Rubik's Cube Solver.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Rubik's Cube Representation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A standard rubik's cube has 6 faces with 3x3 squares. Each face can be represented using a numpy array, with the ordering \n",
    "$$(front, up, down, left, right, top, bottom)$$\n",
    "Each cube operation rotates one face $\\pm90^\\circ$. One way to do this is to use quaternions to define rotations in 3-dimensional space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-23T23:29:06.643101",
     "start_time": "2017-03-23T23:29:06.141755"
    },
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "from Cube import RubiksCube\n",
    "import pandas as pd\n",
    "import itertools\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "%load_ext autoreload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-23T23:29:38.548883",
     "start_time": "2017-03-23T23:29:38.535243"
    },
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-23T23:29:07.575600",
     "start_time": "2017-03-23T23:29:07.563074"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from Solver import SingleMoveScorer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-23T23:42:23.023485",
     "start_time": "2017-03-23T23:42:22.983811"
    },
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "c = RubiksCube(3)\n",
    "c.rotate_cube(2,1,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[True,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False,\n",
       " False]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(0,0,-1) == x for x in c.rots]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Find the indices of array elements that are non-zero, grouped by element.\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "a : array_like\n",
       "    Input data.\n",
       "\n",
       "Returns\n",
       "-------\n",
       "index_array : ndarray\n",
       "    Indices of elements that are non-zero. Indices are grouped by element.\n",
       "\n",
       "See Also\n",
       "--------\n",
       "where, nonzero\n",
       "\n",
       "Notes\n",
       "-----\n",
       "``np.argwhere(a)`` is the same as ``np.transpose(np.nonzero(a))``.\n",
       "\n",
       "The output of ``argwhere`` is not suitable for indexing arrays.\n",
       "For this purpose use ``where(a)`` instead.\n",
       "\n",
       "Examples\n",
       "--------\n",
       ">>> x = np.arange(6).reshape(2,3)\n",
       ">>> x\n",
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])\n",
       ">>> np.argwhere(x>1)\n",
       "array([[0, 2],\n",
       "       [1, 0],\n",
       "       [1, 1],\n",
       "       [1, 2]])\n",
       "\u001b[0;31mFile:\u001b[0m      /usr/local/lib/python3.5/dist-packages/numpy/core/numeric.py\n",
       "\u001b[0;31mType:\u001b[0m      function\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "?np.argwhere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "total size of new array must be unchanged",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-663c3607033b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cube\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: total size of new array must be unchanged"
     ]
    }
   ],
   "source": [
    "np.argwhere(c._cube.reshape(6,3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "b=np.sum(c._cube.reshape(6,6,9),axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "b2=np.sum(c._cube.reshape(6,6,9),axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "c.rotate_cube(2,0,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 9, 9, 6, 6, 6])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(b,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6, 6, 6, 6, 4])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(b2,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2, -3, -3,  0,  0, -2])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(b2,axis=1)-np.max(b,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from CubeEnv import *\n",
    "from JSAnimation.IPython_display import display_animation\n",
    "from matplotlib import animation\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "\n",
    "e = CubeEnv()\n",
    "frames = []\n",
    "for t in range(100):\n",
    "    frames.append(e.render(mode=\"rgb_array\"))\n",
    "    action = e.action_space.sample()\n",
    "    e.step(action)\n",
    "    \n",
    "e.render(close=True)\n",
    "\n",
    "def display_frames_as_gif(frames):\n",
    "    \"\"\"\n",
    "    Displays a list of frames as a gif, with controls\n",
    "    \"\"\"\n",
    "    e.cube.show_layout(frames[0])\n",
    "\n",
    "    def animate(i):\n",
    "        e.cube.update_plot(frames[i])\n",
    "    anim = animation.FuncAnimation(plt.gcf(), animate, frames = len(frames), interval=50)\n",
    "    display(display_animation(anim, default_mode='loop'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gym import Env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mInit signature:\u001b[0m \u001b[0mEnv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mSource:\u001b[0m        \n",
       "\u001b[0;32mclass\u001b[0m \u001b[0mEnv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobject\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\"The main OpenAI Gym class. It encapsulates an environment with\u001b[0m\n",
       "\u001b[0;34m    arbitrary behind-the-scenes dynamics. An environment can be\u001b[0m\n",
       "\u001b[0;34m    partially or fully observed.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m    The main API methods that users of this class need to know are:\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        step\u001b[0m\n",
       "\u001b[0;34m        reset\u001b[0m\n",
       "\u001b[0;34m        render\u001b[0m\n",
       "\u001b[0;34m        close\u001b[0m\n",
       "\u001b[0;34m        seed\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m    When implementing an environment, override the following methods\u001b[0m\n",
       "\u001b[0;34m    in your subclass:\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        _step\u001b[0m\n",
       "\u001b[0;34m        _reset\u001b[0m\n",
       "\u001b[0;34m        _render\u001b[0m\n",
       "\u001b[0;34m        _close\u001b[0m\n",
       "\u001b[0;34m        _seed\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m    And set the following attributes:\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        action_space: The Space object corresponding to valid actions\u001b[0m\n",
       "\u001b[0;34m        observation_space: The Space object corresponding to valid observations\u001b[0m\n",
       "\u001b[0;34m        reward_range: A tuple corresponding to the min and max possible rewards\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m    Note: a default reward range set to [-inf,+inf] already exists. Set it if you want a narrower range.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m    The methods are accessed publicly as \"step\", \"reset\", etc.. The\u001b[0m\n",
       "\u001b[0;34m    non-underscored versions are wrapper methods to which we may add\u001b[0m\n",
       "\u001b[0;34m    functionality over time.\u001b[0m\n",
       "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m__new__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# We use __new__ since we want the env author to be able to\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# override __init__ without remembering to call super.\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0menv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mEnv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_env_closer_id\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0menv_closer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mregister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_closed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# Will be automatically set when creating an environment via 'make'\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;31m# Set this in SOME subclasses\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mmetadata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'render.modes'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mreward_range\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;31m# Override in SOME subclasses\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m_close\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;31m# Set these in ALL subclasses\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0maction_space\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mobservation_space\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;31m# Override in ALL subclasses\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m_reset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m_render\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'human'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m_seed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;31m# Do not override\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0m_owns_render\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mmonitor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mraise\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"env.monitor has been deprecated as of 12/23/2016. Remove your call to `env.monitor.start(directory)` and instead wrap your env with `env = gym.wrappers.Monitor(env, directory)` to record data.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Run one timestep of the environment's dynamics. When end of\u001b[0m\n",
       "\u001b[0;34m        episode is reached, you are responsible for calling `reset()`\u001b[0m\n",
       "\u001b[0;34m        to reset this environment's state.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Accepts an action and returns a tuple (observation, reward, done, info).\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Args:\u001b[0m\n",
       "\u001b[0;34m            action (object): an action provided by the environment\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Returns:\u001b[0m\n",
       "\u001b[0;34m            observation (object): agent's observation of the current environment\u001b[0m\n",
       "\u001b[0;34m            reward (float) : amount of reward returned after previous action\u001b[0m\n",
       "\u001b[0;34m            done (boolean): whether the episode has ended, in which case further step() calls will return undefined results\u001b[0m\n",
       "\u001b[0;34m            info (dict): contains auxiliary diagnostic information (helpful for debugging, and sometimes learning)\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mreset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Resets the state of the environment and returns an initial observation.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Returns: observation (object): the initial observation of the\u001b[0m\n",
       "\u001b[0;34m            space.\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mrender\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'human'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Renders the environment.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        The set of supported modes varies per environment. (And some\u001b[0m\n",
       "\u001b[0;34m        environments do not support rendering at all.) By convention,\u001b[0m\n",
       "\u001b[0;34m        if mode is:\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        - human: render to the current display or terminal and\u001b[0m\n",
       "\u001b[0;34m          return nothing. Usually for human consumption.\u001b[0m\n",
       "\u001b[0;34m        - rgb_array: Return an numpy.ndarray with shape (x, y, 3),\u001b[0m\n",
       "\u001b[0;34m          representing RGB values for an x-by-y pixel image, suitable\u001b[0m\n",
       "\u001b[0;34m          for turning into a video.\u001b[0m\n",
       "\u001b[0;34m        - ansi: Return a string (str) or StringIO.StringIO containing a\u001b[0m\n",
       "\u001b[0;34m          terminal-style text representation. The text can include newlines\u001b[0m\n",
       "\u001b[0;34m          and ANSI escape sequences (e.g. for colors).\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Note:\u001b[0m\n",
       "\u001b[0;34m            Make sure that your class's metadata 'render.modes' key includes\u001b[0m\n",
       "\u001b[0;34m              the list of supported modes. It's recommended to call super()\u001b[0m\n",
       "\u001b[0;34m              in implementations to use the functionality of this method.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Args:\u001b[0m\n",
       "\u001b[0;34m            mode (str): the mode to render with\u001b[0m\n",
       "\u001b[0;34m            close (bool): close all open renderings\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Example:\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        class MyEnv(Env):\u001b[0m\n",
       "\u001b[0;34m            metadata = {'render.modes': ['human', 'rgb_array']}\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m            def render(self, mode='human'):\u001b[0m\n",
       "\u001b[0;34m                if mode == 'rgb_array':\u001b[0m\n",
       "\u001b[0;34m                    return np.array(...) # return RGB frame suitable for video\u001b[0m\n",
       "\u001b[0;34m                elif mode is 'human':\u001b[0m\n",
       "\u001b[0;34m                    ... # pop up a window and render\u001b[0m\n",
       "\u001b[0;34m                else:\u001b[0m\n",
       "\u001b[0;34m                    super(MyEnv, self).render(mode=mode) # just raise an exception\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# then we have to check rendering mode\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0mmodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'render.modes'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodes\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m                \u001b[0;32mraise\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mUnsupportedMode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'{} does not support rendering (requested mode: {})'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0;32melif\u001b[0m \u001b[0mmode\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mmodes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m                \u001b[0;32mraise\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mUnsupportedMode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Unsupported rendering mode: {}. (Supported modes for {}: {})'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_render\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mclose\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Override _close in your subclass to perform any necessary cleanup.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Environments will automatically close() themselves when\u001b[0m\n",
       "\u001b[0;34m        garbage collected or when the program exits.\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# _closed will be missing if this instance is still\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# initializing.\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'_closed'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_closed\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_owns_render\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrender\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_close\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0menv_closer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munregister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_env_closer_id\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# If an error occurs before this line, it's possible to\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;31m# end up with double close.\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_closed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Sets the seed for this env's random number generator(s).\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Note:\u001b[0m\n",
       "\u001b[0;34m            Some environments use multiple pseudorandom number generators.\u001b[0m\n",
       "\u001b[0;34m            We want to capture all such seeds used in order to ensure that\u001b[0m\n",
       "\u001b[0;34m            there aren't accidental correlations between multiple generators.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Returns:\u001b[0m\n",
       "\u001b[0;34m            list<bigint>: Returns the list of seeds used in this env's random\u001b[0m\n",
       "\u001b[0;34m              number generators. The first value in the list should be the\u001b[0m\n",
       "\u001b[0;34m              \"main\" seed, or the value which a reproducer should pass to\u001b[0m\n",
       "\u001b[0;34m              'seed'. Often, the main seed equals the provided 'seed', but\u001b[0m\n",
       "\u001b[0;34m              this won't be true if seed=None, for example.\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_seed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0munwrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Completely unwrap this env.\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m        Returns:\u001b[0m\n",
       "\u001b[0;34m            gym.Env: The base non-wrapped gym.Env instance\u001b[0m\n",
       "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m__del__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0m__str__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mspec\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0;32mreturn\u001b[0m \u001b[0;34m'<{}<{}>>'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mspec\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m            \u001b[0;32mreturn\u001b[0m \u001b[0;34m'<{} instance>'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0;32mdef\u001b[0m \u001b[0mconfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m        \u001b[0;32mraise\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Env.configure has been removed in gym v0.8.0, released on 2017/03/05. If you need Env.configure, please use gym version 0.7.x from pip, or checkout the `gym:v0.7.4` tag from git.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mFile:\u001b[0m           ~/.virtualenvs/TensorFlow/lib/python3.5/site-packages/gym/core.py\n",
       "\u001b[0;31mType:\u001b[0m           type\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "??Env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = RubiksCube"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-20T22:41:36.228945Z",
     "start_time": "2017-03-20T22:41:35.988469Z"
    },
    "deletable": true,
    "editable": true
   },
   "source": [
    "## How Many Rotations are Needed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting from an initial solved cube, I'll rotate the cube a fixed number of times and look at the distribution of their similarity to the intial state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-20T23:22:23.260806Z",
     "start_time": "2017-03-20T23:18:54.765517Z"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_samps = 10000\n",
    "n_rots = 100\n",
    "l=[]\n",
    "for x in range(n_samps):\n",
    "    c = RubiksCube()\n",
    "    for y in range(n_rots):\n",
    "        c.random_rotate()\n",
    "        l.append((y,c.score_similarity()))\n",
    "rot_df = pd.DataFrame(l,columns={\"Rotations\",\"Score\"})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-20T23:23:54.659100Z",
     "start_time": "2017-03-20T23:23:54.359657Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f598e0ebbe0>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZAJLUKANAkhplAEhSowwASWqUASBJjfJ7AJJGYu5/Ibug6VXaqP+F7DU8ApCkRo31EcCR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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f598e0a8c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rot_df[rot_df[\"Rotations\"]==50][\"Score\"].hist()\n",
    "\n",
    "rot_df[rot_df[\"Rotations\"]==99][\"Score\"].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-20T23:24:02.108625Z",
     "start_time": "2017-03-20T23:24:01.829250Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f598e0086d8>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f598e16fb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rot_df[rot_df[\"Rotations\"]==99][\"Score\"].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "TensorFlow",
   "language": "python",
   "name": "tensorflow"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}