts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this algorithm  to solve the `eight_queens` CSP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "solution = min_conflicts(eight_queens)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is indeed a valid solution. \n",
    "<br>\n",
    "`notebook.py` has a helper function to visualize the solution space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22a2b8436a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_NQueens(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets' see if we can find a different solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22a2bb03d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eight_queens = NQueensCSP(8)\n",
    "solution = min_conflicts(eight_queens)\n",
    "plot_NQueens(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution is a bit different this time. \n",
    "Running the above cell several times should give you various valid solutions.\n",
    "<br>\n",
    "In the `search.ipynb` notebook, we will see how NQueensProblem can be solved using a heuristic search method such as `uniform_cost_search` and `astar_search`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper Functions\n",
    "\n",
    "We will now implement a few helper functions that will help us visualize the Coloring Problem. We will make some modifications to the existing Classes and Functions for additional book keeping. To begin we modify the **assign** and **unassign** methods in the **CSP** to add a copy of the assignment to the **assignment_history**. We call this new class **InstruCSP**. This will allow us to see how the assignment evolves over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import copy\n",
    "class InstruCSP(CSP):\n",
    "    \n",
    "    def __init__(self, variables, domains, neighbors, constraints):\n",
    "        super().__init__(variables, domains, neighbors, constraints)\n",
    "        self.assignment_history = []\n",
    "        \n",
    "    def assign(self, var, val, assignment):\n",
    "        super().assign(var,val, assignment)\n",
    "        self.assignment_history.append(copy.deepcopy(assignment))\n",
    "    \n",
    "    def unassign(self, var, assignment):\n",
    "        super().unassign(var,assignment)\n",
    "        self.assignment_history.append(copy.deepcopy(assignment))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define **make_instru** which takes an instance of **CSP** and returns a **InstruCSP** instance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_instru(csp):\n",
    "    return InstruCSP(csp.variables, csp.domains, csp.neighbors, csp.constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now use a graph defined as a dictionary for plotting purposes in our Graph Coloring Problem. The keys are the nodes and their corresponding values are the nodes they are connected to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "neighbors = {\n",
    "    0: [6, 11, 15, 18, 4, 11, 6, 15, 18, 4], \n",
    "    1: [12, 12, 14, 14], \n",
    "    2: [17, 6, 11, 6, 11, 10, 17, 14, 10, 14], \n",
    "    3: [20, 8, 19, 12, 20, 19, 8, 12], \n",
    "    4: [11, 0, 18, 5, 18, 5, 11, 0], \n",
    "    5: [4, 4], \n",
    "    6: [8, 15, 0, 11, 2, 14, 8, 11, 15, 2, 0, 14], \n",
    "    7: [13, 16, 13, 16], \n",
    "    8: [19, 15, 6, 14, 12, 3, 6, 15, 19, 12, 3, 14], \n",
    "    9: [20, 15, 19, 16, 15, 19, 20, 16], \n",
    "    10: [17, 11, 2, 11, 17, 2], \n",
    "    11: [6, 0, 4, 10, 2, 6, 2, 0, 10, 4], \n",
    "    12: [8, 3, 8, 14, 1, 3, 1, 14], \n",
    "    13: [7, 15, 18, 15, 16, 7, 18, 16], \n",
    "    14: [8, 6, 2, 12, 1, 8, 6, 2, 1, 12], \n",
    "    15: [8, 6, 16, 13, 18, 0, 6, 8, 19, 9, 0, 19, 13, 18, 9, 16], \n",
    "    16: [7, 15, 13, 9, 7, 13, 15, 9], \n",
    "    17: [10, 2, 2, 10], \n",
    "    18: [15, 0, 13, 4, 0, 15, 13, 4], \n",
    "    19: [20, 8, 15, 9, 15, 8, 3, 20, 3, 9], \n",
    "    20: [3, 19, 9, 19, 3, 9]\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function will work perfectly for it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "coloring_problem = MapColoringCSP('RGBY', neighbors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "coloring_problem1 = make_instru(coloring_problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BACKTRACKING SEARCH\n",
    "\n",
    "For solving a CSP the main issue with Naive search algorithms is that they can continue expanding obviously wrong paths. In backtracking search, we check constraints as we go. Backtracking is just the above idea combined with the fact that we are dealing with one variable at a time. Backtracking Search is implemented in the repository as the function **backtracking_search**. This is the same as **Figure 6.5** in the book. The function takes as input a CSP and few other optional parameters which can be used to further speed it up. The function returns the correct assignment if it satisfies the goal. We will discuss these later. Let us solve our **coloring_problem1** with **backtracking_search**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = backtracking_search(coloring_problem1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 'R',\n",
       " 1: 'R',\n",
       " 2: 'R',\n",
       " 3: 'R',\n",
       " 4: 'G',\n",
       " 5: 'R',\n",
       " 6: 'G',\n",
       " 7: 'R',\n",
       " 8: 'B',\n",
       " 9: 'R',\n",
       " 10: 'G',\n",
       " 11: 'B',\n",
       " 12: 'G',\n",
       " 13: 'G',\n",
       " 14: 'Y',\n",
       " 15: 'Y',\n",
       " 16: 'B',\n",
       " 17: 'B',\n",
       " 18: 'B',\n",
       " 19: 'G',\n",
       " 20: 'B'}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result # A dictonary of assignments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us also check the number of assignments made."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coloring_problem1.nassigns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us check the total number of assignments and unassignments which is the length of our assignment history."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(coloring_problem1.assignment_history)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us explore the optional keyword arguments that the **backtracking_search** function takes. These optional arguments help speed up the assignment further. Along with these, we will also point out to methods in the CSP class that help make this work. \n",
    "\n",
    "The first of these is **select_unassigned_variable**. It takes in a function that helps in deciding the order in which variables will be selected for assignment. We use a heuristic called Most Restricted Variable which is implemented by the function **mrv**. The idea behind **mrv** is to choose the variable with the fewest legal values left in its domain. The intuition behind selecting the **mrv** or the most constrained variable is that it allows us to encounter failure quickly before going too deep into a tree if we have selected a wrong step before. The **mrv** implementation makes use of another function **num_legal_values** to sort out the variables by a number of legal values left in its domain. This function, in turn, calls the **nconflicts** method of the **CSP** to return such values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(mrv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(num_legal_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(CSP.nconflicts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another ordering related parameter **order_domain_values** governs the value ordering. Here we select the Least Constraining Value which is implemented by the function **lcv**. The idea is to select the value which rules out the fewest values in the remaining variables. The intuition behind selecting the **lcv** is that it leaves a lot of freedom to assign values later. The idea behind selecting the mrc and lcv makes sense because we need to do all variables but for values, we might better try the ones that are likely. So for vars, we face the hard ones first.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(lcv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the third parameter **inference** can make use of one of the two techniques called Arc Consistency or Forward Checking. The details of these methods can be found in the **Section 6.3.2** of the book. In short the idea of inference is to detect the possible failure before it occurs and to look ahead to not make mistakes. **mac** and **forward_checking** implement these two techniques. The **CSP** methods **support_pruning**, **suppose**, **prune**, **choices**, **infer_assignment** and **restore** help in using these techniques. You can know more about these by looking up the source code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us compare the performance with these parameters enabled vs the default parameters. We will use the Graph Coloring problem instance usa for comparison. We will call the instances **solve_simple** and **solve_parameters** and solve them using backtracking and compare the number of assignments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "solve_simple = copy.deepcopy(usa)\n",
    "solve_parameters = copy.deepcopy(usa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'AL': 'B',\n",
       " 'AR': 'B',\n",
       " 'AZ': 'R',\n",
       " 'CA': 'Y',\n",
       " 'CO': 'R',\n",
       " 'CT': 'R',\n",
       " 'DC': 'B',\n",
       " 'DE': 'B',\n",
       " 'FL': 'G',\n",
       " 'GA': 'R',\n",
       " 'IA': 'B',\n",
       " 'ID': 'R',\n",
       " 'IL': 'G',\n",
       " 'IN': 'R',\n",
       " 'KA': 'B',\n",
       " 'KY': 'B',\n",
       " 'LA': 'G',\n",
       " 'MA': 'G',\n",
       " 'MD': 'G',\n",
       " 'ME': 'R',\n",
       " 'MI': 'B',\n",
       " 'MN': 'G',\n",
       " 'MO': 'R',\n",
       " 'MS': 'R',\n",
       " 'MT': 'G',\n",
       " 'NC': 'B',\n",
       " 'ND': 'B',\n",
       " 'NE': 'G',\n",
       " 'NH': 'B',\n",
       " 'NJ': 'G',\n",
       " 'NM': 'B',\n",
       " 'NV': 'B',\n",
       " 'NY': 'B',\n",
       " 'OH': 'G',\n",
       " 'OK': 'G',\n",
       " 'OR': 'G',\n",
       " 'PA': 'R',\n",
       " 'RI': 'B',\n",
       " 'SC': 'G',\n",
       " 'SD': 'R',\n",
       " 'TN': 'G',\n",
       " 'TX': 'R',\n",
       " 'UT': 'G',\n",
       " 'VA': 'R',\n",
       " 'VT': 'R',\n",
       " 'WA': 'B',\n",
       " 'WI': 'R',\n",
       " 'WV': 'Y',\n",
       " 'WY': 'B'}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backtracking_search(solve_simple)\n",
    "backtracking_search(solve_parameters, order_domain_values=lcv, select_unassigned_variable=mrv, inference=mac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "460302"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_simple.nassigns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_parameters.nassigns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TREE CSP SOLVER\n",
    "\n",
    "The `tree_csp_solver` function (**Figure 6.11** in the book) can be used to solve problems whose constraint graph is a tree. Given a CSP, with `neighbors` forming a tree, it returns an assignment that satisfies the given constraints. The algorithm works as follows:\n",
    "\n",
    "First it finds the *topological sort* of the tree. This is an ordering of the tree where each variable/node comes after its parent in the tree. The function that accomplishes this is `topological_sort`, which builds the topological sort using the recursive function `build_topological`. That function is an augmented DFS, where each newly visited node of the tree is pushed on a stack. The stack in the end holds the variables topologically sorted.\n",
    "\n",
    "Then the algorithm makes arcs between each parent and child consistent. *Arc-consistency* between two variables, *a* and *b*, occurs when for every possible value of *a* there is an assignment in *b* that satisfies the problem's constraints. If such an assignment cannot be found, then the problematic value is removed from *a*'s possible values. This is done with the use of the function `make_arc_consistent` which takes as arguments a variable `Xj` and its parent, and makes the arc between them consistent by removing any values from the parent which do not allow for a consistent assignment in `Xj`.\n",
    "\n",
    "If an arc cannot be made consistent, the solver fails. If every arc is made consistent, we move to assigning values.\n",
    "\n",
    "First we assign a random value to the root from its domain and then we start assigning values to the rest of the variables. Since the graph is now arc-consistent, we can simply move from variable to variable picking any remaining consistent values. At the end we are left with a valid assignment. If at any point though we find a variable where no consistent value is left in its domain, the solver fails.\n",
    "\n",
    "The implementation of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psource(tree_csp_solver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now use the above function to solve a problem. More specifically, we will solve the problem of coloring the map of Australia. At our disposal we have two colors: Red and Blue. As a reminder, this is the graph of Australia:\n",
    "\n",
    "`\"SA: WA NT Q NSW V; NT: WA Q; NSW: Q V; T: \"`\n",
    "\n",
    "Unfortunately as you can see the above is not a tree. If, though, we remove `SA`, which has arcs to `WA`, `NT`, `Q`, `NSW` and `V`, we are left with a tree (we also remove `T`, since it has no in-or-out arcs). We can now solve this using our algorithm. Let's define the map coloring problem at hand:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "australia_small = MapColoringCSP(list('RB'),\n",
    "                           'NT: WA Q; NSW: Q V')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will input `australia_small` to the `tree_csp_solver` and we will print the given assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Q': 'R', 'NT': 'B', 'NSW': 'B', 'WA': 'R', 'V': 'R'}\n"
     ]
    }
   ],
   "source": [
    "assignment = tree_csp_solver(australia_small)\n",
    "print(assignment)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`WA`, `Q` and `V` got painted with the same color and `NT` and `NSW` got painted with the other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GRAPH COLORING VISUALIZATION\n",
    "\n",
    "Next, we define some functions to create the visualisation from the assignment_history of **coloring_problem1**. The reader need not concern himself with the code that immediately follows as it is the usage of Matplotib with IPython Widgets. If you are interested in reading more about these visit [ipywidgets.readthedocs.io](http://ipywidgets.readthedocs.io). We will be using the **networkx** library to generate graphs. These graphs can be treated as the graph that needs to be colored or as a constraint graph for this problem. If interested you can read a dead simple tutorial [here](https://www.udacity.com/wiki/creating-network-graphs-with-python). We start by importing the necessary libraries and initializing matplotlib inline.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ipython widgets we will be using require the plots in the form of a step function such that there is a graph corresponding to each value. We define the **make_update_step_function** which return such a function. It takes in as inputs the neighbors/graph along with an instance of the **InstruCSP**. This will be more clear with the example below. If this sounds confusing do not worry this is not the part of the core material and our only goal is to help you visualize how the process works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_update_step_function(graph, instru_csp):\n",
    "    \n",
    "    def draw_graph(graph):\n",
    "        # create networkx graph\n",
    "        G=nx.Graph(graph)\n",
    "        # draw graph\n",
    "        pos = nx.spring_layout(G,k=0.15)\n",
    "        return (G, pos)\n",
    "    \n",
    "    G, pos = draw_graph(graph)\n",
    "    \n",
    "    def update_step(iteration):\n",
    "        # here iteration is the index of the assignment_history we want to visualize.\n",
    "        current = instru_csp.assignment_history[iteration]\n",
    "        #  We convert the particular assignment to a default dict so that the color for nodes which \n",
    "        # have not been assigned defaults to black.\n",
    "        current = defaultdict(lambda: 'Black', current)\n",
    "\n",
    "        # Now we use colors in the list and default to black otherwise.\n",
    "        colors = [current[node] for node in G.node.keys()]\n",
    "        # Finally drawing the nodes.\n",
    "        nx.draw(G, pos, node_color=colors, node_size=500)\n",
    "\n",
    "        labels = {label:label for label in G.node}\n",
    "        # Labels shifted by offset so as to not overlap nodes.\n",
    "        label_pos = {key:[value[0], value[1]+0.03] for key, value in pos.items()}\n",
    "        nx.draw_networkx_labels(G, label_pos, labels, font_size=20)\n",
    "\n",
    "        # show graph\n",
    "        plt.show()\n",
    "\n",
    "    return update_step  # <-- this is a function\n",
    "\n",
    "def make_visualize(slider):\n",
    "    ''' Takes an input a slider and returns \n",
    "        callback function for timer and animation\n",
    "    '''\n",
    "    \n",
    "    def visualize_callback(Visualize, time_step):\n",
    "        if Visualize is True:\n",
    "            for i in range(slider.min, slider.max + 1):\n",
    "                slider.value = i\n",
    "                time.sleep(float(time_step))\n",
    "    \n",
    "    return visualize_callback\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally let us plot our problem. We first use the function above to obtain a step function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "step_func = make_update_step_function(neighbors, coloring_problem1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we set the canvas size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (18.0, 18.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally our plot using ipywidget slider and matplotib. You can move the slider to experiment and see the coloring change. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds upto one second for each time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABTgAAAUyCAYAAAAqcpudAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb34f4e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f9d8fbb23a9f446585fac31b107eb123"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "\n",
    "iteration_slider = widgets.IntSlider(min=0, max=len(coloring_problem1.assignment_history)-1, step=1, value=0)\n",
    "w=widgets.interactive(step_func,iteration=iteration_slider)\n",
    "display(w)\n",
    "\n",
    "visualize_callback = make_visualize(iteration_slider)\n",
    "\n",
    "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
    "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
    "\n",
    "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
    "display(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## N-QUEENS VISUALIZATION\n",
    "\n",
    "Just like the Graph Coloring Problem we will start with defining a few helper functions to help us visualize the assignments as they evolve over time. The **make_plot_board_step_function** behaves similar to the **make_update_step_function** introduced earlier. It initializes a chess board in the form of a 2D grid with alternating 0s and 1s. This is used by **plot_board_step** function which draws the board using matplotlib and adds queens to it. This function also calls the **label_queen_conflicts** which modifies the grid placing 3 in positions in a position where there is a conflict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def label_queen_conflicts(assignment,grid):\n",
    "    ''' Mark grid with queens that are under conflict. '''\n",
    "    for col, row in assignment.items(): # check each queen for conflict\n",
    "        row_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n",
    "                         if temp_row == row and temp_col != col}\n",
    "        up_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n",
    "                        if temp_row+temp_col == row+col and temp_col != col}\n",
    "        down_conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n",
    "                          if temp_row-temp_col == row-col and temp_col != col}\n",
    "        \n",
    "        # Now marking the grid.\n",
    "        for col, row in row_conflicts.items():\n",
    "                grid[col][row] = 3\n",
    "        for col, row in up_conflicts.items():\n",
    "                grid[col][row] = 3\n",
    "        for col, row in down_conflicts.items():\n",
    "                grid[col][row] = 3\n",
    "\n",
    "    return grid\n",
    "\n",
    "def make_plot_board_step_function(instru_csp):\n",
    "    '''ipywidgets interactive function supports\n",
    "       single parameter as input. This function\n",
    "       creates and return such a function by taking\n",
    "       in input other parameters.\n",
    "    '''\n",
    "    n = len(instru_csp.variables)\n",
    "    \n",
    "    \n",
    "    def plot_board_step(iteration):\n",
    "        ''' Add Queens to the Board.'''\n",
    "        data = instru_csp.assignment_history[iteration]\n",
    "        \n",
    "        grid = [[(col+row+1)%2 for col in range(n)] for row in range(n)]\n",
    "        grid = label_queen_conflicts(data, grid) # Update grid with conflict labels.\n",
    "        \n",
    "        # color map of fixed colors\n",
    "        cmap = matplotlib.colors.ListedColormap(['white','lightsteelblue','red'])\n",
    "        bounds=[0,1,2,3] # 0 for white 1 for black 2 onwards for conflict labels (red).\n",
    "        norm = matplotlib.colors.BoundaryNorm(bounds, cmap.N)\n",
    "        \n",
    "        fig = plt.imshow(grid, interpolation='nearest', cmap = cmap,norm=norm)\n",
    "\n",
    "        plt.axis('off')\n",
    "        fig.axes.get_xaxis().set_visible(False)\n",
    "        fig.axes.get_yaxis().set_visible(False)\n",
    "\n",
    "        # Place the Queens Unicode Symbol\n",
    "        for col, row in data.items():\n",
    "            fig.axes.text(row, col, u\"\\u265B\", va='center', ha='center', family='Dejavu Sans', fontsize=32)\n",
    "        plt.show()\n",
    "    \n",
    "    return plot_board_step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us visualize a solution obtained via backtracking. We use of the previosuly defined **make_instru** function for keeping a history of steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "twelve_queens_csp = NQueensCSP(12)\n",
    "backtracking_instru_queen = make_instru(twelve_queens_csp)\n",
    "result = backtracking_search(backtracking_instru_queen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "backtrack_queen_step = make_plot_board_step_function(backtracking_instru_queen) # Step Function for Widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now finally we set some matplotlib parameters to adjust how our plot will look. The font is necessary because the Black Queen Unicode character is not a part of all fonts. You can move the slider to experiment and observe the how queens are assigned. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click.The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds upto one second for each time step.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcgAAAHICAYAAADKoXrqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb328181d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e0cf790018f34082961a812b9bc7eb81"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (8.0, 8.0)\n",
    "matplotlib.rcParams['font.family'].append(u'Dejavu Sans')\n",
    "\n",
    "iteration_slider = widgets.IntSlider(min=0, max=len(backtracking_instru_queen.assignment_history)-1, step=0, value=0)\n",
    "w=widgets.interactive(backtrack_queen_step,iteration=iteration_slider)\n",
    "display(w)\n",
    "\n",
    "visualize_callback = make_visualize(iteration_slider)\n",
    "\n",
    "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
    "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
    "\n",
    "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
    "display(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us finally repeat the above steps for **min_conflicts** solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conflicts_instru_queen = make_instru(twelve_queens_csp)\n",
    "result = min_conflicts(conflicts_instru_queen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conflicts_step = make_plot_board_step_function(conflicts_instru_queen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The visualization has same features as the above. But here it also highlights the conflicts by labeling the conflicted queens with a red background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcgAAAHICAYAAADKoXrqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb30903ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a61406396a92432d9f8f40c6f7a52d3e"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iteration_slider = widgets.IntSlider(min=0, max=len(conflicts_instru_queen.assignment_history)-1, step=0, value=0)\n",
    "w=widgets.interactive(conflicts_step,iteration=iteration_slider)\n",
    "display(w)\n",
    "\n",
    "visualize_callback = make_visualize(iteration_slider)\n",
    "\n",
    "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n",
    "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n",
    "\n",
    "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n",
    "display(a)"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}