20150402_Euler86.ipynb

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  "name": "",
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  "signature": "sha256:9c4189aaf64cea0d48d0fceb4e8ffc29ff4df55422b498ab8bea0b31e155d6a0"
>>>>>>> origin/master
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use a little geometric intuition to compute the paths from the spider to the fly."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib as mpl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def draw_cuboid(a, b, c):\n",
      "    ax = plt.gca()\n",
      "    \n",
      "    # draw base rectangle\n",
      "    ax.add_artist(mpl.patches.Rectangle((0, 0), a, b, color='#DEE7FF'))\n",
      "    \n",
      "    # draw first possible path\n",
      "    ax.add_artist(mpl.patches.Rectangle((0, b), a, c, color='#CEDAFF'))\n",
      "    ax.plot([0, a], [0, b + c], '--k', lw=2)\n",
      "    ax.annotate(\"(a, b+c)\", (a/2., (b+c)/2.), rotation=np.rad2deg(0.5 * np.arctan2((b+c)/2., a/2.)))\n",
      "    \n",
      "    # draw second path\n",
      "    ax.add_artist(mpl.patches.Rectangle((a, 0), c, b, color='#BDCEFF'))\n",
      "    ax.plot([0, a + c], [0, b], '--k', lw=2)\n",
      "    ax.annotate(\"(a + c, b)\", ((a + c)/2., (b)/2.), rotation=np.rad2deg(0.5 * np.arctan2((b)/2., (a+c)/2.)))\n",
      "    \n",
      "    # draw third path\n",
      "    #ax.add_artist(mpl.patches.Rectangle((0, -c), a, c, color='#ADC2FF'))\n",
      "    #ax.add_artist(mpl.patches.Rectangle((0, -c - b), a, b, color='#E6EDFF'))\n",
      "    #ax.plot([0, a], [0, -b -c], '--k', lw=2)\n",
      "    #ax.annotate(\"(a, --b --c)\", ((a)/2., (-b-c)/2.), rotation=np.rad2deg(0.5 * np.arctan2((-b-c)/2., (a)/2.)))\n",
      "    \n",
      "    # draw correct third path\n",
      "    ax.plot([0, a], [0, b], '--k', lw=2)\n",
      "    ax.plot([a, a], [b, b + c], '--k', lw=2)\n",
      "    #ax.annotate(\"(a, --b --c)\", ((a)/2., (-b-c)/2.), rotation=np.rad2deg(0.5 * np.arctan2((-b-c)/2., (a)/2.)))\n",
      "    \n",
      "    # make plot look right\n",
      "    ax.set_xlim(0, a + c)\n",
      "    ax.set_ylim(-b -c, b + c)\n",
      "    plt.axis('equal')\n",
      "    plt.axis('off')\n",
      "    \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_cuboid(6, 5, 3) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "C:\\Anaconda\\lib\\site-packages\\matplotlib\\text.py:52: UnicodeWarning: Unicode equal comparison failed to convert both arguments to Unicode - interpreting them as being unequal\n",
        "  if rotation in ('horizontal', None):\n",
        "C:\\Anaconda\\lib\\site-packages\\matplotlib\\text.py:54: UnicodeWarning: Unicode equal comparison failed to convert both arguments to Unicode - interpreting them as being unequal\n",
        "  elif rotation == 'vertical':\n"
       ]
      },
      {
       "metadata": {},
=======
       "metadata": {
        "png": {
         "height": 255,
         "width": 358
        }
       },
>>>>>>> origin/master
       "output_type": "display_data",
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NWbL+f0lmjhkAMhfGM9wM4xlA+vrp2H7t/2G7uvQcbnYUpBHGMwCkBqXZzVCaAeDeUJoB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\n4AChGQAAAHCA0AwAAAA4QGgGAAAAHPg/5trM688MFgwAAAAASUVORK5CYII=\n",
       "text": [
<<<<<<< HEAD
        "<matplotlib.figure.Figure at 0xa3d6390>"
=======
        "<matplotlib.figure.Figure at 0x1065d9da0>"
>>>>>>> origin/master
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can make this interactive:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.html.widgets import interact"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(lambda a, b, c: draw_cuboid(a, b, c),\n",
      "         a=(1, 10),\n",
      "         b=(1, 10),\n",
      "         c=(1, 10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
<<<<<<< HEAD
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<function __main__.<lambda>>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PHLly6TyKFiuuyKDmpKPycdKRnCq/YX3syH7E6WMctBrbrkdF4rftW2x+rVad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\nSCEY2ERECsHAJiJSCAY2EZFC/B8P1uoAGRH+ZQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa7ea8d0>"
=======
       "metadata": {
        "png": {
         "height": 255,
         "width": 358
        }
       },
       "output_type": "display_data",
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UkBDvug4JDdOg4eMMqcXhcLhteedc/Ge1WpU9ew6NGj9LlavW1pzZU9W1Q1PF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10515e3c8>"
>>>>>>> origin/master
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Nice! We can compute an exact solution to the three paths:\n",
      "\n",
      "$$\n",
      "l_0 = \\sqrt{a^2 + (b + c)^2} = \\sqrt{a^2 + b^2 + c^2 + 2 bc}\n",
      "$$\n",
      "$$\n",
      "l_1 = \\sqrt{(a + c)^2 + b^2} = \\sqrt{a^2 + b^2 + c^2 + 2 ac}\n",
      "$$\n",
      "$$\n",
      "l_2 = \\sqrt{a^2 + b^2} + c\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can compute those three paths:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_paths(a, b, c):\n",
      "    l_0 = math.sqrt(a**2 + b**2 + c**2 + 2 * b * c)\n",
      "    l_1 = math.sqrt(a**2 + b**2 + c**2 + 2 * a * c)\n",
      "    l_2 = math.sqrt(a**2 + b**2) + c\n",
      "    return (l_0, l_1, l_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(lambda a, b, c: print(compute_paths(a, b, c)),\n",
      "        a=(1, 10),\n",
      "        b=(1, 10),\n",
      "        c=(1, 10)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
<<<<<<< HEAD
        "(11.180339887498949, 11.180339887498949, 12.071067811865476)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<function __main__.<lambda>>"
=======
        "(12.041594578792296, 12.041594578792296, 12.313708498984761)\n"
>>>>>>> origin/master
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def is_int(x):\n",
      "    return int(x) == x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols = []\n",
      "for a in range(1, 100):\n",
      "    for b in range(1, a + 1):\n",
      "        for c in range(1, b + 1):\n",
      "            if is_int(min(compute_paths(a, b, c))):\n",
      "                sols.append((a, b, c, compute_paths(a, b, c)))\n",
      "len(sols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
<<<<<<< HEAD
       "prompt_number": 53,
=======
       "prompt_number": 12,
>>>>>>> origin/master
       "text": [
        "1975"
       ]
      }
     ],
<<<<<<< HEAD
     "prompt_number": 53
=======
     "prompt_number": 12
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols[:50]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
<<<<<<< HEAD
       "prompt_number": 54,
=======
       "prompt_number": 13,
>>>>>>> origin/master
       "text": [
        "[(3, 2, 2, (5.0, 5.385164807134504, 5.60555127546399)),\n",
        " (3, 3, 1, (5.0, 5.0, 5.242640687119285)),\n",
        " (4, 2, 1, (5.0, 5.385164807134504, 5.47213595499958)),\n",
        " (6, 4, 4, (10.0, 10.770329614269007, 11.21110255092798)),\n",
        " (6, 5, 3, (10.0, 10.295630140987, 10.810249675906654)),\n",
        " (6, 6, 2, (10.0, 10.0, 10.48528137423857)),\n",
        " (8, 3, 3, (10.0, 11.40175425099138, 11.54400374531753)),\n",
        " (8, 4, 2, (10.0, 10.770329614269007, 10.94427190999916)),\n",
        " (8, 5, 1, (10.0, 10.295630140987, 10.433981132056603)),\n",
        " (8, 8, 7, (17.0, 17.0, 18.31370849898476)),\n",
        " (9, 6, 6, (15.0, 16.15549442140351, 16.81665382639197)),\n",
        " (9, 7, 5, (15.0, 15.652475842498529, 16.40175425099138)),\n",
        " (9, 8, 4, (15.0, 15.264337522473747, 16.041594578792296)),\n",
        " (9, 9, 3, (15.0, 15.0, 15.727922061357855)),\n",
        " (12, 3, 2, (13.0, 14.317821063276353, 14.36931687685298)),\n",
        " (12, 4, 1, (13.0, 13.601470508735444, 13.649110640673518)),\n",
        " (12, 5, 4, (15.0, 16.76305461424021, 17.0)),\n",
        " (12, 6, 3, (15.0, 16.15549442140351, 16.41640786499874)),\n",
        " (12, 7, 2, (15.0, 15.652475842498529, 15.892443989449804)),\n",
        " (12, 8, 1, (15.0, 15.264337522473747, 15.422205101855956)),\n",
        " (12, 8, 8, (20.0, 21.540659228538015, 22.42220510185596)),\n",
        " (12, 9, 7, (20.0, 21.02379604162864, 22.0)),\n",
        " (12, 10, 6, (20.0, 20.591260281974, 21.620499351813308)),\n",
        " (12, 11, 5, (20.0, 20.248456731316587, 21.278820596099706)),\n",
        " (12, 12, 4, (20.0, 20.0, 20.97056274847714)),\n",
        " (15, 4, 4, (17.0, 19.4164878389476, 19.524174696260026)),\n",
        " (15, 5, 3, (17.0, 18.681541692269406, 18.811388300841898)),\n",
        " (15, 6, 2, (17.0, 18.027756377319946, 18.15549442140351)),\n",
        " (15, 7, 1, (17.0, 17.46424919657298, 17.55294535724685)),\n",
        " (15, 10, 10, (25.0, 26.92582403567252, 28.027756377319946)),\n",
        " (15, 11, 9, (25.0, 26.40075756488817, 27.601075237738275)),\n",
        " (15, 12, 8, (25.0, 25.942243542145693, 27.209372712298546)),\n",
        " (15, 13, 7, (25.0, 25.553864678361276, 26.849433241279208)),\n",
        " (15, 14, 6, (25.0, 25.238858928247925, 26.518284528683193)),\n",
        " (15, 15, 5, (25.0, 25.0, 26.213203435596427)),\n",
        " (16, 6, 6, (20.0, 22.80350850198276, 23.08800749063506)),\n",
        " (16, 7, 5, (20.0, 22.135943621178654, 22.46424919657298)),\n",
        " (16, 8, 4, (20.0, 21.540659228538015, 21.88854381999832)),\n",
        " (16, 9, 3, (20.0, 21.02379604162864, 21.35755975068582)),\n",
        " (16, 10, 2, (20.0, 20.591260281974, 20.867962264113206)),\n",
        " (16, 11, 1, (20.0, 20.248456731316587, 20.4164878389476)),\n",
        " (16, 15, 15, (34.0, 34.438350715445125, 36.93171219946131)),\n",
        " (16, 16, 14, (34.0, 34.0, 36.62741699796952)),\n",
        " (18, 12, 12, (30.0, 32.31098884280702, 33.63330765278394)),\n",
        " (18, 13, 11, (30.0, 31.78049716414141, 33.20360331117452)),\n",
        " (18, 14, 10, (30.0, 31.304951684997057, 32.80350850198276)),\n",
        " (18, 15, 9, (30.0, 30.886890422961002, 32.43074902771996)),\n",
        " (18, 16, 8, (30.0, 30.528675044947494, 32.08318915758459)),\n",
        " (18, 17, 7, (30.0, 30.23243291566195, 31.758836806279895)),\n",
        " (18, 18, 6, (30.0, 30.0, 31.45584412271571))]"
       ]
      }
     ],
<<<<<<< HEAD
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "(99, 99, 69, (195.0, 195.0, 209.0071426749364))"
       ]
      }
     ],
     "prompt_number": 55
=======
     "prompt_number": 13
>>>>>>> origin/master
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le pattern est le suivant : c'est toujours la premi\u00e8re distance qui est la plus petite ! Et il y a des couples donn\u00e9s o\u00f9 $a + b = \\text{cte}$.\n",
      "\n",
      "Donc on va adopter une nouvelle strat\u00e9gie : \n",
      "\n",
      "- boucle sur a\n",
      "- boucle sur l_0\n",
      "- boucle sur b "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols = []\n",
      "for l0 in range(1, 196):\n",
      "    for a in range(1, l0):\n",
      "        s = math.sqrt(l0 * l0 - a *a)\n",
      "        if is_int(s):\n",
      "            if s % 2 == 0:\n",
      "                b = c = s / 2\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            if s % 2 == 1:\n",
      "                b = (s + 1) / 2\n",
      "                c = b - 1\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            \n",
      "len(sols)"
     ],
     "language": "python",
     "metadata": {},
<<<<<<< HEAD
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "4598"
       ]
      }
     ],
     "prompt_number": 60
=======
     "outputs": [],
     "prompt_number": 14
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols[:50]"
     ],
     "language": "python",
     "metadata": {},
<<<<<<< HEAD
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "[(3, 2.0, 2.0, 5),\n",
        " (3, 3.0, 1.0, 5),\n",
        " (4, 2.0, 1.0, 5),\n",
        " (6, 4.0, 4.0, 10),\n",
        " (6, 5.0, 3.0, 10),\n",
        " (6, 6.0, 2.0, 10),\n",
        " (8, 3.0, 3.0, 10),\n",
        " (8, 4.0, 2.0, 10),\n",
        " (8, 5.0, 1.0, 10),\n",
        " (12, 3.0, 2.0, 13),\n",
        " (12, 4.0, 1.0, 13),\n",
        " (9, 6.0, 6.0, 15),\n",
        " (9, 7.0, 5.0, 15),\n",
        " (9, 8.0, 4.0, 15),\n",
        " (9, 9.0, 3.0, 15),\n",
        " (12, 5.0, 4.0, 15),\n",
        " (12, 6.0, 3.0, 15),\n",
        " (12, 7.0, 2.0, 15),\n",
        " (12, 8.0, 1.0, 15),\n",
        " (8, 8.0, 7.0, 17),\n",
        " (15, 4.0, 4.0, 17),\n",
        " (15, 5.0, 3.0, 17),\n",
        " (15, 6.0, 2.0, 17),\n",
        " (15, 7.0, 1.0, 17),\n",
        " (12, 8.0, 8.0, 20),\n",
        " (12, 9.0, 7.0, 20),\n",
        " (12, 10.0, 6.0, 20),\n",
        " (12, 11.0, 5.0, 20),\n",
        " (12, 12.0, 4.0, 20),\n",
        " (16, 6.0, 6.0, 20),\n",
        " (16, 7.0, 5.0, 20),\n",
        " (16, 8.0, 4.0, 20),\n",
        " (16, 9.0, 3.0, 20),\n",
        " (16, 10.0, 2.0, 20),\n",
        " (16, 11.0, 1.0, 20),\n",
        " (15, 10.0, 10.0, 25),\n",
        " (15, 11.0, 9.0, 25),\n",
        " (15, 12.0, 8.0, 25),\n",
        " (15, 13.0, 7.0, 25),\n",
        " (15, 14.0, 6.0, 25),\n",
        " (15, 15.0, 5.0, 25),\n",
        " (20, 8.0, 7.0, 25),\n",
        " (20, 9.0, 6.0, 25),\n",
        " (20, 10.0, 5.0, 25),\n",
        " (20, 11.0, 4.0, 25),\n",
        " (20, 12.0, 3.0, 25),\n",
        " (20, 13.0, 2.0, 25),\n",
        " (20, 14.0, 1.0, 25),\n",
        " (24, 4.0, 3.0, 25),\n",
        " (24, 5.0, 2.0, 25)]"
       ]
      }
     ],
     "prompt_number": 57
=======
     "outputs": [],
     "prompt_number": 15
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len([x for x in sols if x[0] < 100])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
<<<<<<< HEAD
        "1968"
       ]
      }
     ],
     "prompt_number": 63
=======
        "CPU times: user 852 ms, sys: 9.84 ms, total: 862 ms\n",
        "Wall time: 862 ms\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l = [0, 2, 3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l.index(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "0"
       ]
      }
     ],
     "prompt_number": 25
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
<<<<<<< HEAD
      "len([x for x in sols if x[0] < 101])"
=======
      "%%time\n",
      "sols = []\n",
      "for a in range(1, 100):\n",
      "    for b in range(1, a + 1):\n",
      "        for c in range(1, b + 1):\n",
      "            if memo_func.get_result(a, b, c):\n",
      "                mini = min(compute_paths(a, b, c))\n",
      "                sols.append((a, b, c, compute_paths(a, b, c)))\n",
      "len(sols)"
>>>>>>> origin/master
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
<<<<<<< HEAD
        "2053"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Je ne sais pas pourquoi, mais il m'en manque 7 !"
     ]
=======
        "CPU times: user 154 ms, sys: 2.95 ms, total: 157 ms\n",
        "Wall time: 157 ms\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "[(3, 2, 2, (5.0, 5.385164807134504, 5.60555127546399)),\n",
        " (3, 3, 1, (5.0, 5.0, 5.242640687119285)),\n",
        " (4, 2, 1, (5.0, 5.385164807134504, 5.47213595499958)),\n",
        " (6, 4, 4, (10.0, 10.770329614269007, 11.21110255092798)),\n",
        " (6, 5, 3, (10.0, 10.295630140987, 10.810249675906654)),\n",
        " (6, 6, 2, (10.0, 10.0, 10.48528137423857)),\n",
        " (8, 3, 3, (10.0, 11.40175425099138, 11.54400374531753)),\n",
        " (8, 4, 2, (10.0, 10.770329614269007, 10.94427190999916)),\n",
        " (8, 5, 1, (10.0, 10.295630140987, 10.433981132056603)),\n",
        " (8, 8, 7, (17.0, 17.0, 18.31370849898476)),\n",
        " (9, 6, 6, (15.0, 16.15549442140351, 16.81665382639197)),\n",
        " (9, 7, 5, (15.0, 15.652475842498529, 16.40175425099138)),\n",
        " (9, 8, 4, (15.0, 15.264337522473747, 16.041594578792296)),\n",
        " (9, 9, 3, (15.0, 15.0, 15.727922061357855)),\n",
        " (12, 3, 2, (13.0, 14.317821063276353, 14.36931687685298)),\n",
        " (12, 4, 1, (13.0, 13.601470508735444, 13.649110640673518)),\n",
        " (12, 5, 4, (15.0, 16.76305461424021, 17.0)),\n",
        " (12, 6, 3, (15.0, 16.15549442140351, 16.41640786499874)),\n",
        " (12, 7, 2, (15.0, 15.652475842498529, 15.892443989449804)),\n",
        " (12, 8, 1, (15.0, 15.264337522473747, 15.422205101855956)),\n",
        " (12, 8, 8, (20.0, 21.540659228538015, 22.42220510185596)),\n",
        " (12, 9, 7, (20.0, 21.02379604162864, 22.0)),\n",
        " (12, 10, 6, (20.0, 20.591260281974, 21.620499351813308)),\n",
        " (12, 11, 5, (20.0, 20.248456731316587, 21.278820596099706)),\n",
        " (12, 12, 4, (20.0, 20.0, 20.97056274847714)),\n",
        " (15, 4, 4, (17.0, 19.4164878389476, 19.524174696260026)),\n",
        " (15, 5, 3, (17.0, 18.681541692269406, 18.811388300841898)),\n",
        " (15, 6, 2, (17.0, 18.027756377319946, 18.15549442140351)),\n",
        " (15, 7, 1, (17.0, 17.46424919657298, 17.55294535724685)),\n",
        " (15, 10, 10, (25.0, 26.92582403567252, 28.027756377319946)),\n",
        " (15, 11, 9, (25.0, 26.40075756488817, 27.601075237738275)),\n",
        " (15, 12, 8, (25.0, 25.942243542145693, 27.209372712298546)),\n",
        " (15, 13, 7, (25.0, 25.553864678361276, 26.849433241279208)),\n",
        " (15, 14, 6, (25.0, 25.238858928247925, 26.518284528683193)),\n",
        " (15, 15, 5, (25.0, 25.0, 26.213203435596427)),\n",
        " (16, 6, 6, (20.0, 22.80350850198276, 23.08800749063506)),\n",
        " (16, 7, 5, (20.0, 22.135943621178654, 22.46424919657298)),\n",
        " (16, 8, 4, (20.0, 21.540659228538015, 21.88854381999832)),\n",
        " (16, 9, 3, (20.0, 21.02379604162864, 21.35755975068582)),\n",
        " (16, 10, 2, (20.0, 20.591260281974, 20.867962264113206)),\n",
        " (16, 11, 1, (20.0, 20.248456731316587, 20.4164878389476)),\n",
        " (16, 15, 15, (34.0, 34.438350715445125, 36.93171219946131)),\n",
        " (16, 16, 14, (34.0, 34.0, 36.62741699796952)),\n",
        " (18, 12, 12, (30.0, 32.31098884280702, 33.63330765278394)),\n",
        " (18, 13, 11, (30.0, 31.78049716414141, 33.20360331117452)),\n",
        " (18, 14, 10, (30.0, 31.304951684997057, 32.80350850198276)),\n",
        " (18, 15, 9, (30.0, 30.886890422961002, 32.43074902771996)),\n",
        " (18, 16, 8, (30.0, 30.528675044947494, 32.08318915758459)),\n",
        " (18, 17, 7, (30.0, 30.23243291566195, 31.758836806279895)),\n",
        " (18, 18, 6, (30.0, 30.0, 31.45584412271571)),\n",
        " (20, 8, 7, (25.0, 28.160255680657446, 28.540659228538015)),\n",
        " (20, 9, 6, (25.0, 27.51363298439521, 27.93171219946131)),\n",
        " (20, 10, 5, (25.0, 26.92582403567252, 27.360679774997898)),\n",
        " (20, 11, 4, (25.0, 26.40075756488817, 26.825424421026653)),\n",
        " (20, 11, 10, (29.0, 31.953090617340916, 32.82542442102665)),\n",
        " (20, 12, 3, (25.0, 25.942243542145693, 26.323807579381203)),\n",
        " (20, 12, 9, (29.0, 31.38470965295043, 32.3238075793812)),\n",
        " (20, 13, 2, (25.0, 25.553864678361276, 25.853720883753127)),\n",
        " (20, 13, 8, (29.0, 30.870698080866262, 31.853720883753127)),\n",
        " (20, 14, 1, (25.0, 25.238858928247925, 25.413111231467404)),\n",
        " (20, 14, 7, (29.0, 30.4138126514911, 31.413111231467404)),\n",
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        " (72, 15, 15, (78.0, 88.28363381737297, 88.54590403278758)),\n",
        " (72, 16, 5, (75.0, 78.64477096412705, 78.7563556583431)),\n",
        " (72, 16, 14, (78.0, 87.47571091451616, 87.7563556583431)),\n",
        " (72, 17, 4, (75.0, 77.87810988975015, 77.97972695272672)),\n",
        " (72, 17, 13, (78.0, 86.68333173107735, 86.97972695272672)),\n",
        " (72, 18, 3, (75.0, 77.12976079309465, 77.21590126111789)),\n",
        " (72, 18, 12, (78.0, 85.90692637965812, 86.21590126111789)),\n",
        " (72, 19, 2, (75.0, 76.40026177965623, 76.46475676452586)),\n",
        " (72, 19, 11, (78.0, 85.14693182963201, 85.46475676452586)),\n",
        " (72, 20, 1, (75.0, 75.69015788066504, 75.72616676907762)),\n",
        " (72, 20, 10, (78.0, 84.40379138403677, 84.72616676907762)),\n",
        " (72, 21, 9, (78.0, 83.67795408588812, 84.0)),\n",
        " (72, 22, 8, (78.0, 82.96987405076617, 83.28612089887484)),\n",
        " (72, 23, 7, (78.0, 82.28000972289685, 82.58438992278762)),\n",
        " (72, 24, 6, (78.0, 81.60882305241266, 81.8946638440411)),\n",
        " (72, 25, 5, (78.0, 80.95677859203639, 81.21679604916491)),\n",
        " (72, 26, 4, (78.0, 80.32434251209281, 80.55063683601855)),\n",
        " (72, 27, 3, (78.0, 79.71198153351854, 79.89603370785778)),\n",
        " (72, 27, 27, (90.0, 102.61578825892242, 103.89603370785778)),\n",
        " (72, 28, 2, (78.0, 79.12016177940993, 79.25283166331187)),\n",
        " (72, 28, 26, (90.0, 101.92153844992725, 103.25283166331187)),\n",
        " (72, 29, 1, (78.0, 78.54934754662193, 78.62087348130012)),\n",
        " (72, 29, 25, (90.0, 101.24228365658294, 102.62087348130012)),\n",
        " (72, 30, 24, (90.0, 100.57832768544127, 102.0)),\n",
        " (72, 31, 23, (90.0, 99.92997548283498, 101.39005038906404)),\n",
        " (72, 32, 22, (90.0, 99.29753269845128, 100.79086241436883)),\n",
        " (72, 33, 21, (90.0, 98.68130522039117, 100.20227269466452)),\n",
        " (72, 33, 32, (97.0, 109.11003620199197, 111.20227269466452)),\n",
        " (72, 34, 20, (90.0, 98.08159868191383, 99.62411694957753)),\n",
        " (72, 34, 31, (97.0, 108.4665847162157, 110.62411694957753)),\n",
        " (72, 35, 19, (90.0, 97.49871794028884, 99.05623023850174)),\n",
        " (72, 35, 30, (97.0, 107.83784122468327, 110.05623023850174)),\n",
        " (72, 36, 18, (90.0, 96.93296652842108, 98.49844718999243)),\n",
        " (72, 36, 29, (97.0, 107.2240644631605, 109.49844718999243)),\n",
        " (72, 37, 17, (90.0, 96.38464608017192, 97.95060222135473)),\n",
        " (72, 37, 28, (97.0, 106.6255128944288, 108.95060222135473)),\n",
        " (72, 38, 16, (90.0, 95.85405573057407, 97.41252974819048)),\n",
        " (72, 38, 27, (97.0, 106.04244433244644, 108.41252974819048)),\n",
        " (72, 39, 15, (90.0, 95.34149149242423, 96.88406438373708)),\n",
        " (72, 39, 26, (97.0, 105.47511554864494, 107.88406438373708)),\n",
        " (72, 40, 14, (90.0, 94.847245611035, 96.365041127896)),\n",
        " (72, 40, 25, (97.0, 104.92378186092989, 107.365041127896)),\n",
        " (72, 41, 13, (90.0, 94.37160589923221, 95.85529554590944)),\n",
        " (72, 41, 24, (97.0, 104.38869670610895, 106.85529554590944)),\n",
        " (72, 42, 12, (90.0, 93.91485505499116, 95.35466393669883)),\n",
        " (72, 42, 23, (97.0, 103.87011119662864, 106.35466393669883)),\n",
        " (72, 43, 11, (90.0, 93.47726996441435, 94.86298349093002)),\n",
        " (72, 43, 22, (97.0, 103.36827366266692, 105.86298349093002)),\n",
        " (72, 44, 10, (90.0, 93.05912099305473, 94.38009243891595)),\n",
        " (72, 44, 21, (97.0, 102.88342918079665, 105.38009243891595)),\n",
        " (72, 45, 9, (90.0, 92.66067126888301, 93.90583018850944)),\n",
        " (72, 45, 20, (97.0, 102.41581909060729, 104.90583018850944)),\n",
        " ...]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print([x[3] for x in sols])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
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       ]
      }
     ],
     "prompt_number": 30
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols = []\n",
      "for a in range(1, 101):\n",
      "    for l0 in range(a + 1, 3 * a):\n",
      "        s = math.sqrt(l0 * l0 - a *a)\n",
      "        if is_int(s):\n",
      "            if s % 2 == 0:\n",
      "                b = c = s / 2\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            if s % 2 == 1:\n",
      "                b = (s + 1) / 2\n",
      "                c = b - 1\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            \n",
      "len(sols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
<<<<<<< HEAD
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 107,
       "text": [
        "2060"
       ]
      }
     ],
     "prompt_number": 107
=======
       "ename": "KeyboardInterrupt",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-18-8e28895c92d5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_cell_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'time'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'sols = []\\nfor a in range(1, 1000):\\n    for b in range(1, a + 1):\\n        for c in range(1, b + 1):\\n            if memo_func.get_result(a, b, c):\\n                sols.append((a, b, c))\\nlen(sols)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_cell_magic\u001b[0;34m(self, magic_name, line, cell)\u001b[0m\n\u001b[1;32m   2160\u001b[0m             \u001b[0mmagic_arg_s\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvar_expand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2161\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2162\u001b[0;31m                 \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmagic_arg_s\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcell\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2163\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2164\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n",
        "\u001b[0;32m/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m    191\u001b[0m     \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 193\u001b[0;31m         \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    194\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtime\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[1;32m   1127\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1128\u001b[0m             \u001b[0mst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1129\u001b[0;31m             \u001b[0mexec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mglob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlocal_ns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1130\u001b[0m             \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mclock2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1131\u001b[0m             \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m<timed exec>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n",
        "\u001b[0;32m<ipython-input-14-cca5f62c8447>\u001b[0m in \u001b[0;36mget_result\u001b[0;34m(self, a, b, c)\u001b[0m\n\u001b[1;32m      7\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mis_int\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcompute_paths\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m<ipython-input-11-4c1df54d6a89>\u001b[0m in \u001b[0;36mis_int\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mis_int\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
       ]
      }
     ],
     "prompt_number": 18
>>>>>>> origin/master
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols = []\n",
      "for a in range(1, 1819):\n",
      "    for l0 in range(a + 1, 3 * a):\n",
      "        s = math.sqrt(l0 * l0 - a *a)\n",
      "        if is_int(s):\n",
      "            if s % 2 == 0:\n",
      "                b = c = s / 2\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            if s % 2 == 1:\n",
      "                b = (s + 1) / 2\n",
      "                c = b - 1\n",
      "                while b <= a and c >= 1:\n",
      "                    sols.append((a, b, c, l0))\n",
      "                    b += 1\n",
      "                    c -= 1\n",
      "            \n",
      "len(sols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 109,
       "text": [
        "1000457"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sols[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 110,
       "text": [
        "(1818, 1818.0, 606.0, 3030)"
       ]
      }
     ],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}