recursion_examples.ipynb

{
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vyo3P7BOg246"
      },
      "source": [
        "# Recursion examples\n",
        "\n",
        "adopted from: https://github.com/rasbt/algorithms_in_ipython_notebooks\n",
        "\n",
        "https://github.com/AbhishekSinhaCoder/Data-Structures-Concepts-through-Notebook"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b3WIZabXg24_"
      },
      "source": [
        "# Examples using Recursion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2epyKFR-g24_"
      },
      "source": [
        "**Important Note**\n",
        "\n",
        "For most cases, using function recursion should be avoided in Python are better be implemented using for/while loops most of the time (although, I must admit that recursive solutions do look elegant). One of the reasons is that stacking recursive calls can easily blow up memory or at least result in the popular yet nasty \"RuntimeError: maximum recursion depth exceeded\". Also, keep in mind that Python does not optimize tail recursion in favor of having the full tracebacks for debugging; related to that, please see Guido van Rossums blog posts \"[Tail Recursion Elimination](http://neopythonic.blogspot.com.au/2009/04/tail-recursion-elimination.html)\" and \"[Final Words on Tail Calls](http://neopythonic.blogspot.com.au/2009/04/final-words-on-tail-calls.html).\" If you do like to play around with recursion more efficiently, I highly recommend taking a look at [Haskell](https://www.haskell.org) or other functional programming languages. That being said, below are some examples of recursive function implementations in Python for illustrative purposes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "92oVoFP6g25A"
      },
      "source": [
        "## Review: Running time and big-$\\mathcal{O}$: Recursive Algorithms for Computing Powers\n",
        "\n",
        "As example of the use of linear recursion, we consider the problem of raising a number $x$ to an arbitrary nonnegative integer, $n$. That is, we wish to compute the power function, defined as $power(x,n) = xn$. (We use the name “power” for this discussion, to differentiate from the built-in Python function _pow_ that provides such functionality.) We will consider two different recursive formulations for the problem that lead to algorithms with very different performance.\n",
        "A trivial recursive definition follows from the fact that $x^n = x \\cdot x^{n−1}$ for $n > 0$.\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "power(x,n) ==\\left\\{\n",
        "                \\begin{array}{ll}\n",
        "                        1 \\ if \\ n = 0\\\\\n",
        "                        x \\ power(x, n − 1) \\ otherwise.\n",
        "                \\end{array}\n",
        "              \\right.\n",
        "\\end{equation}\n",
        "\n",
        "This definition leads to a recursive algorithm shown below:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zcgA1_fJg25B"
      },
      "outputs": [],
      "source": [
        "# in case we did not know about Pythons x**n statement :)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gpllds2_g25C",
        "outputId": "2de44e98-d256-4927-9982-f905dfa6f982"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "256"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**8"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "554524352**0 # our base case"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3PeqrPoOg25C"
      },
      "outputs": [],
      "source": [
        "# so the idea is to reduce the problem to a simpler instance of the same problem\n",
        "## to start with we need a base case\n",
        "## so base case for power would be x to 0 which is 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BM9mM8yBg25D",
        "outputId": "38e62f87-e650-4d99-efc1-dafd64289b9c"
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      "outputs": [
        {
          "data": {
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              "1"
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          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kCT51rdgnnUK"
      },
      "source": [
        "## Basic (naive) power function - recursive"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "L0eRo9Eog25D"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Indeed 2**8 is 256\n"
          ]
        }
      ],
      "source": [
        "def basicpower(x, n, verbose=False):\n",
        "    '''Compute the value x**n for integer n.\n",
        "    n - has to be a non-negative integer''' \n",
        "    if verbose:\n",
        "        print(f\"Computing {x}^{n}\")\n",
        "    if n == 0:\n",
        "        return 1 # base case without base case our recursive function will run forever\n",
        "    else:\n",
        "        return x  * basicpower(x, n-1, verbose=verbose) # our recursive call so we are calling the function on itself on a smaller problem space\n",
        "    \n",
        "# let's assert it works\n",
        "assert basicpower(2, 8) == 2**8, \"Test case 1 failed\"\n",
        "print(f\"Indeed 2**8 is {basicpower(2, 8)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Basic Naive Power Function without verbose output\n",
        "\n",
        "```python"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [],
      "source": [
        "def basicpower_withoutverbose(x, n):\n",
        "    '''Compute the value x**n for integer n.\n",
        "    n - has to be a non-negative integer''' \n",
        "    if n == 0:\n",
        "        return 1 # base case without base case our recursive function will run forever\n",
        "    else:\n",
        "        return x  * basicpower_withoutverbose(x, n-1) # our recursive call so we are calling the function on itself on a smaller problem space"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a1_VXKJnh_fW",
        "outputId": "c3f4bf1c-6fb5-4ba9-dcd6-4757dd2dd867"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Computing 2^8\n",
            "Computing 2^7\n",
            "Computing 2^6\n",
            "Computing 2^5\n",
            "Computing 2^4\n",
            "Computing 2^3\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "256"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2, 8, verbose=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H6g3qPgDg25E"
      },
      "source": [
        "# How to make a recursive function in two easy steps\n",
        "* figure out the base case\n",
        "* figure out how to reduce problem to a subset of the same problem"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dITIs2wxg25F"
      },
      "source": [
        "A recursive call to this version of power(x,n) runs in $\\mathcal{O}(n)$ time."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**1000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of digits is 302\n"
          ]
        }
      ],
      "source": [
        "print(f\"Number of digits is {len(str(2**1000))}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2,1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "375828023454801203683362418972386504867736551759258677056523839782231681498337708535732725752658844333702457749526057760309227891351617765651907310968780236464694043316236562146724416478591131832593729111221580180531749232777515579969899075142213969117994877343802049421624954402214529390781647563339535024772584901607666862982567918622849636160208877365834950163790188523026247440507390382032188892386109905869706753143243921198482212075444022433366554786856559389689585638126582377224037721702239991441466026185752651502936472280911018500320375496336749951569521541850441747925844066295279671872605285792552660130702047998218334749356321677469529682551765858267502715894007887727250070780350262952377214028842297486263597879792176338220932619489509376"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2, 2500)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1230231922161117176931558813276752514640713895736833715766118029160058800614672948775360067838593459582429649254051804908512884180898236823585082482065348331234959350355845017413023320111360666922624728239756880416434478315693675013413090757208690376793296658810662941824493488451726505303712916005346747908623702673480919353936813105736620402352744776903840477883651100322409301983488363802930540482487909763484098253940728685132044408863734754271212592471778643949486688511721051561970432780747454823776808464180697103083861812184348565522740195796682622205511845512080552010310050255801589349645928001133745474220715013683413907542779063759833876101354235184245096670042160720629411581502371248008430447184842098610320580417992206662247328722122088513643683907670360209162653670641130936997002170500675501374723998766005827579300723253474890612250135171889174899079911291512399773872178519018229989376"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2, 3000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [],
      "source": [
        "# we can increase the recursion limit\n",
        "import sys\n",
        "sys.setrecursionlimit(5000)\n",
        "# so this could solve the problem for small values of n but it will not work for large values of n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "ename": "",
          "evalue": "",
          "output_type": "error",
          "traceback": [
            "\u001b[1;31mThe Kernel crashed while executing code in the current cell or a previous cell. \n",
            "\u001b[1;31mPlease review the code in the cell(s) to identify a possible cause of the failure. \n",
            "\u001b[1;31mClick <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. \n",
            "\u001b[1;31mView Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
          ]
        }
      ],
      "source": [
        "for n in range(2000,3000, 10):\n",
        "    print(f\"Working on {n} and the number of digits is {len(str(basicpower(2,n)))}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 386
        },
        "id": "kdMeUVfLg25F",
        "outputId": "7eae8b86-31c4-44c0-dd0e-90e88d108e9e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "330 µs ± 21.5 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "838 ns ± 34.7 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**1000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "26.2 µs ± 3.29 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "150 ns ± 7.74 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**100"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.26 µs ± 46 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10.3 ns ± 0.792 ns per loop (mean ± std. dev. of 7 runs, 100,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**10"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WDe5fVAdiiXZ",
        "outputId": "4ce785f2-96f9-464e-cfd0-64c4b5323c8b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "5000\n"
          ]
        }
      ],
      "source": [
        "# import sys no need to import sys again\n",
        "print(sys.getrecursionlimit())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000\n"
          ]
        }
      ],
      "source": [
        "sys.setrecursionlimit(100_000)\n",
        "print(sys.getrecursionlimit())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xXwl6LbKilNk",
        "outputId": "8de4cbf3-3732-4bbe-f215-42877c08da90"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "9516908214257811601907599988159363584840065290620124537956939899622020205826587990689077212775400643774711832257235027522909345571487396529861315719055325605011013378863743193233193022939505515969530853007049198118833591724018432564205433218231411731277088674906521042072098232413978624"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2,950)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "17_Lvvuui2pK"
      },
      "outputs": [],
      "source": [
        "sys.setrecursionlimit(6000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NS0cuVT8g25F",
        "outputId": "342bf19d-92c3-497c-bd79-65d3f0579c9c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "263 µs ± 30 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QCH7sFtgi9IH",
        "outputId": "55f88258-7fe7-44ed-f250-308201e7d678"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "557 µs ± 17.6 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,2000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tzHI2BsTg25G",
        "outputId": "7ce6f5a7-8567-4823-91e7-79209ebe367c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.38 ms ± 48.6 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,4000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
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            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2,4000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "173766203193809456599982445949435627061939786100117250547173286503262376022458008465094333630120854338003194362163007597987225472483598640843335685441710193966274131338557192586399006789292714554767500194796127964596906605976605873665859580600161998556511368530960400907199253450604168622770350228527124626728538626805418833470107651091641919900725415994689920112219170907023561354484047025713734651608777544579846111001059482132180956689444108315785401642188044178788629853592228467331730519810763559577944882016286493908631503101121166109571682295769470379514531105239965209245314082665518579335511291525230373316486697786532335206274149240813489201828773854353041855598709390675430960381072270432383913542702130202430186637321862331068861776780211082856984506050024895394320139435868484643843368002496089956046419964019877586845530207748994394501505588146979082629871366088121763790555364513243984244004147636040219136443410377798011608722717131323621700159335786445601947601694025107888293017058178562647175461026384343438874861406516767158373279032321096262126551620255666605185789463207944391905756886829667520553014724372245300878786091700563444079107099009003380230356461989260377273986023281444076082783406824471703499844642915587790146384758051663547775336021829171033411043796977042190519657861762804226147480755555085278062866268677842432851421790544407006581148631979148571299417963950579210719961422405768071335213324842709316205032078384168750091017964584060285240107161561019930505687950233196051962261970932008838279760834318101044311710769457048672103958655016388894770892065267451228938951370237422841366052736174160431593023473217066764172949768821843606479073866252864377064398085101223216558344281956767163876579889759124956035672317578122141070933058555310274598884089982879647974020264495921703064439532898207943134374576254840272047075633856749514044298135927611328433323640657533550512376900773273703275329924651465759145114579174356770593439987135755889403613364529029604049868233807295134382284730745937309910703657676103447124097631074153287120040247837143656624045055614076111832245239612708339272798262887437416818440064925049838443370805645609424314780108030016683461562597569371539974003402697903023830108053034645133078208043917492087248958344081026378788915528519967248989338592027124423914083391771884524464968645052058218151010508471258285907685355807229880747677634789376"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "basicpower(2,8000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3.6 ms ± 149 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,8000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10.2 ms ± 330 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,16000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Fq0HFKT5g25G"
      },
      "outputs": [],
      "source": [
        "# not satisfied with performance of our basic power we have an improvement in mind"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Testing timing without verbose and with verbose output\n",
        "\n",
        "As Donald Knuth said \"Root of all evil in programming is premature optimization\". We will test this tiny optimization right now."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "351 µs ± 19.2 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2, 1_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "306 µs ± 16.7 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower_withoutverbose(2, 1_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "6.16 ms ± 147 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2, 10_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "5.78 ms ± 197 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower_withoutverbose(2, 10_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "24.9 µs ± 1.44 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2, 100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "22.9 µs ± 1.86 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower_withoutverbose(2, 100)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yLiRf6iIniBE"
      },
      "source": [
        "## Improved Power Function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "7-Tpf-DLg25G"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Indeed 2**8 is 256\n",
            "Indeed 2**9 is 512\n",
            "Indeed 2**10 is 1024\n"
          ]
        }
      ],
      "source": [
        "\n",
        "def power(x, n):\n",
        "    '''Compute the value x**n for integer n.''' \n",
        "    if n == 0: # this is our base case\n",
        "        return 1 \n",
        "    else:\n",
        "        partial = power(x, n // 2) # remember that x^4*x^4 == x^8 or (x^4)^2 == x^(4*2) == x^8\n",
        "        result = partial * partial # so x^4*x^4 == x^8\n",
        "    if n % 2 == 1:  # for odd powers we need to multiply by the number\n",
        "        result *= x # so x^9 = x^4 * x^4 * x\n",
        "    return result\n",
        "\n",
        "# assert it works\n",
        "assert power(2, 8) == 2**8, \"Even Test case 1 failed\"\n",
        "# now test with 9\n",
        "assert power(2, 9) == 2**9, \"Odd Test case 2 failed\"\n",
        "print(f\"Indeed 2**8 is {power(2, 8)}\")\n",
        "print(f\"Indeed 2**9 is {power(2, 9)}\")\n",
        "# let's do 10 as well\n",
        "assert power(2, 10) == 2**10, \"Even Test case 3 failed\"\n",
        "print(f\"Indeed 2**10 is {power(2, 10)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Computing 2^8\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "256"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# let's make this same function with verbose flag\n",
        "def power_verbose(x, n, verbose=False):\n",
        "    '''Compute the value x**n for integer n.''' \n",
        "    if verbose:\n",
        "        print(f\"Computing {x}^{n}\")\n",
        "    if n == 0: # this is our base case\n",
        "        return 1 \n",
        "    else:\n",
        "        partial = power_verbose(x, n // 2, verbose=verbose) # remember that x^4*x^4 == x^8 or (x^4)^2 == x^(4*2) == x^8\n",
        "        result = partial * partial # so x^4*x^4 == x^8\n",
        "    if n % 2 == 1:  # for odd powers we need to multiply by the number\n",
        "        result *= x # so x^9 = x^4 * x^4 * x\n",
        "    return result\n",
        "\n",
        "power_verbose(2, 8, verbose=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.25"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**(-2) # our functions do not support it yet"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XYOLUdpmg25G",
        "outputId": "30e98fe5-c98a-416d-fee8-90fab83cd1ed"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "256"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "power(2,8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n-op6Wwig25H",
        "outputId": "7708346d-ce38-4785-a4e1-e1735388d40e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "512"
            ]
          },
          "execution_count": 27,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "power(2,9)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1, 2, 4)"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "power(2,0),power(2,1),power(2,2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709376"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "power(2,10_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Computing 2^10000\n",
            "Computing 2^5000\n",
            "Computing 2^2500\n",
            "Computing 2^1250\n",
            "Computing 2^625\n",
            "Computing 2^312\n",
            "Computing 2^156\n",
            "Computing 2^78\n",
            "Computing 2^39\n",
            "Computing 2^19\n",
            "Computing 2^9\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709376"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# let's do a verbose version\n",
        "power_verbose(2, 10_000, verbose=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "_7GO7neRg25H"
      },
      "outputs": [],
      "source": [
        "import math\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p001vTOxg25H",
        "outputId": "f118deed-7a77-4780-9a33-13e5dd143db8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "10.0"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.log2(1024)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "13.287712379549449"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# so for 10_000 we need 14 recursive calls\n",
        "math.log2(10_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hDMJ_wfog25H",
        "outputId": "d51559c2-93f1-4118-8c14-847e7670afe2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "20.0"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.log2(1024*1024) # for Million we need 20 recursive calls"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lz6Q4R5Cg25H",
        "outputId": "513506c4-b2ae-4c52-eb47-e13e31b9589b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "332.19280948873626"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.log2(10**100) # log n of googool that is 10 with 100 zeros more than atoms in the universe"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Googool - sidenote on history\n",
        "\n",
        "Invention of the term \"googol\" is attributed to the nine-year-old nephew of mathematician Edward Kasner. The term was introduced in his 1940 book \"Mathematics and the Imagination\" and is used to describe a very large number. The term \"googolplex\" was coined to describe an even larger number, namely $10^{googol}$, or equivalently, $10^{10^{100}}$. The number of atoms in the observable universe is estimated to be around $10^{80}$.\n",
        "\n",
        "The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner.\n",
        "Src: https://en.wikipedia.org/wiki/Googol"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4vQzBnBmg25I"
      },
      "outputs": [],
      "source": [
        "# so if we were playing the guess the number with yes and no questions we could figure out any number up to googool in 333 questions\n",
        "\n",
        "# not bad when we consider that number of atoms in Universe is something 10**80"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qtizfdtvg25I",
        "outputId": "cc5e108b-f7a5-4db6-d515-00d4bea35a69"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "2.72 µs ± 74.4 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "power(2,1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "878 ns ± 18.9 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**1000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "338 µs ± 7.53 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "basicpower(2,1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1UV9BcFxg25I",
        "outputId": "c11b1379-260c-416f-fcfe-6d5b59b53492"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3.97 µs ± 244 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "power(2,2000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-bbjy5QtkDua",
        "outputId": "39543945-5a69-4e1f-f2f5-ef17e6af1f4b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "7.95 µs ± 438 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "power(2,4000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Yf6sgkeLg25I",
        "outputId": "3d5e96ab-173b-4f77-cea9-a07ee85b55be"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "8.63 ms ± 195 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "power(2,2_000_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {},
      "outputs": [
        {
          "ename": "ValueError",
          "evalue": "Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit",
          "output_type": "error",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "Cell \u001b[1;32mIn[50], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;66;03m# catch is that we are starting to deal with huuuge numbers\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNumber of digits is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mpower\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m2_000_000\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
            "\u001b[1;31mValueError\u001b[0m: Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit"
          ]
        }
      ],
      "source": [
        "# catch is that we are starting to deal with huuuge numbers\n",
        "print(f\"Number of digits is {len(str(power(2,2_000_000)))}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1000000"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sys.set_int_max_str_digits(1_000_000)\n",
        "sys.get_int_max_str_digits()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of digits is 602060\n"
          ]
        }
      ],
      "source": [
        "# catch is that we are starting to deal with huuuge numbers\n",
        "print(f\"Number of digits is {len(str(power(2,2_000_000)))}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3.321928094887362"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.log2(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2000000.0288078852"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "3.321928094887362*602060"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iHu36-Rzk47z",
        "outputId": "0322ac49-1277-4ade-83ed-4240c110adce"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 4.55 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "1000000 loops, best of 5: 831 ns per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**1000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t7kWrfcilCFq",
        "outputId": "0c1f4618-3c63-4da5-f65f-05e90701829c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1000000 loops, best of 5: 1.8 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**2000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ucvznre4lKQE",
        "outputId": "17b0fe61-d3e0-45ec-fd96-fffd5673f539"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100 loops, best of 5: 8.71 ms per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "2**2_000_000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DeDm5OFxlcJU",
        "outputId": "9cf213e7-a211-40f0-d2a0-2cdb1b583db4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "256.0"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.pow(2,8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yYIb_xfqli6p",
        "outputId": "c130e8f3-b44a-48f7-b408-592502f14a5e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "211 ns ± 19.3 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.pow(2,1_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QqTa_QqElqNx",
        "outputId": "b12f54c4-0843-49e7-f8f4-7c49d51f916a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.0715086071862673e+301"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.pow(2,1_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yiNTKbizlt0b",
        "outputId": "0cc3afae-93b5-4a6c-a140-495421d3661e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**1_000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dUV_m7oblzJ7",
        "outputId": "72964f3a-20e4-42be-9ca0-bf2ed2b9fd8a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 30.28 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "1000000 loops, best of 5: 241 ns per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.pow(2,1_010)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5M5fSDvng25I"
      },
      "source": [
        "To analyze the running time of the revised algorithm, we observe that the exponent in each recursive call of function power(x,n) is at most half of the preceding exponent. As we saw with the analysis of binary search, the number of times that we can divide $n$ in half before getting to one or less is $\\mathcal{O}(log n)$. Therefore, our new formulation of the power function results in $\\mathcal{O}(logn)$ recursive calls. Each individual activation of the function uses $\\mathcal{O}(1)$ operations (excluding the recursive calls), and so the total number of operations for computing power(x,n) is O(logn). This is a significant improvement over the original $\\mathcal{O}(n)$-time algorithm.\n",
        "\n",
        "**Exercise:** Test the two functions with a timer and see the difference. Identify the base case and stopping conditions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dgQt-3s2g25J"
      },
      "outputs": [],
      "source": [
        "# so we got the famous stack overflow\n",
        "# technically we could adjust the recursion depth in Python but it would not really help in the long run"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tOQDOKGUg25J"
      },
      "outputs": [],
      "source": [
        "%%timeit\n",
        "power(2,100_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QKRPqdQJg25J"
      },
      "outputs": [],
      "source": [
        "%%timeit\n",
        "2**100_000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gMT2Kelhg25J"
      },
      "outputs": [],
      "source": [
        "%%timeit\n",
        "power(2,1_000_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J3O53srSg25J"
      },
      "outputs": [],
      "source": [
        "%%timeit\n",
        "2**1_000_000"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Computing 2^8\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n",
            "Computing 2^9\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n",
            "Computing 2^8\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n",
            "Indeed 2**8 is 256\n",
            "Computing 2^9\n",
            "Computing 2^4\n",
            "Computing 2^2\n",
            "Computing 2^1\n",
            "Computing 2^0\n",
            "Indeed 2**9 is 512\n",
            "Computing 2^-1\n",
            "Computing 2^0\n",
            "Computing 2^-1\n",
            "Computing 2^0\n",
            "Indeed 2**-1 is 0.5\n",
            "Computing 2^-2\n",
            "Computing 2^-1\n",
            "Computing 2^0\n"
          ]
        },
        {
          "ename": "AssertionError",
          "evalue": "Negative Test case 4 failed",
          "output_type": "error",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
            "Cell \u001b[1;32mIn[66], line 32\u001b[0m\n\u001b[0;32m     30\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mIndeed 2**-1 is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mfull_power(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m     31\u001b[0m \u001b[38;5;66;03m# let's do -2\u001b[39;00m\n\u001b[1;32m---> 32\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m full_power(\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNegative Test case 4 failed\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m     33\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mIndeed 2**-2 is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mfull_power(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
            "\u001b[1;31mAssertionError\u001b[0m: Negative Test case 4 failed"
          ]
        }
      ],
      "source": [
        "# let's make a complete power function that also works on negative powers\n",
        "def full_power(x, n, verbose=True):\n",
        "    '''Compute the value x**n for integer n.''' \n",
        "    if verbose:\n",
        "        print(f\"Computing {x}^{n}\")\n",
        "    if n == 0: # this is our base case\n",
        "        return 1 \n",
        "    else:\n",
        "        # check if n is negative\n",
        "        if n < 0 and n % 2 == 1: # if n is negative and odd we need to round up\n",
        "            next_pow = n // 2 + 1 # so we need to round up\n",
        "        else:\n",
        "            next_pow = n // 2\n",
        "        partial = full_power(x, next_pow) # remember that x^4*x^4 == x^8 or (x^4)^2 == x^(4*2) == x^8\n",
        "        result = partial * partial # so x^4*x^4 == x^8\n",
        "    if n % 2 == 1:  # for odd powers we need to multiply by the number\n",
        "        result *= x # so x^9 = x^4 * x^4 * x\n",
        "    if n < 0:\n",
        "        return 1/result\n",
        "    return result\n",
        "\n",
        "# assert it works\n",
        "assert full_power(2, 8) == 2**8, \"Even Test case 1 failed\"\n",
        "# now test with 9\n",
        "assert full_power(2, 9) == 2**9, \"Odd Test case 2 failed\"\n",
        "print(f\"Indeed 2**8 is {full_power(2, 8)}\")\n",
        "print(f\"Indeed 2**9 is {full_power(2, 9)}\")\n",
        "# now negatives\n",
        "assert full_power(2, -1) == 2**-1, \"Negative Test case 3 failed\"\n",
        "print(f\"Indeed 2**-1 is {full_power(2, -1)}\")\n",
        "# let's do -2\n",
        "assert full_power(2, -2) == 2**-2, \"Negative Test case 4 failed\"\n",
        "print(f\"Indeed 2**-2 is {full_power(2, -2)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# FIXME make it work with negative numbers \n",
        "# FIXME make it work with floats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Computing 2^-2\n",
            "Computing 2^-1\n",
            "Computing 2^0\n",
            "Computing 2^-3\n",
            "Computing 2^-1\n",
            "Computing 2^0\n",
            "Computing 2^-4\n",
            "Computing 2^-2\n",
            "Computing 2^-1\n",
            "Computing 2^0\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "(4.0, 2.0, 0.0625)"
            ]
          },
          "execution_count": 67,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "full_power(2, -2), full_power(2, -3), full_power(2, -4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            " -10//2 is -5 and n//2+1 is -4\n",
            " -9//2 is -5 and n//2+1 is -4\n",
            " -8//2 is -4 and n//2+1 is -3\n",
            " -7//2 is -4 and n//2+1 is -3\n",
            " -6//2 is -3 and n//2+1 is -2\n",
            " -5//2 is -3 and n//2+1 is -2\n",
            " -4//2 is -2 and n//2+1 is -1\n",
            " -3//2 is -2 and n//2+1 is -1\n",
            " -2//2 is -1 and n//2+1 is 0\n",
            " -1//2 is -1 and n//2+1 is 0\n",
            " 0//2 is 0 and n//2+1 is 1\n",
            " 1//2 is 0 and n//2+1 is 1\n",
            " 2//2 is 1 and n//2+1 is 2\n",
            " 3//2 is 1 and n//2+1 is 2\n"
          ]
        }
      ],
      "source": [
        "for n in range(-10,4):\n",
        "    print(f\" {n}//2 is {n//2} and n//2+1 is {n//2+1}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(-1, -1, -2)"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# now let's see what happens whne we divie negative integer using // operator\n",
        "-2 // 2, -1 //2, -3 // 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(0.5, 0.25, 0.125, 0.0625)"
            ]
          },
          "execution_count": 57,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**-1,2**-2,2**-3,2**-4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fm85Fo4Ag25J"
      },
      "source": [
        "# We humans operate better on visual data - 1 picture and 1000 words"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {},
      "outputs": [],
      "source": [
        "# in python we can pass functions as arguments\n",
        "import matplotlib.pyplot as plt\n",
        "import time\n",
        "from IPython.utils import io as iuio"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "id": "AY7uwayQg25K"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "testing function_1 with the automatic measure\n",
            "run-time for function 1 result in seconds: \n",
            "[0.0, 0.0010042190551757812, 0.0019931793212890625]\n"
          ]
        }
      ],
      "source": [
        "\n",
        "def automatic_time(input_array, func_name):\n",
        "    # input_array contains all elements of input,\n",
        "    #   preferably sorted from small to big,\n",
        "    #   each element could also be a tuple, which is requried\n",
        "    #   for functions that need more than 1 input\n",
        "    # func_name is the name of the function (as object, not str)\n",
        "    # this function also suppresses printing output from the {func_name}\n",
        "    ret = []\n",
        "    for val in input_array:\n",
        "#         print(time.process_time_ns())\n",
        "#         start = time.process_time()\n",
        "        start = time.time()\n",
        "\n",
        "        with iuio.capture_output() as suppressed: # suppress output from the function\n",
        "            if isinstance(val, tuple):\n",
        "                _ = func_name(*val) #unrolling the tuple to pass multiple arguments to our function\n",
        "                # func_name(*val) #unrolling the tuple to pass multiple arguments to our function\n",
        "            else:\n",
        "                _ = func_name(val) # just a single argument function\n",
        "                # func_name(val) # just a single argument function\n",
        "                \n",
        "        ret.append((time.time() - start)) # 10e9 converts unit from second to nanosecond\n",
        "    return ret\n",
        "\n",
        "my_input_arr = [(2,1_000),(2,2_000),(4,4_000)] # so our inputs are tuples of (base, power)\n",
        "print(\"testing function_1 with the automatic measure\")\n",
        "print(f\"run-time for function 1 result in seconds: \\n{automatic_time(my_input_arr, basicpower)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "id": "TfApv7Bsg25K"
      },
      "outputs": [],
      "source": [
        "seconds = time.time()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "54.0"
            ]
          },
          "execution_count": 71,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "seconds // 60 // 60 // 24 // 365\n",
        "# so around 54 years since start of the epoch which was in 1970"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {},
      "outputs": [],
      "source": [
        "# there is year 2038 problem based on this epoch\n",
        "# so we will have to deal with it at some point\n",
        "# https://en.wikipedia.org/wiki/Year_2038_problem\n",
        "# similar to Y2K problem (https://en.wikipedia.org/wiki/Year_2000_problem) but for 2038"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "bumFvwBWg25K",
        "outputId": "014bd2f4-126b-44c3-bd45-94bb3ba9f08a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [(2,i) for i in range(100, 50_000+1, 100)] # we will use list comprehension to generate our input\n",
        "\n",
        "# input_arr_t = [(i,i) for i in range(1, 1000)]\n",
        "\n",
        "# fun1 = automatic_time(input_arr, function_1)\n",
        "results = automatic_time(input_arr, basicpower) # this is our naive function\n",
        "results_2 = automatic_time(input_arr, power) # this is our improved function\n",
        "# fun3 = automatic_time(input_arr, function_3)\n",
        "# fun4 = automatic_time(input_arr_t, function_4)\n",
        "# fun5 = automatic_time(input_arr_t, function_5)\n",
        "\n",
        "plt.plot([el[1] for el in input_arr], results, color=\"red\") # we only want to see the i as x\n",
        "plt.plot([el[1] for el in input_arr], results_2, color=\"blue\") # we only want to see the i as x\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "# add legend\n",
        "plt.legend([\"basicpower\", \"power\"])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "gwi88tvUg25K",
        "outputId": "417d38b5-3b3a-4314-e244-4ab2fca1e120"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [(2,i) for i in range(100_000, 20_000_000, 100_000)]\n",
        "\n",
        "results = automatic_time(input_arr, power)\n",
        "# mathpow_results = automatic_time(input_arr, math.pow) # math.pow does n ot like large powers\n",
        "\n",
        "plt.plot([el[1] for el in input_arr], results)\n",
        "# plt.plot([el[1] for el in input_arr], mathpow_results)\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "yfdHt21QoEX9",
        "outputId": "3a3431f9-2b8e-40fb-e1f7-8343a442becf"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [(2,i) for i in range(1_000, 100_000, 1_000)]\n",
        "\n",
        "results = automatic_time(input_arr, power)\n",
        "# mathpow_results = automatic_time(input_arr, math.pow) # math.pow does n ot like large powers\n",
        "\n",
        "plt.plot([el[1] for el in input_arr], results)\n",
        "# plt.plot([el[1] for el in input_arr], mathpow_results)\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1tq0h7qxg25L"
      },
      "outputs": [],
      "source": [
        "math.pow(2,800_000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I0YqzuEyg25L"
      },
      "source": [
        "# so it certainly looks linear but the jumps in our speed indicates how OS and computer hardware might affect an algorithm in real life"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y20PkNpEg25L"
      },
      "source": [
        "## Factorial"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "8Wqy0YSYg25L"
      },
      "outputs": [],
      "source": [
        "# so again base case for stopping will be 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "id": "iOAR7YEBg25L"
      },
      "outputs": [],
      "source": [
        "def factorial(x):\n",
        "    if x <= 1: # our base\n",
        "        return 1 # not x! as factorial of 0 is considered 1! # TODO find out why factorial of 0 is 1\n",
        "    else:\n",
        "        return x * factorial(x-1) # so we want to be sure that our problem space keeps getting smaller"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GuqQ_NEFg25L",
        "outputId": "2b14cb04-689d-4039-8893-0895aa192f0b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 74,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import math\n",
        "math.factorial(0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M64s0jrPobQu",
        "outputId": "aa8e5ddb-f970-4edd-ad54-aa360f94ca93"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(120, 720, 5040, 40320)"
            ]
          },
          "execution_count": 75,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "math.factorial(5),math.factorial(6),math.factorial(7),math.factorial(8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "id": "q9n00D4ig25L"
      },
      "outputs": [],
      "source": [
        "# regular loop based algorithm should need less memory\n",
        "def factorial_loop_top_down(x):\n",
        "    res = 1  # try not to put 0 as a multiplier...\n",
        "    while x > 1:\n",
        "        res *= x\n",
        "        x -= 1\n",
        "    return res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gv2nwPnyg25L",
        "outputId": "036676f1-a7dc-499c-8ec7-4a80ef061c5b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "120"
            ]
          },
          "execution_count": 72,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "factorial_loop_top_down(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {},
      "outputs": [],
      "source": [
        "# let's make a loop based factorial from bottom up\n",
        "def factorial_loop_bottom_up(x):\n",
        "    res = 1  # try not to put 0 as a multiplier...\n",
        "    for i in range(2, x+1):\n",
        "        res *= i\n",
        "    return res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6V7f8f9Jg25M",
        "outputId": "14d966f2-a3b0-4eba-908a-f9a30736c27a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "120"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "factorial(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o3Q_UPH2g25M",
        "outputId": "caa73b9d-e288-43fb-f833-f3d064deb57b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "factorial(1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YggWjevIg25M"
      },
      "source": [
        "5! = 5 x 4 x 3 x 2 x 1 = 120"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZmkJVVd9g25M",
        "outputId": "00db0733-291e-4bce-fa43-97a0c991f085"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "120"
            ]
          },
          "execution_count": 78,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "factorial(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ivp-VY2wg25M",
        "outputId": "b7ae34dd-819b-4eeb-8ec5-73112a297612"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "835 ns ± 29.3 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "id": "hP5kKbqyg25N"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "13.8 µs ± 341 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "id": "A_7hZ_DKg25N"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "7.81 µs ± 179 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop_bottom_up(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "9.56 µs ± 338 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop_top_down(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xYcKrj94g25N",
        "outputId": "fddf3032-df13-44a1-da05-cadefc231b18"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.26 µs ± 26.3 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.factorial(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "399 µs ± 14.2 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop_top_down(1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "380 µs ± 22.3 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop_bottom_up(1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "51.5 µs ± 1.81 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.factorial(1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g_KZj8iyg25O",
        "outputId": "2048c181-1dba-4706-d5a9-9e0bb9512478"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "573 µs ± 3.79 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial(1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wZFw43Xjg25O",
        "outputId": "8c9a884d-2f90-4cd9-8d6c-0f1e1220d243"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "451 µs ± 74.2 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop(1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mIyBU1jCg25O",
        "outputId": "2c6f6a94-8f7f-4ee7-f20b-c49642d86024"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1.33 ms ± 50.5 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "factorial_loop(2000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cMW-cGNng25P",
        "outputId": "f7ad9635-a57a-4cb4-c0b0-58d0bf8199e8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              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            ]
          },
          "execution_count": 69,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "factorial(5000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x7eo-_O6pTN3",
        "outputId": "96826d08-7c41-4bfa-acbb-b1b849a45bd4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "16326"
            ]
          },
          "execution_count": 70,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "len(str(factorial(5000)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UXf3GsFEpZbc",
        "outputId": "0d3101be-5311-47b9-fd87-d6ef4bed9305"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "51.4 µs ± 5.25 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.factorial(1_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e1oLDYY_pfz0",
        "outputId": "8db2719f-f45b-4a18-8a32-ecd25fbe3d0b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10000 loops, best of 5: 136 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "math.factorial(2_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5jR6nEzhg25P"
      },
      "outputs": [],
      "source": [
        "%%timeit\n",
        "factorial(5000) #"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "id": "BJIOIlgEg25P"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(1_000, 30_000, 1_000)]\n",
        "\n",
        "results = automatic_time(input_arr, factorial)\n",
        "top_down = automatic_time(input_arr, factorial_loop_top_down)\n",
        "bottom_up = automatic_time(input_arr, factorial_loop_bottom_up)\n",
        "built_in = automatic_time(input_arr, math.factorial)\n",
        "plt.plot(input_arr, results)\n",
        "plt.plot(input_arr, top_down)\n",
        "plt.plot(input_arr, bottom_up)\n",
        "plt.plot(input_arr, built_in)\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "# add legend\n",
        "plt.legend([\"recursive, factorial_loop_top_down, factorial_loop_bottom_up, built_in\"])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "P-rRP7CAg25P",
        "outputId": "147fadf8-549e-4a23-d54c-fe4e9d9f29e0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(100, 2_000, 100)]\n",
        "\n",
        "fun2 = automatic_time(input_arr, factorial_loop)\n",
        "plt.plot(input_arr, fun2, color='red')\n",
        "fun1 = automatic_time(input_arr, factorial)\n",
        "plt.plot(input_arr, fun1, color='blue') # blue is recursive\n",
        "# add legend\n",
        "plt.legend([\"loop\",\"recursive\"])\n",
        "\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "25Sm34H7g25P",
        "outputId": "c514ca6a-cd52-4c5e-a6a4-c2066ab6352d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(100, 5_000, 100)]\n",
        "\n",
        "fun3 = automatic_time(input_arr, math.factorial)\n",
        "plt.plot(input_arr, fun3, color='green')\n",
        "fun2 = automatic_time(input_arr, factorial_loop)\n",
        "plt.plot(input_arr, fun2, color='red')\n",
        "fun1 = automatic_time(input_arr, factorial)\n",
        "plt.plot(input_arr, fun1, color='blue')\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "pGvv6HzIqUHd",
        "outputId": "c3c09702-5784-4a8a-a74d-f212830b25de"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(1000, 100_000, 1000)]\n",
        "\n",
        "fun3 = automatic_time(input_arr, math.factorial)\n",
        "plt.plot(input_arr, fun3, color='green')\n",
        "fun2 = automatic_time(input_arr, factorial_loop)\n",
        "plt.plot(input_arr, fun2, color='red')\n",
        "# fun1 = automatic_time(input_arr, factorial)\n",
        "# plt.plot(input_arr, fun1, color='blue')\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y1k3lTftg25P"
      },
      "source": [
        "# Exercise: Fibonacci\n",
        "\n",
        "The sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci sequence: $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, \\cdots$ (each number is the sum of the previous two, e.g., $144=55 + 89$).\n",
        "\n",
        "As you covered Fibonacci in Semester 1, this should be familiar. The twist is we are going to look at a variety of ways of implementing it and the complexity of execution for each.\n",
        "\n",
        "A direct implementation of the description above would lead to pseudo code like this:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "id": "l5Rt1jI-g25R"
      },
      "outputs": [],
      "source": [
        "def bad_fibonacci(n):\n",
        "  \"\"\"Return the nth Fibonacci number.\"\"\"\n",
        "  if n <= 1:\n",
        "    return n\n",
        "  else:\n",
        "    return bad_fibonacci(n-2) + bad_fibonacci(n-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1, 1, 2, 3, 5, 8, 13)"
            ]
          },
          "execution_count": 85,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "bad_fibonacci(1), bad_fibonacci(2),bad_fibonacci(3),bad_fibonacci(4),bad_fibonacci(5),bad_fibonacci(6),bad_fibonacci(7)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5S8hIQJyg25R",
        "outputId": "053b2bab-3738-46f2-d826-18c67e0a0597"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0 0\n",
            "1 1\n",
            "2 1\n",
            "3 2\n",
            "4 3\n",
            "5 5\n",
            "6 8\n",
            "7 13\n",
            "8 21\n",
            "9 34\n"
          ]
        }
      ],
      "source": [
        "for n in range(10):\n",
        "    print(n, bad_fibonacci(n))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S5lFoD_9sl24",
        "outputId": "8ad64be0-193d-46fd-840d-0e9a5ae67c56"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "2 1 1.0\n",
            "3 2 2.0\n",
            "4 3 1.5\n",
            "5 5 1.6666666666666667\n",
            "6 8 1.6\n",
            "7 13 1.625\n",
            "8 21 1.6153846153846154\n",
            "9 34 1.619047619047619\n",
            "10 55 1.6176470588235294\n",
            "11 89 1.6181818181818182\n",
            "12 144 1.6179775280898876\n",
            "13 233 1.6180555555555556\n",
            "14 377 1.6180257510729614\n",
            "15 610 1.6180371352785146\n",
            "16 987 1.618032786885246\n",
            "17 1597 1.618034447821682\n",
            "18 2584 1.6180338134001253\n",
            "19 4181 1.618034055727554\n"
          ]
        }
      ],
      "source": [
        "# https://en.wikipedia.org/wiki/Golden_ratio\n",
        "for n in range(2,20):\n",
        "    print(n, bad_fibonacci(n), bad_fibonacci(n)/bad_fibonacci(n-1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Fibonacci spiral\n",
        "\n",
        "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Fibonacci_Spiral.svg/500px-Fibonacci_Spiral.svg.png\" width=\"400\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rHzyAHNQg25R",
        "outputId": "08b28c23-b7d1-4c3c-c08c-faa7059bbfbb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "13.3 µs ± 1.09 µs per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3HsMQwNig25S",
        "outputId": "2bb5748a-d62f-494c-8534-39579a881de4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10000 loops, best of 5: 72.5 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(12)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PaLAommIg25S",
        "outputId": "0d635c89-372b-4a1a-8e2b-e8e9619bc883"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1000 loops, best of 5: 494 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(16)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Sww1jqIig25S",
        "outputId": "67e55fed-24c5-4f96-8ced-3a2aae675d89"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "2.12 ms ± 31.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7dJ1oQ8Bg25S",
        "outputId": "b484691f-6fe5-4ccd-8bfe-f49a8084e636"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "16.3 ms ± 644 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(24)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2178309"
            ]
          },
          "execution_count": 90,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "bad_fibonacci(32)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "43Ma-Ef6g25S",
        "outputId": "18597e00-c4a7-45a1-d119-32767251cb95"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "512 ms ± 20.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "bad_fibonacci(32)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "EVfz99O8g25S",
        "outputId": "3dc4ee4d-c0b0-45a1-da95-46095a13436c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(1, 35, 1)]\n",
        "\n",
        "fun2 = automatic_time(input_arr, bad_fibonacci)\n",
        "plt.plot(input_arr, fun2, label = \"Bad Fibonacci\")\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NvMNf7SAg25S"
      },
      "outputs": [],
      "source": [
        "# so bad_fibonacci looks like an exponational complexity"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HnpbABl2g25S"
      },
      "outputs": [],
      "source": [
        "arr = [2**n for n in range(30)]\n",
        "plt.plot(list(range(30)), arr)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oNSfZDqPg25S"
      },
      "outputs": [],
      "source": [
        "# sure smells like exponential"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "a2wso8Qog25T"
      },
      "outputs": [],
      "source": [
        "# what is so bad about bad fibonacci ?\n",
        "# so for each recursive call you get new 2 recursive calls\n",
        "# it is like that story of inventor of chess in India\n",
        "# he asked for 1 grain of rice on first square\n",
        "# 2 on 2nd , 4 on 3rd, 8 on 4th,\n",
        "# the story modification is that king realized the problem\n",
        "# to get out of it king said ok, you have to count the rice \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8fTWpPTdg25T",
        "outputId": "b3911552-cfb6-4496-9386-f854d0eac466"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4294967296"
            ]
          },
          "execution_count": 90,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**32 # he could count half a board"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9QCNhk1cg25T",
        "outputId": "03206d20-3acb-4ff3-e45f-02fa7feff8c4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "18446744073709551616"
            ]
          },
          "execution_count": 91,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "2**64 # not likely for a human..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "id": "oe18J_S7g25T"
      },
      "outputs": [],
      "source": [
        "\n",
        "\n",
        "def good_fibonacci(n):\n",
        "  \"\"\"Return pair of Fibonacci numbers, F(n) and F(n-1).\"\"\"\n",
        "  if n <= 1:\n",
        "    return (n,0)\n",
        "  else:\n",
        "    (a, b) = good_fibonacci(n-1) # looks linear here\n",
        "    return (a+b, a) # using the fact that we have the previous number\n",
        "  \n",
        "# Note: a bit like using accumulator in loop based approach"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "prMV6nl4uBDU",
        "outputId": "f14e176a-9511-4d30-f5da-fed251aec986"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(55, 34)"
            ]
          },
          "execution_count": 93,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "good_fibonacci(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 94,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zXEq5EGtuJw7",
        "outputId": "dd718f91-435e-40eb-944e-e98aba5ea14a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(354224848179261915075, 218922995834555169026)"
            ]
          },
          "execution_count": 94,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "good_fibonacci(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CL2m7G19g25T",
        "outputId": "f3ec1525-dc1e-4512-b2d8-43c8186967b8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000 loops, best of 5: 1.97 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "good_fibonacci(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RxyaoRwQg25T",
        "outputId": "610bead7-0432-4bf6-c1d5-48ba7ca3b64a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000 loops, best of 5: 4.14 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "good_fibonacci(20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f_NpPtkwg25T",
        "outputId": "35f9a2da-49bf-48b3-d230-4cc5ada4d15c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "4.8 µs ± 395 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "good_fibonacci(30)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "VKKv6Lw_g25T",
        "outputId": "13f9f2cc-24e8-465a-9f9d-bf16cf30588e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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uEhMT8eyzz3qij0RERFRL1ZoapPXr12Pz5s1o0KCB9bWGDRtizpw56Nevn66dIyIiIvIFzRmksLAwlJaW2rx+8eJFhIaG6tIpIiIiIl/SHCDdddddGDt2LLZs2QJBECAIAjZv3ownnngC99xzjyf6SERERD4geGEArNbUIC1YsACtW7dGcnIywsPDER4ejn79+qFNmzZ49913PdFHIiIi8jFPPWas1tQg1atXD9999x2OHDlinebfsWNHtGnTRvfOERERke8YRPkdswAEOZHu8deARyuX1kECgDZt2jAoIiIiqsXEQ2xmQUCQBwbEas0Q25AhQ/DGG2/YvP7mm29i6NChunSKiIiI/IvJ7FxuyF8DHq00B0i//fYb7rzzTpvX77jjDvz222+6dIqIiIh8TzzE5qESJL8dktMcIKlN5w8JCUFJSYkunSIiIiLfkw+xXUs0B0hdunTB119/bfP6smXL0KlTJ106RURERP7FJAiYt/oQXl+1X9f9+uuQnOYi7WnTpuH+++/H0aNH8Ze//AUAkJGRga+++grLly/XvYNERETkG+IhtiuVJizIOAwAGNUvAU1jInQ5hr/mpTRnkO6++26sWLECR44cwVNPPYXnn38ef/75J3799VcMHjxYcwcWLlyIhIQEhIeHIykpCVu3brXbfvny5ejQoQPCw8PRpUsXrFq1SvK+IAiYPn06mjZtioiICKSkpODw4cOSNocOHcK9996LRo0aITo6Gv3798fatWs1952IiKg2Ew+xVZpEn1dJwxpPrZHkS5oDJAAYNGgQNm7ciLKyMpw9exZr1qzBgAEDNO/n66+/RlpaGmbMmIHt27ejW7duSE1NRWFhoWL7TZs2Yfjw4Rg9ejSys7MxePBgDB48GHv27LG2efPNN7FgwQIsWrQIW7ZsQZ06dZCamoorV65Y29x1112oqqrCmjVrkJWVhW7duuGuu+5Cfn6+9otBRERkRyAHD+Kum0Wz2AwG9Xa1hUsBUlFRET7++GNMmTIF58+fBwBs374dp06d0rSfefPmYcyYMRg1ahQ6deqERYsWITIyEkuWLFFs/+6772LgwIGYOHEiOnbsiFdeeQU9evTA+++/D6D6h3D+/PmYOnUq7r33XnTt2hVffPEF8vLysGLFCgDA2bNncfjwYbz44ovo2rUr2rZtizlz5uDSpUuSQIuIiAJbpcmM82UVPu3D74fP4MbXfsWv+wp02Z+3gy3x4arsBUiiz8vKq/D9zjyUXql06hgGACVXKvHO6kM4euai653VmeYAadeuXWjXrh3eeOMNvPXWWygqKgIAfPPNN5g8ebLT+6moqEBWVhZSUlJqOmM0IiUlBZmZmYrbZGZmStoDQGpqqrV9Tk4O8vPzJW1iYmKQlJRkbdOwYUO0b98eX3zxBcrKylBVVYUPP/wQTZo0Qc+ePVX7W15ejpKSEskHERH5p6wTF9D2pZ/Q45XVeC/jsOMNPOSRT7bi7MUK/OOLbW7vy2QWcN+/NmGsDvty+piiCMlkNls/N8giJHHgtmJHHp79KhvPfJVtfW3PqWI89tkfOJBffe98VvSeWQCe+nI73s04jJR563U/B1dpDpDS0tIwcuRIHD58GOHh4dbX77zzTk3rIJ09exYmkwmxsbGS12NjY1WHuvLz8+22t/xrr43BYMCvv/6K7OxsREVFITw8HPPmzUN6ejrq16+v2t/Zs2cjJibG+hEfH+/0uRIRkXe99O1u6+dzVx/yYU/0cyC/BDtOFuEXN7NRpVcq8e/M4ygsveKwrSAJkOy0U3ht3cEz1s/v/2AT1hwoxMMfbQEAfL8zT9J2w5GzV4/nsEteozlA+uOPP/D444/bvN68efOAqOERBAFPP/00mjRpgt9//x1bt27F4MGDcffdd+P06dOq202ePBnFxcXWj5MnT3qx10REdK3TK3iYtmIPpn23F8MXb3bYVrx4dqUoQpJPzXfUt4qq6m3P+XjIUwvNAVJYWJji8NKhQ4fQuHFjp/fTqFEjBAUFoaBAGgkXFBQgLi5OcZu4uDi77S3/2muzZs0arFy5EsuWLUO/fv3Qo0cP/Otf/0JERAQ+//xz1f6GhYUhOjpa8kFERBRoVl/NQB09U+awrfjxIia7NUh+lPrRieYA6Z577sGsWbNQWVldfGUwGJCbm4sXXngBQ4YMcXo/oaGh6NmzJzIyMqyvmc1mZGRkIDk5WXGb5ORkSXsAWL16tbV9YmIi4uLiJG1KSkqwZcsWa5tLly4BqK53EjMajTCb7eQPiYiI/IS3irXFx5EUaUNeg+SV7niV5gBp7ty5uHjxIpo0aYLLly9jwIABaNOmDaKiovDaa69p2ldaWho++ugjfP7559i/fz+efPJJlJWVYdSoUQCARx99VFL4PX78eKSnp2Pu3Lk4cOAAZs6ciW3btmHcuHEAqoO1CRMm4NVXX8X333+P3bt349FHH0WzZs2sazQlJyejfv36GDFiBHbu3IlDhw5h4sSJyMnJwaBBg7ReDiIiIq8QByHeCkjEQ2xVoiE2ecaoNgZImlfSjomJwerVq7Fx40bs3LkTFy9eRI8ePWxmlzlj2LBhOHPmDKZPn478/Hx0794d6enp1iLr3NxcSaanb9++WLp0KaZOnYopU6agbdu2WLFiBTp37mxtM2nSJJSVlWHs2LEoKipC//79kZ6ebi0ob9SoEdLT0/HSSy/hL3/5CyorK3H99dfju+++Q7du3TSfAxERkbd5Kx5RG2KTB0S1cYhNc4Bk0a9fP/Tr1w8ArFP9XTFu3DhrBkhu3bp1Nq8NHToUQ4cOVd2fwWDArFmzMGvWLNU2vXr1ws8//6y5r0RERL4iDkKqh748/xQz8QNqK8UBkqxdbcwgaR5ie+ONNyQPq33ggQfQsGFDNG/eHDt37tS1c0RERGTLW/GIoDbEJouIamF8pD1AWrRokXUNoNWrV2P16tX46aefcMcdd2DixIm6d5CIiIikzF5K2ZhUirRththqYQpJ8xBbfn6+NUBauXIlHnjgAdx+++1ISEhAUlKS7h0kIiIiKe8VaSvXIMnVvvDIhQxS/fr1rYskpqenW4uzBUGAyWTSt3dEREQEwDd1PuJjVkqG2NTbOd5nYIRTmjNI999/Px566CG0bdsW586dwx133AEAyM7ORps2bXTvIBEREUl5K8ZQncUmzxlp6I+dRJRf0RwgvfPOO0hISMDJkyfx5ptvom7dugCA06dP46mnntK9g0RERCSNQbw1rd7sZA2SlpqoWptBCgkJwT//+U+b15977jldOkRERET2+WahSDvT/F3cpz/TXINERERE3ifOvHgrxjCbxRkkO9P8tWSQAqSkmwESERFRgPHWMJVkiE2nDFKAjLAxQCIiIgo03hqmEh/H7qNGNM1ic7NTXsIAiYiIKND4YB2kStEQm7wDWobNvLXIpbtcfhZbRUUFCgsLYZZcMKBly5Zud4qIiIikfDKLTTzNXzTEZpPB0pJBcrNP3qI5QDp8+DAee+wxbNq0SfK6IAgwGAxcLJKIiMjDfDKLzd4Qm6Z9BkaIpDlAGjlyJIKDg7Fy5Uo0bdoUBoPnnyZMRER0rRPHFV6bxSZZB0k0i03WA23rILnfL2/QHCDt2LEDWVlZ6NChgyf6Q0RERA74fBbbNfCoEc1F2p06dcLZs2c90RciIqKAdbr4Mqat2IMjhRc9dATvrYNUUVWdLXJ2JW09p/m/v+Yw0vec1rBHz9AcIL3xxhuYNGkS1q1bh3PnzqGkpETyQURE16ZKk9nuE999yRtZiye/3I5/bz6BwQs3emT/4ktrCVze+vkAXl+13/G2ZgEzvtuD/2476bDt5G92of20n3DiXBlEz6dVfBZbYckVzP5pP06cK3PyLBwPx739yyE88eV2p/fnKZqH2FJSUgAAt912m+R1FmkTEV27yqtM6PN6BmKjw5E+4WZfd8eGWQCC3CyZLbpUgSCjAVHhIYrv7z5VDAC4WF7l8jEqqswoKLmC+AaRNu9J4goBKL1SiYVrjwIAHuuXiNX78tHnuoZoGxtlvSdbrD1YiM8zTwAA6oQG2e3DV1urg6iPfj8mCSwrTeKVtKv/fearbGzJOY8P1x9z+hz9M4S2pTlAWrt2rSf6QUREAezA6VJcuFSJC5cqvXrczzbm4JONOVj6jz6KQYVFpcmMIKP9wAAACkuv4NSFy7ihZX3J61cqTeg+azUAIGf2nYoTlPSYsjR00Sbs/LMY/308Gb0TG0jeE2de9p4uwahP/7B+/emmHGuQcuCVgbjz3d9xffMYvDf8BgBAkQvfF7MgPaZSdvCP4+e179dPs4xymgOkAQMGeKIfREREms38YR8A4JWV+7D40V5u76/3axkAgBVP90P3+HrW108VXbZ+rpaN0mNS984/q7NQy7edtAmQxBmkqd/ukby3I7fI+vm6g2dw7GwZjp0tswZIrhAEQTLEplSDZDQY7A6Zmc0CjEbphXl0yVaX++RNTgVIu3btQufOnWE0GrFr1y67bbt27apLx4iIiJx1pcps932ta+9sPnZOEiCJVQ87KWWQDNBrAElpL/bqqIJEQYhe6wyZzdJjVplsp/kbDfbPWemdA/mluvTP05wKkLp37478/Hw0adIE3bt3h8FgUPxGsQaJiIh8wdGwjdZRHbtZEbW3dFwWUOnwkhIkWQNxgKRXobxZEGSPGlHIIBkB2LntmwUBQS5eGKXskzc5FSDl5OSgcePG1s+JiIjUyAuEvcFRUKA1q2KvuTce86GUhBCfg/xd8fXWLYMkyB5Wa7I9vsFB8ONOV0yCAKOeUadGTgVIrVq1UvyciIhIThD0qcfRwuTgTizYH4HTRO1Qep6y8hBbzef2giClYNGV74cAQXJdJStpC5YhNvv7cCdYqzIJCHFcV+8xmtdBIiIisscXc5QcDbFpzfrYq/dRDZB0HWJzkEGyczp6DbEJgqwGyWybQTJ6MBIWB2S+wACJiIh05YtHSTjKIGmNGeztTi0r4mi4SdPxHbxm73SU+udKHGMWBJjVFooUnNuvOxkkXy86ygCJiIh05Y8ZJM01SC68p28GSek1ZzNI+vTBLEgDT/Gz2CxXwVERtTuxchUDJCIiqk188SxSxxkk/Yq01TNI+nFUgyRvIQ6elK6FK9ktsyDIhthsV9J2NMTmbg2SL7kUIBUVFeHjjz/G5MmTcf589Sqa27dvx6lTp3TtHBERBR5vzPKSc5Q10XqftncO6jVIOg6xKdYgOe4DoONK1bJZbOKMjtkaIDnchct8XYOkeSXtXbt2ISUlBTExMTh+/DjGjBmDBg0a4JtvvkFubi6++OILT/STiIgChC8ySA6LtDWvg2RvX77KIKlP8xfTrUgbgmRf4oyOpS+OgkJ3Zg8GXA1SWloaRo4cicOHDyM8PNz6+p133onffvtN184REVHgqQ1DbPZOQvUtD0dI0gySvYUsdVoHySzdl+RhtVf/dZxBcr0vlYE2xPbHH3/g8ccft3m9efPmyM/P16VTREQUuHwxxObNIm1v1CApH8N2iEtJpUKmx9U+iDdXmsXmuAbJ5cMHXgYpLCwMJSUlNq8fOnTIuto2ERFdu/wxg+RuAkn8tfosNj1rkGxfs5dBEn9ZUWVbTO3aNH9pkCL+/N+bj2Pg/N9w7mKF3X3I+6mlH76uQdIcIN1zzz2YNWsWKisrAVT/QOTm5uKFF17AkCFDdO8gEREFFl/83a/7o0bszBJTzSDpOc1f4So6E6QBQHmVyal2Dvtg8yy2moBl1e58HMgvRYWD6nh3kkABN4tt7ty5uHjxIpo0aYLLly9jwIABaNOmDaKiovDaa695oo9ERBRAfLFQpN4Pq7XJIKl+UUPXEiTFDJJzEVK5KIPkTj2SzRCbCwGLPNDTco18vQ6S5llsMTExWL16NTZs2IBdu3bh4sWL6NGjB1JSUjzRPyIiCjA+ySA5HGJzrwZJ+hw05W30HGJTOobtMo3ir2tekWSQHOzHHgGyhSJdCFjcelhtoAVIFv3790f//v317AsREdUCPqlBclCuovVeK8+8SJ6DphJiePr5vNKVtKV9EA9HVShkkMTBm7PfH7MgPW89AiSDweB0B6r0WhLcRS4FSH/88QfWrl2LwsJCmGVFVPPmzdOlY0REFKB8sQ6Szhkk+Tk4l0HSdghNHZD1Qf6uOHgRD7Ep79m5a1Fdg1TzdaULAYtbK2kHWgbp9ddfx9SpU9G+fXvExsZKolI904tERBSYfLOStr41SLbbOzN13tOz2NQLxcXZlvJKhQySg30rqX5YrfIsNmfJt9ByhQJuiO3dd9/FkiVLMHLkSA90h4iIAp0/rqSt68NqvZBBUuqvJIMke1u89pFSDZKkfsnZAMns/hCbO489cSVjpSfNs9iMRiP69evnib4QEVEt4A9F2vbWMXKG/MYuzSApb+PJhbQLSq5IF2qUvS9eM0g89V4p0HI2WDTLhthcqQkK5CJtzQHSc889h4ULF+rWgYULFyIhIQHh4eFISkrC1q1b7bZfvnw5OnTogPDwcHTp0gWrVq2SvC8IAqZPn46mTZsiIiICKSkpOHz4sM1+fvzxRyQlJSEiIgL169fH4MGDdTsnIqJrmV6PutBCnt2QD/O5m0GS1iApZXcESWBy9MxFTcez3V/N5xsOn0XS6xmY9L9dkuOJiYu0xUNsllclQ2x2jysNwsSBoivxijvDrb6uQdIcIP3zn//EwYMH0bp1a9x99924//77JR9afP3110hLS8OMGTOwfft2dOvWDampqSgsLFRsv2nTJgwfPhyjR49GdnY2Bg8ejMGDB2PPnj3WNm+++SYWLFiARYsWYcuWLahTpw5SU1Nx5coVa5v//e9/eOSRRzBq1Cjs3LkTGzduxEMPPaT1UhAR0VWuDOHoSZ7xkWcf3F1J2yyoZ28AYMwX21B0qdL69W1z12NF9inV/W8+dg5jvtiGU0WXlY8v+nz2T/sd9k8cnF0RDbHN++UQhi/eLH2OmpPPmZMvFOmK0itVuFheZf1ay/4CbiXtZ599FmvXrkW7du3QsGFDxMTESD60mDdvHsaMGYNRo0ahU6dOWLRoESIjI7FkyRLF9u+++y4GDhyIiRMnomPHjnjllVfQo0cPvP/++wCqv5nz58/H1KlTce+996Jr16744osvkJeXhxUrVgAAqqqqMH78eLz11lt44okn0K5dO3Tq1AkPPPCA1ktBROQ39uYV40ihetbiYnkV/rvtJC6U2X80hNiFsgq8+L9dyDpxwWFbaeZBvwjJbBaQdeI8LleY7LZzNMSm9UYvby/I3quoMqNYFBD9ut/2D/uPNxyTfJ114gL+te4ITGYBDy7ejNX7CvDc1ztQWHoFr6/aj5yzZaL+Vx/xYH4p9ubZPt7LZohNlEESf/7ZpuPIPHYOP++teVaqvcSM+DrKp/m74q73NiDptV+dOracr1fS1lyk/fnnn+N///sfBg0a5NaBKyoqkJWVhcmTJ1tfMxqNSElJQWZmpuI2mZmZSEtLk7yWmppqDX5ycnKQn58vWbQyJiYGSUlJyMzMxIMPPojt27fj1KlTMBqNuOGGG5Cfn4/u3bvjrbfeQufOnVX7W15ejvLycuvXSs+jIyLyheJLlRi0YAMA4Pgc5d/Nk7/ZjR925uGGlvXw7VPO1ZG+/MNerNiRh2V/nFTdr4Wg+oV7Ps88jpd/2IfeCQ3w3yeS1Y8vy3wUlpZL3j9fVoHHPvsDQ3u2wB1dmkre25dXgiqzGV1b1JO8/t2OU/hg3VEs+ntP2RpEwK1vr8Oposv446UUNI4KU+zTnlPS+8SQDzYBABrWCbW+dvL8JYz/agcyj53D/2X9aXM+P+zMUzlf2RCbKNuiNDRV4WDqv4V8ppweo1xlDoJbNQFXg9SgQQO0bt3a7QOfPXsWJpMJsbGxktdjY2ORn5+vuE1+fr7d9pZ/7bU5dqw6op85cyamTp2KlStXon79+rjllltw/vx51f7Onj1bkimLj4/XcLZERJ5TUFpTQqA2fGK50WbnFjm936Nnyhw3sh5X9LnTWzm2dEsuAGDrcfXfz3LZJ4skwzoA8Eb6Aaw5UIgn/7Nd8nqVyYw7F/yOe97fiNIrNRkhQRAwftkOHMgvxeRvdtsEYJahsU1Hz2o9JUmmzywI1gzdeVF2z1EWTv6ueBab0swxZ5fhkdRamd0fYnNHZaAFSDNnzsSMGTNw6dIlT/TH4ywLW7700ksYMmQIevbsiU8//RQGgwHLly9X3W7y5MkoLi62fpw8edJbXSYicpqef3Vrm7bueJaX5/tQLb+4OmBs06QuYqOrsztnZBklC3G2RVxDJD6FsooqSSZFPtymleT5Zg4SO2qBkvywVQ5mrjlLsq3B4NMAyRRoK2kvWLAAR48eRWxsLBISEhASEiJ5f/v27SpbSjVq1AhBQUEoKCiQvF5QUIC4uDjFbeLi4uy2t/xbUFCApk2bStp0794dAKyvd+rUyfp+WFgYrrvuOuTm5qr2NywsDGFhymlUIiJ/4as/uqUZJB2DNBcmz1sKkptEhV0NGMtVn9Wmdv+XrzkkyIaeLNy9hwuCoHi9rOsXOXkpxeendK7OXkXxz48B1Wsh+YqvZ7FpDpD0mg4fGhqKnj17IiMjw7pPs9mMjIwMjBs3TnGb5ORkZGRkYMKECdbXVq9ejeTk6nHpxMRExMXFISMjwxoQlZSUYMuWLXjyyScBAD179kRYWBgOHjxofZZcZWUljh8/jlatWulybkREvuKrv/g9NYvNlQySpbg3OMho3V4ts6aaoRFnxCCtxZEPQ2kl3kItcLN8H53duziQcSeosfcMOm8LuABpxowZuh08LS0NI0aMQK9evdC7d2/Mnz8fZWVlGDVqFADg0UcfRfPmzTF79mwAwPjx4zFgwADMnTsXgwYNwrJly7Bt2zYsXrwYQPUY64QJE/Dqq6+ibdu2SExMxLRp09CsWTNrEBYdHY0nnngCM2bMQHx8PFq1aoW33noLADB06FDdzo2IyBd8dT/zVA2SKywFyyFGA4xXIyS16yJZfFElCBIEacBkdpCtcUQ6xGY/s+Xs7sVF2u4Mswqi4Mpg8G2A5OsibZceVquXYcOG4cyZM5g+fbp1Nll6erq1yDo3NxdGY02ZVN++fbF06VJMnToVU6ZMQdu2bbFixQrJ7LNJkyahrKwMY8eORVFREfr374/09HSEh4db27z11lsIDg7GI488gsuXLyMpKQlr1qxB/fr1vXfyREQe4MoNWw/OPavMOyqtGSQDjA4ySGr3YEHWRi14cu35ZI7rtbTuVdwNpZ8BZ/cn39aXZUABMc2/QYMGOHToEBo1aoT69evbrYa3NxNMybhx41SH1NatW2fz2tChQ+1megwGA2bNmoVZs2aptgkJCcHbb7+Nt99+W1NfiYj8nc+G2FQCCHe58hB0S8FycJDRmkFSuy7iYE58KEEW8Kmdn7vXWzXAsmSQXMjHKQ37ORu02qz/5NMhtgAo0n7nnXcQFRVl/dyVH1giIvI8QeWeYjB4dvjNmayIK1y521hqV0KMNVurBTJqtUX2V9IWF2m7N8Sm3i/XL6I7GST5M+dYg+TAiBEjrJ+PHDnSU30hIiI3+eyGpjKLLfPoOdSvE4IOcdEu7daVv8crRUXalgySWiAjfl3tgbTVNUgQtVPe3hWqmS2bT5yn1CdnfyzktWS+rAPydQ2S5nWQgoKCFJ+Vdu7cOQQFBenSKSIicp4zGQlP5/2VZrGdPH8Jwz/ajIHzf3d5v67NYrtapB1kgKWMVXUkS3S9xBkL21lsyjVWrsSj0iUD7LdxJURQHGJzdls7Q4veVunjdZA0B0hq45Hl5eUIDQ1VfI+IiDzH3VlVelCaxebuE+1dZVmBOdhYk0FSY1YJLm2G2wTlbdy93urLD1iOrX3/ikNsTtcgibfhLDanLFiwAEB1wdzHH3+MunXrWt8zmUz47bff0KFDB/17SEREdqnd2MUMHi5CktYgVX+uxywkVxaKrCnSNjismZUssCjJIEHyuTRQcLMGyZk2gvRfLdyJK8yyIUdfBdxAgNQgAdXF2UD1D/6iRYskw2mhoaFISEjAokWL9O8hERHZ5RdDbAoZJD2GSFwaYrNmkByHV+KAQG1NJLNsqEmSdXKzSFu1jea91nClT9ZtbYq03eiIm6oC5VEjOTk5AIBbb70V33zzDdcMIiLyE9InsPumD0o1SHo8bNSVwK5SMs3fflu1NY0EWcSnlqVzJcshn7qvGDC5UYOklPVxdqhMPuTo22n+AZJBsli7dq0n+kFERC5yN6OhB/GN9MS5Moxbuh1NosPtbOE5lkBHvJK2GnHgUGVniE06i00lkHKSlgySa0Xgtq85u6SQPJC6lmex+XQlbSIicp/aVHVvEh/25R/2Iff8JRzIL3V/xy6MsSlN81ejVoMkJsgyKZJhOQ9db2sNkk4PbnF2P/KH8vp2iM23AZLmWWxERORfnJk27un1fcU34Ioq/WpHXFooUlKkbb+toBIgSabyQzYUJ9lGe/+cue3rHeg6uzvpEJuuXdDM1ytpM0AiIgpwalPVvUl82MhQ2zXxXK1lcadIO8RodLi92rWzne5e87W7GTunhtjcmMWmuD8n25mdyKh5i6+PzwCJiCjAOVMT48p0eS3Ehw0PsQ2QvHmvqxRlkBwOsanNYhO1MQuCJEPmfhDheBtfhQbi8/F1BqcyEB5WK7Zr1y7F1w0GA8LDw9GyZUuEhYW53TEiInKOdKq6b/ogvpWpZ5C0B2muDbE5X4OkFuzIV8uWznaD4jZ60n32mJO7k5ynjwMUX2eQNAdI3bt3t7vwVkhICIYNG4YPP/wQ4eG+mcFARHQtcWqIzdM1SKLjRigESK7e6+zdb9SCCEvmI8ToTA1Szedq6yAB6oGU54fY9AkSnJ/mrzyrzxd8ncHSPMT27bffom3btli8eDF27NiBHTt2YPHixWjfvj2WLl2KTz75BGvWrMHUqVM90V8iIpKR1s74qAZJ9LlSBsnVftmLb9Tu3+JZbI5W0laf5q8+bOnNOh299u5ssKPng3jd5etZbJozSK+99hreffddpKamWl/r0qULWrRogWnTpmHr1q2oU6cOnn/+ebz99tu6dpaIiGw59agRD/dBfNwIhRokzxzTQQYpyOBwoUi1GiQxs+CDDBIErMg+hVW78zXvX4mjfpZeqURUeIhfPNfPwtcZLM0ZpN27d6NVq1Y2r7dq1Qq7d+8GUD0Md/r0afd7R0REDikNE23PvYAHF2dib16xR49ddKkCu/4sgjjXoVT3oyWQ+F/Wn/jvtpMAbGex5Z67hFW7T1evTaSyvTWDpPKw2o1HzuLppduRV3RZ9cGz8u6qPc7FZBZwpdLk+KTE+3IiL1RyuQoTvt6BsxfLNe1bjVrwt+dUMdYeLESXmb/g1ZX7JEGnrzM4vs5gaQ6QOnTogDlz5qCiosL6WmVlJebMmWN9WO2pU6cQGxurXy+JiGqJSpMZi387in15JbrtUymjcf+/NmHzsfN46KMtuh2n0mTG55uO40hhzQKQN72xFve8vxGbj5236YOYpYuXKqrsBhRXKk14fvlOTPq/XSi6VGEz++7BxZl46j/bsTzrT5vjnC+rvi9ZitaDjFDMID388Rb8uOs0HvvsD9UFICVZOQiqdV7/3fYnOkxLVz0fJc7Eino8x05MLdi4670NGPXpHwCAjzfk4FDBRet7vq4B8nUGSfMQ28KFC3HPPfegRYsW6Nq1K4DqrJLJZMLKlSsBAMeOHcNTTz2lb0+JiGqBzzcdx+urDgA4gONzBumyT3vPYiu+XKnLMYDqvr/6434AsPa9tLwKALDmQKG1nVLi4cDpErSNjUK3l39BaJARHz7aE22b1EWL+pE4X1aBDUfOIvX6WMlN8VKFyWZsMK/4CgDg49+P4Z5uzSTv9XhlNZ79SxtrJshoMNitQTqQX6o+zV8SEMkXlFTdpVO2515w2OZcWYXDNlo4m42Z/M1u6+dXKn0cIAXKw2ot+vbti5ycHPznP//BoUOHAABDhw7FQw89hKioKADAI488om8viYhqib06Zo4spIsaqqyDpEMR0o6TRarvifevlEH626JMa21ShclszVocnzMID320GQfySzH25uvw7G1trduYzIJq7dShgouKmZgFa46gW3w9AFcDJLtnZG8ByJrX5dP83X3e3dEzZW5t7wpf1xMpadUwEgsf6gEAmPbdHmTnFkne9/UQm0vPYouKisITTzyhd1+IiMgFTj1qxMNl2uK9qwVpl1WG1izPbPtx12k885c2ov3YD+zUanksxw9y4mG1gkpRsvQcpAtF6h1seCMM8NVDjO1ZP/FW6+ffPtUP/912EpP+r2atxYAbYgOAw4cPY+3atSgsLIRZNkY5ffp0XTpGRFQb6b4AILw3NdvRlHkLLaUrz36VrbqtWRDsBnZqp2rJYBkMgNFBpa14H1VqNUiCZ6+xNzIlvg42nBEXLV07MeCG2D766CM8+eSTaNSoEeLi4iT/YQwGAwMkIiIvU8981PD0w2rFmRotGZbvd+ZJvtayppPauVqCLEc1SIDswbOiG7K8KFttFlug8McMkpw82+froE5zgPTqq6/itddewwsvvOCJ/hARkUbODLHpwW6oIa5BcrETgiDYFJzbi28cZZCMBsdDbNJ1f5Rft2kXAMGGnD/WIMnJs32+vs6ap/lfuHABQ4cO9URfiIhqPWeHqbRwJuuix1HtdV0ciLiTYZEPZdm9XCqHsRzeaHB83s5N85ceytc3blf4eLTKKfJgVu+lDrTSHCANHToUv/zyiyf6QkRU63mkBkn88FQPZgrsBRvi99xZX1CyUKHZ7KAGSWWIzVqD5MxK2jWfS2qQxLVQZkGWpQu8ACkQ+iwPkHwdiGoeYmvTpg2mTZuGzZs3o0uXLggJCZG8/+yzz+rWOSIicszsVA2Spx82UsOdINCkYShL7d2adZCUV/UWU8u+2WSQJJktu7v0S74ueHaGPJgNuBqkxYsXo27duli/fj3Wr18vec9gMDBAIiLyMsmN3YP3QXtBlieG2CpN9ofY1I5jeTnI6LhIW1AJyCT7FvzjgcDucCfWCA0yosILAZbRGOBF2jk5OZ7oBxHRNcEzNUjiz703xCYOLiQLRbpxLxXXATnMIDmc5u94iE19mr90f0rPuwsk7jw2JCzESwGSwhCbIAhezX5K+uOToxIR+bET58pw05tr8O/M47rv2zPrIHlnFps8QlILFFytgzIYDJJApMpstntzVJ3mLxpic3RvlT5qRDzNXzrEFuiz2NwJWsOvroDuaUrBrC+vtVMZpLS0NLzyyiuoU6cO0tLS7LadN2+eLh0jIvKVWT/sw8nzlzHtu714JDnB191xyJkMkif+BhdnXMSBjDtBoL1ARL5ftaOI10HSNM1fVpjtzDaBwp3i/bBg7+RSlL5XVWYBwd6Jz2w4FSBlZ2ejsrLS+rkaX6XBiIj0VF7l/wWtYmrT0/Umn1EmCZDE/XGjC+IbeZVJsLtftVMVrBkkA4IcjLFVmZSvnfxZbIGeQXKnz97KICmFEL6sQ3IqQFq7dq3i50REtVGgZQicGmLT4e9X+Q3MZBIU33PnZiyd5i/YfQiu+jT/mj6FBNnPfohrc9SDJVkNUoD9fLgrPMQ7GSSlYNbkzpoRbmINEhHVWr/uK8CM7/ZoXnAu0O5/0myH94q0K0XBhb1ARgvpQpFmWQZJul9HNVBGgwHBjjJIKtk3yTWVfR0Ij+3QU7iXxriUhtgqPTkt0wHNs9jKysowZ84cZGRkKD6s9tixY7p1jojIHf/4YhsAoHWTunhUQy2R2lPi/ZXSVHWDQRroeaIAQlrgXPO6ewFSzbaVsuyB/F6pFvharkeQ0YBgRxkkk+21qz6WNEIS/0wEwJJCumKRtpP+8Y9/YP369XjkkUfQtGlT1h0Rkd/LL76iqX3gZZBsMx9Gg0EyFKTH72r5LqpUAgp3AgjJquBm6RRvsyBIAj+1qec11wCaMkjq2aTAf1itO0KCvHOfV/oZ9fsaJLGffvoJP/74I/r16+eJ/hAR6U5rbBBotz+l7I3RAJg8fFzx6sziYEyvWWxVZnmRtoAggwFVV9tUVtmf5m8wGBDs4OYuOQc70/zVFpS8FjjKwulF6TvlyxXANZ91/fr10aBBA0/0hYjII+w9z0tRgN3/lB414mh6uyvszWLTayaddLaYWVbbJD2vCpNyCGjpi9GpIm3lzJdkIW1BkNZGXWMZJEdZOL34WwZJc4D0yiuvYPr06bh06ZIn+kNEpDutv98DbQhFUBli05vNEJtJmu2R98EV8keNSN4zC5LvTYVKBkkQXQNXp/mbbDJI0n5cSxxdQ08eM6BqkObOnYujR48iNjYWCQkJNg+r3b59u26dIyLShcZgIdBuf9KZXzXZEzFX4iX5JrY1SOLhKZUCZ41s1xuS1iBJAiTVGiQts9hE0/xVsmCCTZF2oP2EuMcXAVJIkAEms6B5BqqeNAdIgwcP9kA3iIg8R+uvd09OlfcEbw2xyUlnsekzxCZfB0kcrpoFWYZJZUFPk7UGyfEQmzhLJRkmlO36Wh5i84XQICOuVJoDK4M0Y8YM3TuxcOFCvPXWW8jPz0e3bt3w3nvvoXfv3qrtly9fjmnTpuH48eNo27Yt3njjDdx5553W9wVBwIwZM/DRRx+hqKgI/fr1wwcffIC2bdva7Ku8vBxJSUnYuXMnsrOz0b17d93Pj4h8y5+KtNX2faXS5PJ0arPC8Jb8nPUJl6R7EQcXJoVhPleYJLPYzHZnj6llFyzBTfU0f/tnblLLgsmDIEE5kCLPCA0OAlAVWDVIFhUVFfjzzz+Rm5sr+dDq66+/RlpaGmbMmIHt27ejW7duSE1NRWFhoWL7TZs2Yfjw4Rg9ejSys7MxePBgDB48GHv27LG2efPNN7FgwQIsWrQIW7ZsQZ06dZCamoorV2yn+k6aNAnNmjXT3G8iChxasyn2EgQXy6vw8958XKk0idoLmLf6EL7fmedS//bmFaPDtHS8/MNe62vFlyox+Ztd+OP4ecVt9pwqxsnz1bWgSs9iMzoxLHIwvxTbcy9Yv/5uxynM++WgagbNZiVt1Wn+rt3UBNkQWqVJ/rU0IFIbYrMMm2ldKFJtiK3665rPt+Qof09qK18kzEKvBrZVgbSS9qFDh3DTTTchIiICrVq1QmJiIhITE5GQkIDExETNHZg3bx7GjBmDUaNGoVOnTli0aBEiIyOxZMkSxfbvvvsuBg4ciIkTJ6Jjx4545ZVX0KNHD7z//vsAqv+DzZ8/H1OnTsW9996Lrl274osvvkBeXh5WrFgh2ddPP/2EX375BW+//bbDfpaXl6OkpETyQRQo0vfkY+fJIl93w2c0D7HZeW/c0u14/N9ZmLVyn/W1P45fwIKMw3j2q2yX+vLO6kMAgE83HgdQHRy9/MNefLX1JIYuyrRpv+XYOdz13gbc9OZaPPNVNi6WV1nfq6lBkh5JaYZQ6vzfcP+/NuFMaTkAYPyyHViw5gh+3lvgVN/F9Tvnyiqsn+s1zf9yhQknztdMCJIXba/afVplH9X/Vq+DpGWhSPE0f2k7cQ3SaY3rapF2IVcfkFvlw5W0NQdIo0aNgtFoxMqVK5GVlYXt27dj+/btyM7O1lygXVFRgaysLKSkpNR0yGhESkoKMjNtfykAQGZmpqQ9AKSmplrb5+TkID8/X9ImJiYGSUlJkn0WFBRgzJgx+Pe//43IyEiHfZ09ezZiYmKsH/Hx8ZrOlcgbrlSasOnIWclf2ul7TuOJL7Nw3782+rBnvqV5iM3ODX7dwTMAgKVbajLm50XBgSvEwcuPu06j12ur8U32KZt2JVcqIQgCFq0/an3th515+GzTcevXZidqkFbuysPhglLr13lFlyXvZx4961S/1TJF7oyKiC/9+2uP4NiZMtHxpDdLtUDOwpl1kMT/V8QZJEvQaPHJhhy7+6nNGkeF6bq/MTclYumYJJvX64bVVP1YascCqgZpx44dyMrKQocOHdw++NmzZ2EymRAbGyt5PTY2FgcOHFDcJj8/X7F9fn6+9X3La2ptBEHAyJEj8cQTT6BXr144fvy4w75OnjwZaWlp1q9LSkoYJJHfGb8sGz/vLcA/+idi6l2dAMB687yWyya0riLtTAJEvEsts3zEuxaE6pWixZu/t+awTaYEqB6GG7RgA+7sEofLlepLQFru9/ZqkMYtlWa65MNJB0XBk7Svojb5pXjp2z027QDXi5irZNP45cpVirLVOJNBEg/T2RvOuVLp2UxGk6gwFMqCMl+Zc38XvPjNbuvXY266TjVADDZWr9iu9m0LCzbiwRvjcfv1cXj44y0AgJcGdVJs2zgqDG/9rSvCQoLw26EzaBAZKgmavE3zkTt16oSzZ53768JfvffeeygtLcXkyZOd3iYsLAxhYfpG0UR6s/xF/emm49YA6XKFp9dTrn20PovN1VnQglAdyIgDLLUbzce/V9+gVu3OR5/r1BfrNVnrb2pec1RULH9bKRgQBOlCkQPf/U21r64WMVeZBbsZA6XA0R6jExmkClHQpdeU8ru7NcMPV+vRPnq0F8ZcfSagPQkN6zgMkDrERaGwtNyasfxt4q2IiQjBmYvlSJm33qb9S3d2xOyf9qv+cdSrVX30bdMIQ3o0x4C31gEAfp5wM1o1jLQGSJPv6IC4mHD8PulWHC4sxa3tm+Cxz/7A2quZ1N0zU1FYegVfbT2Jx/onYPuJIjzxZRYA4PX7uqB/m0Zo2bB6lOb7cf1Qx0HAM7RXdeLhnm6+rw3WHCC98cYbmDRpEl5//XV06dLFZh2k6Ohop/fVqFEjBAUFoaBAmiYtKChAXFyc4jZxcXF221v+LSgoQNOmTSVtLDPU1qxZg8zMTJuAp1evXnj44Yfx+eefO30ORP5IPER0rSaOxNdAzyJtJVr2L390hhEGp1b6dnaowRJEiPvkaCaQbUGybXuzLINk7xq5Os2/ymS2u98KzRkkg8PniEkCJJ3SrH9Paok3hnTBnxcuo1VDxyUcABAW4rjipX+bRqgwmfFF5gkAQHiIETGRIYiJDFFsf2uHxogMC1LN9P3r7z3QJCocAPDT+Jtw4VIF2sdFobzK9o+q+AaRiG9QfS4tG9ScU0RoEFo1rIMX76geVUpoVPNe9/h61uAIALq2qOfwHP2J5hqklJQUbN68GbfddhuaNGmC+vXro379+qhXrx7q16+vaV+hoaHo2bMnMjIyrK+ZzWZkZGQgOTlZcZvk5GRJewBYvXq1tX1iYiLi4uIkbUpKSrBlyxZrmwULFmDnzp3YsWMHduzYgVWrVgGonlH32muvaToHIn93rS7ZIr7Xaa9BctxGvEvx/h0FMuJ3xev1KO1LzNmgQzyDy9k+yTM+Su21/Bi5Gmc4GmLTmuExGB0PsYn3qbauklYGgwGRocFoFxuFEAfHt4hwcokH8ffV0UxFg8Fg9/jia9OxaTT6tm5kcwyln8cOTdUTId5Yf8tbNGeQ1q5dq2sH0tLSMGLECPTq1Qu9e/fG/PnzUVZWhlGjRgEAHn30UTRv3hyzZ88GAIwfPx4DBgzA3LlzMWjQICxbtgzbtm3D4sWLAVT/QEyYMAGvvvoq2rZti8TEREybNg3NmjWzLnLZsmVLSR/q1q0LAGjdujVatGih6/kR+YKkzuUazSGJZ7/oOYtNiXiIrMpsRpDRuZud+JEY8tfknA+QLNP8xa+Z7QaJ8oBGKcAxC4LT19GdITZ7m2rNIAU5Mc1fXIOk1xCb+Fo7s9wCAKfXwBL/rDkKRgywXx+nNvwoCf4Vvut/69kCf+ScR68E26FeoxPBfqDQHCANGDBA1w4MGzYMZ86cwfTp05Gfn4/u3bsjPT3dWmSdm5sLo+h/et++fbF06VJMnToVU6ZMQdu2bbFixQp07tzZ2mbSpEkoKyvD2LFjUVRUhP79+yM9PR3h4eG69p3IX0kftOm7fviSeMKTnrPYlEiGs0wCnK0rtQQ9zhR5i7M69rpnKTQW39jkj+yQk5+vUoBTXS/l3IV0Z4jN3rZq6x6pqa5BclCk7YEaJFfiAmczSNIAyX5bRzVYasGjowxSSJAR84Z1V9zW4GDbQKI5QPrtt9/svn/zzTdr7sS4ceMwbtw4xffWrVtn89rQoUMxdOhQ1f0ZDAbMmjULs2bNcur4CQkJAfdoASKyT5xB8syDW5X/ktey8q/aqtf22jqiNDzmqLhZPutMaRaall+Rrg6xmQX7w4Gah9gM6lkSiwrRtdFaBG7vuFqFO1GDJN+3o4DV0aNW1IYf3fnvEiQOkHRav91XNAdIt9xyi81r4m+SycQZM0T+5FqN/d1ZX05rDZL4D/EqDTdxtUUdlftU0yl7zS1BhPzhqpqG2BRrkLQEfq7/0NkbRnOlSNvhEJsnMkguRBhhrtQgOZFBsjvEpvKeK/0XH7NmPy7vxi9oLtK+cOGC5KOwsBDp6em48cYb8csvv3iij0Tkhms0PnJrBV5xMOBMdlnyIFMN6ZOaB8s6buvsfi1DbOLTd3QtzIIgOU+lDJJZcP6G51aAZCdI0R4gObEOkmjGll7P/XIlLnA0285C/LPizNCsvf06Ux+lNViSZLg0bel/NGeQYmJibF7761//itDQUKSlpSErK0uXjhGRPq7V4WN3nrgufUAq4OjeJb7GWqaK1zwSw4kaJCd3a7nJSwIes/0Ca0G20J/iLDYN19OdOMNeEKQ1w+PMNH/xsJqes9i0CnJytpt42MrRz43RaHAYIDo+njbioOuayyCpiY2NxcGDB/XaHRGRW+w+md0ByVR8lbu9+Je/JIPkIJJRejq9M4WtkrWt7BVpX80WifvksAbJLL1GSkNsZsH5mhJ3Mkj2gqAKjTVC1TVIGoq0dXrul0sZJCdnu2mZJWaA+jCap0gPF9gRkuYM0q5duyRfC4KA06dPY86cOdaFGInIf1yjCSRZgKRtW3Ew4szNXvLEeSeGs+Sfi28qaodzeojtajuTLINkdxuTWdpeqRMahtjc+ZnTqwbJaKgOPEODnX/UiF5F2q7sJcjZITYN0/ydmcXniNYsUFAtqkHSHCB1794dBoPBJt3ap08fLFmyRLeOERG5QxynaM4gaawpMmsIRiQZpKt91DrN3x5Lkbj4d7SjGqQqs2AzrChntvO8LT3pFyBVX9NQBwGCeFhNrwejujKs7eyCktIibcez2BzN4nNE69buFHj7G80BUk5OjuRro9GIxo0bc40hIj/FhSLdy2io1TKJh5vETRzVyShlkJy5pYiPYe8eZC3SlgV5drcxS9cfUrrBC3Bv6MxZ9oq0tdQgWQMkBxmkcp1mrom5Emc5+8BjcTNHmxgMvh1iC/RQSVPurbKyEo899hgqKirQqlUrtGrVCvHx8QyOiPyYdNHIaydY0pLVsbsfJ7YV79/hYz2UAiTxUikq3yNni84tQ2ySYT8HQ0dVJsEmoJLzRnAE6BcgWS5pmKMhNp0Ks6VcyCA5memR1qs5WklbhyJtjRkhyarwbh3Z9zRduZCQEJsaJCLyb+JfUtdQfCSZsu3OzV3rEJszBdEWls3E2QO1GWROr6RtKdKWBW32CqxNsmegWY4l/9nxRoBtL2Ap98AQmye4cpmcnsWmIV4xGpwPvPQ4XvUxlTOrgUjzT87f//53fPLJJ57oCxF5gGT2kw/74W3llTU3U60JJKeyT2qz2BzWINnuW7LQpEK9kFlw/vuoNMTmqAap0ixAkNRsWf6VDrvpVKJjl90aJE1DbFf/9fIQE+Da/zNna4W0rApvcLBQpFP70NheHOcFesZacw1SVVUVlixZgl9//RU9e/ZEnTp1JO/PmzdPt84RkfvEv6LMgoCggK8McOw/W07gpW/3WL/W+otaPJy1YM1hvDq4i00b8VWUFES7UIMkf5abXKXJLA1O7GaQbIfYqkz2a5BMsmegWTNI4uFZeKeeze46SC5kkHzBlbjA2VohLfGO0cGjRjyhNg2xaQ6Q9uzZgx49egAADh06JHmvNlWvE9VGAf4HnSKTWcDj/85Cu9i6mDSwAwBIgiNLGy3ECZcvN+fiqVvaoFm9CPX2kmyNoxok28/FvzuVtjeZBafXdbIEaFpqsKrMguI0f2lfvZRBsrsOkoYAyQeZIwtXhnSDg4wwGhxnOzVlkGD/YbXO7cSNGqQA/32jOUBau3atJ/pBRJ4iu8nVNplHz+HX/QX4dX+BNUCS03pjlwcUVyrtP2NSkq3RsA6SJfMkzswoZaCqZDVCdgMks21wU+VgJW35/pWWCqiuQbKzE53YK8TWNotNj954T7CxejjM7KCGTUsiwmB0fnac6j60thev6RXgOSTvV68RkVcF9q8oxyqceEC2O0NsaqQraUuHs+wxK2RqxIdT2t6miNreEJvJsk9xBsnBOkgms806SGabtZEEnxdpV1Q5f/xAHGJzJpjREu8Y4Pz6Sqr7cKNIW6eFyX1GcwaJiAKL1lWhayOt5y2f2m/5q13+es7ZMpw4VybLIDkIkMy2n4v3q7QSd5XJLJvFZi+DVL29uL3Daf6yAMzSD+lDe72TQbI3U03LEJsvSz5cyZwEB1mm5Ns/R61F2sFBmrviFnGQF+i/bxggEdVy8qna1yKtawHKM0iWX/ny4OfWt9cBAIb3jre+5rgGyTZgFW+ilEGpDmCU96HUVr7P6oUi7U/zl2eu5GsjHcgv9c5CkXYzSI6zhRa+HGJzLYNk9EgGye1HjWgcZAu0oU17OMRGVMspPRw1kJwpLcev+wrcW+xR6xCbTQZJ+XWL9QfPWD8X1xCZzAI+3ZiDHSeLFPti+VQaNCn3R1zbZG/oosokIGN/geS1LzefsLseTqVJwIhPt0peu1JpkmSqxnyxDcuz/lQ/sE725ZWovrf52Hmn9xOIQ2zOzGTTmhlzuwZJ4+aGWlSkzQCJ6Bpy4twljPp0K7bmSG808llSevj492O4673fUXSpwq393PHub/jHF9vw1dZcp7eRLw7obO3MkcJSvLJyH0qvVMm2r/5XLZDJK75i/VycQfp+5ym8/MM+DF64Ebv+LLLZzrI/R/3788JlnDx/2WY7JaeKLmP059skr207cQHHz11S3WbjkbM4dqZM8lrO2TKf3OBKy6scN3KCTzNILgyxRYYFOzUlX0vgJ8D9R424szWLtInIr4l/ST31n+1Ye/AMHvgw0/qa2Szg9nfWI2Xeeqceq+GsV3/cjz2nSrD4t2Nu7efsxeoA65d9BQ5a1ogIlRZeOHtagxZswCcbcmxer5n27rgOSDxUtWp3vvVzy3UQ7+PomYt4I/0Azlwst9uv99celnytFCBFhbteMbH7VLHNa6+t2o9jZ8sUWgcGpWn+kaFBmHXv9S7vc0RyK5vX/nl7O5vX5N+e3okNHO67Q1wUurSIsXm9X5uGkq+1xDuhQUYYDAak/bWmj2NuSsRzKe2QPuEmp/bRskGk8weUaVg3zOVt/QFrkIhqOfEv6z8v2GYRii9X4ujV7MG5sgo0jtL3l5pez7rSMoOqTmgQii9XWr929jlmagXCgkKtkFrQJZ4xVnyppg+WrJQ4CE37706n+iXOHlUfw/bgrRvXlQzluSs7V799AcDtnWIlQe7r93XBlG93W78ODTIqFmHf1bUpGtUNw2ebjms6nlKiJfX6ODyanIA2jeti3+kSvPrjfgDAS3d2RMem0fj7J1sAANumpuDvH2/BgfxSAMAvz92M4suVuDGhAYKDjNYg+qlbWuMfN12HjAOFqKgyY+/V4cHm9aVrZn0yohc+XH8M7689Yn2teb0IPH97O6T9dyf6t2mE8JAgjL+tLVZfvUZ9rmuA+3u0QOr1cej28i8AgNZN6qJri3qK5zv5jg6Y/dMB69ffj+tnfVDvs7e1xWP9E5F14gL6tm7oVKbqqzF9cKSwFH3bNHLYVm7pP5JQfLkSze2sHRYIGCAR1XLy1ZC9zd0aCAtn6ogEoboYuV5kqGTYy93p6SaF2WZq/RHPGBPXDZkUiqedVS4rTlbaR3iI/w4IzLr3egzv3RJtX/oJQHUAO7x3PMqrTHj5h30AgMcHXIcdJ4vw++Gz1u3G3nwdptzZEWazIAmQFj/SE2P/nYXm9SIw74Fu+PsnW2xm6omHopaOScKyrScxdVBHAEDfNo2qP1o3QtOYcNSvEwoAWPhQD7RqGIlGdcMwsm8CXvymOoBrUT8C7WKjAABTB3XExNT2MBoM1gDk26f6AQB2nCxCYckVtG5cV9KXqPAQ/DO1PR7sHY9GdcNQXmVGTEQIAKBVwzpo1bA6S9O5eQx+n3QrGtQJRZ2wmtvz/57si83HzuGBXvEIMhrw9dg+aBojDT4eH9Aap4uv4LNNxxEeYrQJpOqGBWNAu8bq3ySZ5NYNkdy6oeOGClwJqvwRAySia4ijOMETNQN6Tbd2Zk0VswAEGYCGdUM1b2tPTXAjLbAOCzbaZJ3E2R1xPVKlwgrXzpIfQ2nBxPAQL8/n1uCRPq0kPwdlFSYYDAb8pUMTa4AUEmTEQ71bWgOkMTclYsqd1QGNeLgsLNiI26+Pw+bJt6FJVBiMRsPVYEj9uvZtXR0MyXVqFi35elDXptbPxT+24plcBoNB9Vp3j6+n2gcAaFG/OhASb9+zVX1Jm3iFIa2erepL2iVdpxy4TBrYHvENInF7p1i7/SDnMEAiquV8PXNNr2JZZ4bJLM+akwdlzg6x2dtv9b/S15WGhMTrGImzGu5kkOQreSsNsYV7e8EbDdSCZHHgERwkXSjR0dPt42LCRW1t9+/uj500KHJzZ14SGRqM0f0Tfd2NWsN/c7JEpAtHAZL4Xa1rnjhDr+nWzgyTqc0KczdIVNuv0m5N4iE2UQBlXZ/IhQjpSqU8g2S7jzA/HmKz+OjRXogICcJ7w28AIA08go3S54ZpmX3lkSn94gxSgARIpC9mkIhqOUf3Y8mwkQeG2PTKIMnPo8pkxsVyx9Pxxa+7e2xnYptKs23WCKipR9Ijo6f0vDdvP7XdFX/tFIs9L6daMz7SAMl4dSXpq1+rrNukFKx4OD7yyB8O5P/8/38UEbnFUcZCsraPB56dpFsNkiywGLIoE91nrcafF2zXB5Kfh7MF3mqUapDU24qG2ESfW6b/6xEgmRQySJaCYX8nHg4TZ36qH7XhWgZJr4kAYuK+MYN0bQqM/1FE5DJHN2TJs8E8UK+k1/CHPNDbeXVK+6rdp2vayDJIva4Wtu4/XSIZ7lJi7xlgNTVIjq9PlWSIzTabpMclVnqciXxxzEAgzyBpqUES88QQm7RIm65Fgfc/iog00TLE5pkASZ/9qJ2H0qNULK9ZbriHCi5i0v922d3/5Qr153yZzcqZKSVVKrPYLJ+7WzAOKBdphwVIBklMkkGS1SDZezSKvf1YuJu5lARITCFdkwLvfxQRaeLrITalFY1d4cyjUATLekVXz0lcl/PN9lMAgMyj5/DBuqM2Q2qVdk5eaSVtNZLCbEmRtn41SEp99cQwk6dJMkjWp9lX03I+njh1yRCb/runAMAibaJazhdDbOLgQ68/vp3pm3woTOkmO/yjzQCAVg0jcWeXmnVv7AVgZlngZY8kayQeYjM5n4VyRKkbARkgSab5S4fYfD6LTYQJpGsTM0hEtZwvhtjEwYZ+0/wdt5GvV2TvJntC9vDWKoXCZ7X92iOpQRJtUHqlCmXlVW6v6q0mEIeBjJIaJOkQm1oNktKMMk+sgyTZVwBeW3IfAySiWs5RzYsnAiRxYBDkgVlsguRzcRvp+1qyKkqFzxYma22TxgySKF1UWl6Fbi//YrcY3B0BmECSBB5Gg2wWm4YaJE/EL57OSpH/Y4BEVMs5uqk78wBWrcRBgl73GXGgJ17B2qQQOFkOr2VtIHuz3JQeVqu6n6tBkSAINgs6VpkFnCurcLpPWgTiDV0c1AUZpTVIvh5iC8DLSTpjgERUy/lkiE0UGHhiiE0ceEj7L33N3tpA8kUx7WaQXKhBcqaoXE+BXoMUZIRsmr+b6yC5eTm4OCQxQCKq5RzdqD0xi008tKRbBkl0HhWiYSrxLD15rVDdMOfnodirQTJpCHosmSh7AZcnBGLGwyC6AxkN8mn+zt+ePDPEpv8+KbAwQCKqxZx6fpkHZrGJgwO9apLFfRM/zV5c0yN/ZlpUuIYAyU50KFj363g/liDK2wGSL4fYXM1eifscZJQ/rJZDbORbDJCIajFn7tGeLtLWb+mAms/FGSRxgCR/FltUeIhkHxfs1P84U6TtzLlYhv8crdytN72K4V06tosBknirIIMBIaIaJC1Bj9K5u381GCFd6xggEdVizgwJKdXwuH1clRohd5hVirSvVJps2ljOQ55BeuarbNX9OzPE5tyz2HyTQfJlxiNEhwyS0WhAkIaZa2LM9pAnMEAiqsWcW1yx5nO9CovFKz3rFnSp1CBJAyTLv8pDbBuOnFXdv/0hNun+7bEM/9kLuDzBl0NswS4+B07c5epZbI5Xr1Y6TU+cO2uQiAESUS2mZXHF6vb6LxSpXwap5vNKSQZJqQap+uto2RCbPfZnsTm/DpKlraWP3opbfHlD1zIlX0x8bYwGaQ2Slp8aT8zg4+KQxACJqBZz5sGoggeG2MQBjKNnwTlLMsQmziBV1WSQBFmtUF0HRdric9drJe1K2RBbeHCQ44104Mtp/q7XIEmLskNUVs92RHGWv7sPq3Vra6oN/CJAWrhwIRISEhAeHo6kpCRs3brVbvvly5ejQ4cOCA8PR5cuXbBq1SrJ+4IgYPr06WjatCkiIiKQkpKCw4cPW98/fvw4Ro8ejcTERERERKB169aYMWMGKio8s4AbkbtKrlTi3MVyTdsIguBkzYz4c+X2giBoCnSkGSSnN7NLrQZJfIpXKs2Yt/qQ9TEi9m7cb6YfROLkVXjqP1lX+6w+xGY5tjNDkJb9WIb+wkK882vWlxkPVzNIkoUiDQbJg4217FGvByJL96n7LinA+PxH4Ouvv0ZaWhpmzJiB7du3o1u3bkhNTUVhYaFi+02bNmH48OEYPXo0srOzMXjwYAwePBh79uyxtnnzzTexYMECLFq0CFu2bEGdOnWQmpqKK1euAAAOHDgAs9mMDz/8EHv37sU777yDRYsWYcqUKV45Z6rdBEHA7j+LUXqlUpf9mc0Cbpi1Gsmz10jqbQCg+FIlLleYFLd74sss69Pt7e5fFGF8ujEHt81dh//L+lPS5pmvsnHdlFVIePFH/LI33+E+xcNV81Yfwv7TJdav/7xwCSOWbMXM7/fi130FmLAsGxfLq3DuYjnOi2aZlV6plMw6K7pUicLS6v/D8hWqLe56bwMWZNT8MeRMbcqq3fl44f924ffD6vVJZeUmTP5mNzL2Fzjc3968Evx++Aymrdhj7bc3BGINkrjP7nTfI9P8mUO65jm/SIiHzJs3D2PGjMGoUaMAAIsWLcKPP/6IJUuW4MUXX7Rp/+6772LgwIGYOHEiAOCVV17B6tWr8f7772PRokUQBAHz58/H1KlTce+99wIAvvjiC8TGxmLFihV48MEHMXDgQAwcONC6z+uuuw4HDx7EBx98gLfffluxn+Xl5Sgvr/kLvqSkRLHdte7sxXI8+1U2EhvVwSv3dvbIX3b+bu3BQjz22TbEN4jA75P+4tQ2FVVmPPPVdiRf1xAj+yVK3vvzwmWYzAJMEHCmtBzxDSIBVGcoBry9FkWXKhEVHozSK1WS7X7eW4CL5VkOjy0OkH7ZVx0A/HP5ToQEGfDz3nxc3ywGK3edtrYZ++8szLr3ekz/bi8A4N+je+PCpUp8l30KL9zRAV9tzUWnptGSY9y7cCP+90Rf1K8Tgv5vrAUArD90Bp9tOg4AWLEjz9o2KbEBii9X4kB+qU1fe7+Wgd0zb8fCtUccnhdQnaH49qm+uO9fm+y2+3rbSbvvz1q5z6njAdUZrUc+qcmCh4cYJXVSnhJkBEYkt8LnmSfstnusXyKWbMzR9dgFJVdc2k5epC2mJfHYpnFdZJ24IN23Sz2q0bl5jJt7oEDn0wxSRUUFsrKykJKSYn3NaDQiJSUFmZmZittkZmZK2gNAamqqtX1OTg7y8/MlbWJiYpCUlKS6TwAoLi5GgwYNVN+fPXs2YmJirB/x8fFOneO1Zu2BQmw6eg7/2ZKL4+fKfN0dn7AEEyfPX1Z8/+T5S1i0/ihKRBmmH3bm4ee9BZj5g+2NeN/pYsX9nCktt2Yn5MGRxcYj51T7+dFvx9BvzhqcPH9J8f3xy3Zg1e58vPXzQZv3LMERUB0MPPtVNjIOFOL2d37DpxuPY+L/7ZK0r6gy4+73N2CTnf5YbMk5rxgcWXSZ+Qu25px3uB+gOrMQ5qUaIDVrnr/F48eIjQ7DnV2a4uV7O+Otv3W123ZUvwRsfek269dpf22Hr8b0kbRp26Su9fM7u8TZ7OObp/oic/JfrEGNvQfwfj+un+p74mHBllcDfzVP3tIaADDz7utt3ptyZ0c8lNQS//dEMl4Z3BnR4cGY+0A3u/tzpHFUGDIn/wW7Zt7u1n4ocPk0g3T27FmYTCbExsZKXo+NjcWBAwcUt8nPz1dsn5+fb33f8ppaG7kjR47gvffeU80eAcDkyZORlpZm/bqkpIRBkgJxbYi314EJFPf9ayPOXqzAofxSzBvWHQBQVqEc4ADAqaKav87F19TdKfmvrdoPAJjzk/L/NU8o9/LiiQaDtqfCy3VrEYOdfyoHqEpuatsIALD52Dn0bFUfHzzcE/XrhKJOaBDKZEOhf+0Ui9X7lIfsUq+Pxc97C5DSMRa/iob1Pht1I0xmAf/efALrDp4BAMx7oBvu7d7cGqz8rWcLnDx/CQvWHMFzKe2QcaAAu/4sxo0J9dGmSRRa1I+AwWDAor/3xL68Yjx5S2uEBBlxY0J9/HG8OguTPuFmXKk04UB+KTrERWHV7prfnSkdY9GjZf3qduNvQnmVGQfyS/HP5TsxqGtT/HnhMnaeLAIA/D7pVmvGU82O6X9FpUlAnauPhWkSFYbC0nL0alVf0m5SanuM6peAJlHhNvuIiQzB6/d1AQD0SmiAh3u31CV73TQmwu19UODy+RCbr506dQoDBw7E0KFDMWbMGNV2YWFhCAsL82LPApNJxxt4bXX2YnVdzcajNTUv9gpszZJrqn8AWmHnr3+L0GCjU+0cKa9UrpfyFPnUcWekXh+LAe2aoFt8DD5cf0xTgDSgXWP846brbF5fP+lWFF+uxNRv9yDzWHUW7bXBnXFr+yb4ac9pa/3TV2P6IDI0CJ2aRSO/+AqaRIch6/gFmAWgW3yMdWXw2zrGoqLKjGNnL6J9bJTk58dgMCDt9vYYfdN1iIkIweMDrkNe0WVc17iupE8DO8dhYOea7NCHj/TC9O/24IFe8QgyGlAnLBg9rwYpn426ESM//QP92jTEO8NqMjNtY6MAANc3i0bHplFoczXzlHvuEppEhyMmwvEyC/UiQyVf//7CrbhSYUZMpHRbg8GgGBwpuRaH9kl/Pg2QGjVqhKCgIBQUSP+KKigoQFycbVoXAOLi4uy2t/xbUFCApk2bStp0795dsl1eXh5uvfVW9O3bF4sXL3b3dAjqT1kn++w9JkJ8HcVBkb2FDbVwJs7SK9iVF5l7mtFg0DzDKjjIiIeSWgLQPn1d7QGrjeqGVX9E1fyRFRkWjIeSWmLzsZphx9BgA7rF1wMAa+alb5tGivsMDTaiQ1y04nsArMFJeEiQTXCkpEGdULz/UA/F925p3wTH5wxS3dZgMOD6ZjU1O5bAyRVhwUE+HxYlAnxcgxQaGoqePXsiIyPD+prZbEZGRgaSk5MVt0lOTpa0B4DVq1db2ycmJiIuLk7SpqSkBFu2bJHs89SpU7jlllvQs2dPfPrppzByTqcuxBkOxkfOs3cfFscm4rV69Fqp2Zm1kvQKkOzVqniC0aB9hpX4sRlaZ0c5CqjEb1s+Fwdwwfw9ROQ3fD7ElpaWhhEjRqBXr17o3bs35s+fj7KyMuustkcffRTNmzfH7NmzAQDjx4/HgAEDMHfuXAwaNAjLli3Dtm3brBkgg8GACRMm4NVXX0Xbtm2RmJiIadOmoVmzZhg8eDCAmuCoVatWePvtt3HmzBlrf9QyV+QcZpBcmx5s70Ysvo4ms3I2yR16LeToDG9nkAwuZJCOn6spWtc6UhPioN5JnCm0fM/FNVK+XOyRiKR8HiANGzYMZ86cwfTp05Gfn4/u3bsjPT3dWmSdm5srye707dsXS5cuxdSpUzFlyhS0bdsWK1asQOfOna1tJk2ahLKyMowdOxZFRUXo378/0tPTER5ePX69evVqHDlyBEeOHEGLFi0k/dHrUQvXKtYgucZeosKsEhTZW9hQC29+l7wx3V3MaNAedOScrZl9qXXbIAcZIIPCuj/ibdwpKCciffk8QAKAcePGYdy4cYrvrVu3zua1oUOHYujQoar7MxgMmDVrFmbNmqX4/siRIzFy5EhXukoOVJn0f0jptUDyDCpBkNxI1R4mq7ZYolbezPSVV3m/Bknr4yuKL9csv6B1dWpHGST5ytHybTjERuQ/+L+RdCXOcDAb5zzxEJs88yYt0jartnOVlm+TowDAEe9nkAwIcqPPWheIdhTgBCnUNwVJapCYQSLyFwyQSFfiAIkZJOeJpyXLa4s8XYOkhbuzi7xfg6Q96Hg0uZX1c3uzC5U4GpJTGmITz3zjEBuR/2CARLoSz6xiDZLzxPdVewGSZJq/lxddDAkyuH0D9/osNqP2dZCmDupk/dyZITZxAOawSFv0G9egmEHir2Qif8H/jaSrKsk0fwZIzpIMsZnkAVLN55Jp/l4OQIOM2meEyXl/HaTqDM3E1PZObxMaXPNr0ZkhRS2z0JRmK0qm+TODROQ3GCCRrjjE5tpTycWbVMpmp6mupK1Tkbazgo1GtzMcV7y+DlL1lX361jYubV+/TqjDNuIicLWFIuX9ERO/whokIv/BAIl0JZ3Fdo1GSCLOrjEkbmW/SFv/lbSdFazHEJsPapDc0biu48cLuZtBku6Lv5KJ/AX/N9ZShSVXsGxrLi5XePeGJFmnhwGS08Ng0un7sgySyjR/b9d4BRsNDjMkjvjiUSPuaBzlTIDk/JCcowQRM0hE/sMv1kEi/d3/wSb8eeEyDuSXYuY913vtuOJhH9YgVWd5Qp34O0Rtppr8PU88asRZ1UNsAVak7WaA5MzDUUM0FFk7eogqAyQi/8EMUi3154XLAIBf9xc4aKkv8c3dyyNAfsnZDJI4lpQvAGlWyRr5pEg74DJI7m3fqK7jGiTxNXF3iI2PGiHyHwyQSFeVrEGSkM9IExM/s81+Bqnmc1/WIIUEGQJuoUitK2HL1Q13nGSXTvN3tFCk/X25218i0g8DpFrO2zGKJIN0jQZI4vOWz0hTY78GyT9msQW5sKaQ3BWvP2rEve0jQhwvjKlnkTYR+Q8GSKSrSk7zd6mQWhxLOjuLzdtF2iFBRs3PNZPzdszsbkDi3EKRzhdpM0NEFDgYINVy3v59LM5wXKsZJHuF1GqF62rPWwOktVySTJOXh9iqa5AC6wbvjYxNSLDzNUhaH11CRL7DACnA5Zwtw4Rl2ThUUOrrrgCQFhhfqxkkcYAjL6QWXx8BytdKHlRJhuzEj3Lx9iy2IGPArdPjjXhESw2SYvzEoInILwXWbzuyMfLTrVixIw9DF2X6uisA5LPYrs0ISTLTTFZPpFZYbVIZRgPk6yDVbF/pi3WQAmyWlTcySOKskKNp+o6m+ROR/2CAFOBOnLsEACi+XKn4vjujXLv/LMav+2yXCbC3vpG3V9I+d7Ec2bkXbF53dw2mU0WXce5iuer7ZrOgWANkNgv4dX+h9esqs2Dty7EzF/H74bOK/RTsBkhqNUheXkk7IIfYvHAQ0TEcroPEbBFRwOBCkdcIyw341/2F+HFXHl67rwvqhFV/+/OKLqNBnVCEi2bsmM0C7n5/AwBg9XM3o0lUOGIiQ/DboTN4eul2zLm/KwZ1bQoA2Hb8PKZ9txcv33O95AZeUWXGlUqTZL9ixZcrsXpfAf7aKRYxESE4X1ZRfWxBQHR4CDL2F2B/fikm3NYWGQcKsWRDDob0bIHiy5V4rF8CDAYDbnpzLS5VmPDVmD7o2ao+Hv/3NkRHXO3nrW2Q0LAOPtmQg9n3d8GnG3OQe/4SQoON6NwsBk/e0hrbTlzADS3rITTIiCqzgA/XH8Xxc5fw0+7TiAoPQUqnJkhsVBcLMg6jTmgQPh3VG78fPoP31x5BlUlAZGgQzl4sR6+EBpj3QDcsXHtUco53vPs7gowGRIUHo+iSNIgtKClHz1d/xcKHemDWD/sk123zsXP4ZEMOggwGnBEFavN/PYxOTaPRukld7y8UGWQIuKfNezIgadOkLo4UXsTg7s2xNec8AMcPm2UCiShwGAQud+ySkpISxMTEoLi4GNHR0brt98vNJ3Ck8CLu79EcXVvUs76ec7YMTWPC8fx/d0KAgBvi6+O/207icOFFa5tfnrsZO04WYWjPFkicvAoA0KJ+BH6fdCse+WQrqsxmbD5W/Yt8eO94NIuJQJcWMRj56R9oUCcUX4/tgxnf78Wmo+dQLzLE5oa+ZGQvPPbZNuvXL97RAXN+OqDp/GIiQlB8uRKhQUZUmNzLgNzVtSlW7jrt1j7EDAbvz7IKJIO6NkVMRAiWbsn1dVfsGtqzBdrHRaFOWDCG925pfT3hxR8dbnt3t2Z4b/gNktf+vfkE5qzajzLZY3v2zxqIPy9UB9wD3lpnfS0iVH1pgLyiy+g7Zw16tqqP/z3ZFwAwb/UhLMg4DAA4PmeQU+dIRK5z9v7NDJKf+XlvPn4/fBZdmsdYA6StOefxwIeZaBIVhsLS6mzCqt35Ntve/s5vAGzXbim5XIUNR6RDO19tPSn5+nxZBf56dXsANsERAElwBEBzcATUDAW6GxwB0DU4AhgcORIbFY7OzaM1BUjDe7fEV1v1D6huad8YeUWXcajgouT1T0b0wq3tmyjW+qRPuAkPLMpEyZUq9G3dEHlFl3H83CW8Mrgz/p7UEocLL+K6RnVstnukTys81LslPt90HLNWVmf6urWIQURoENrGRqGiyoywYCMiQoMQFmw/w9asXgR2z7wdkaE1v3qH3RiPBRmHkXp9rCuXgog8hAGSn7HMghHXt3yb/ScAWIMjR3afKta/Yy6yDEMEig5xUTiQ7/kZgY/0aYV/bz6B0CAjRt+UiA/WVQ/N9W/TCPENIlWDikf6tEKdsGAsWl/d/qa2jfD74bPo3DwakaHBOFp4ET8+exN+2JmH11btBwA0rxeBH5/tD4PBgOjwYFSaBEz/bg+W/XESDeuEIshowOeP9cb4ZdnWgGP8bW3x6/4ChAUbsT23CAAQHRGM2zrGok2TukhoWAcfj+iFjP0FmP7dXrx2X2cAwLil2bhYXgUACA8xYlS/BMm5NI0Jx+niK0jpGItHk1vhkw05aNUwEs+ltEOlyYyf9uSjSVQYtuScx0uDOqL4ciVGf/YHerZqgPt7NMfp4iu4qW0j67Dtx78fw6s/Vp/nymf6o3PzGNVr3iEuGrtmpuJU0WU0rhuG0GAjLpRVoH6d6seJtIuNUt02yGjAiL4JaBoTjlNFl3F/jxbW90KDjdg543YYDM4VYUeFh0i+bl4vAgdeGegwuCIi72KA5Gcs66hI17hxr3DB5MPUSOO6YQEVIEXLbl6umJjaHiuyT0mGPy2v/6VDE7RpUhchQUbc1bUpWjWsgyCjwRogxUaHI6FhpHWbfm0aYuORcwCA5//aDs/c1hY/ijJniY3qYOHDPRAZEgSDwYDyKhMiQ4Mx5ubr0KVFDNo0qYuo8GCEBddkFUODDXhlcGc8PqA1EhvVgSAIMBgMeP+hHvh+Rx6evKU16oQF47m/tgMALFx7BCt3ncajyQmIiQjBr2kDrPu6rWMsbutYk/nY83IqLpZXIchgQFiwEUZj9b/lVWbsmnk7osKCJYsl3tyuseQajeibAAC4o0t1fVujumH4blx/6/vyAGh0/0QM7ByH5vUinF6EsXm9COvnluDIGUFGg7Vfcmp1ds5yd3si0h8DJD9jWYlXz1WSvf3MLrHwkMD6qzhMY39vbd8Yaw+ekbwWEmSA0nevZYNIdGxaM96ddF1DAMCFq8XpQPXaSOK1hsJFgU3DumEAbB9tIQ7qxEM3fa7uX0lIkBGJV4eTLIFFu9go/DO1vU3bp29tg6dvbaO6L7m6YdJfK1um3IZKk6BL8ClnMBjQon6k44ZERBoxQPIzQVdnCcmf6O4Ob892Egu0hQW1/iUfqjAsojbTS+0xFOKARxCka+mI+2O5lFoWJvQH9SKdz9IQEfkL///teo2xLMTnzho38omJ3n5ml5i7T3/3NmceTmpRvS6QQoAUZFAcFA1SCZzEAZXJLEgeVyHOaFkyPeJjuvvwWCIiUsYAyc9YbnhHCi9a11Zxl/zp8N6kFhT4Ky1DgsFByitLq2WQ1NbIEb9uEgRJUCnOIFnW9JFkkBggERF5RGDdva4BluzAf7f9iQc+zMSRQvdnVPkyg+To0Qv+RssQW7BR+dlkauccoppBEg+xCZKgUlyDpDTEFmgBKBFRoOBvVz8jH5Laf7oUUCz5dY4g6FvPpJU8WPD3ISEtAVKQ0aAYDKllitTOXTz7ymyGLINU81/UmkESvR9oj/4gIgoUDJD8jPwmqkdo49MMkuwGHu7na71o6V9IkEFxarlaIORMPZZJkNYgiQM2aw2SKGsUaBk6IqJA4d93q2uQ8qwk12+CBoN8TSXvktfj+Pt6L2EaM0hK1GaWOTOjTxAEyTWTZpBsjxtoswSJiAIFf7v6GflN1938wJ8XLuOK7BlS3iQ/H38PkLTWICmtTagWODmT7THLpvmLF3gMunowcQDGDBIRkWcwQPIz8llJegyOffT7MR324hr5sJLWhRi9TessNiXOrHekxmQWJO3CFab5SzNIDJCIiDzBv+9W1yDlWUnuhUl/HL/g1vbukJ+PeFaWP9LSP7VMkTPrHakx2wyxiaf5V/8rDsCYQSIi8gwGSH7GExkBX66DJM+m+PujRyJCtS0UqfTdCjEaFIfenBtiky0UGaw0i008xObf15OIKFDxt6ufkQcUlVVmuP2wWh/OYgu8GiTn/0sYVR6OqlqD5ETwK5/mLy4at3wXgznERkTkcQyQ/Ix8eObY2YvQOsQmTxhV+fRRI4E1i02PIUC1mWXODrFJpvmL+mMJdKULRTJAIiLyBD6s1s/IM0gL1x7VvI8qH07rl7PNIPl3TK5lmj8ATUNpTmWQBEESVIqvl+UZe+JAS3mQj4iI3OXfd6trkB4ZAV/WHMnJg4Uwfy/S1iGAU53d5lQGCaoLRVoSgRxWIyLyPAZIfsaZm6gj5ZX+GyA5s5q0L+kxBKg2lBbk5DR/SQ2SqEjbfDWDxGE1IiLPY4DkZ/S4+ZX7UwZJVo/j7w9X1RqgKg1xqWV4nJnFJn9YrXi4zRIgqa3UTURE+uFvWj+jx/AJM0iu0+P6qwVCzgQ28pW0xf2xBEhMIBEReZ5fBEgLFy5EQkICwsPDkZSUhK1bt9ptv3z5cnTo0AHh4eHo0qULVq1aJXlfEARMnz4dTZs2RUREBFJSUnD48GFJm/Pnz+Phhx9GdHQ06tWrh9GjR+PixYu6n5tWeqxrU+HXGST/vrvrsfCi2jk6s2v5StrifV2NjxQfkEtERPryeYD09ddfIy0tDTNmzMD27dvRrVs3pKamorCwULH9pk2bMHz4cIwePRrZ2dkYPHgwBg8ejD179ljbvPnmm1iwYAEWLVqELVu2oE6dOkhNTcWVK1esbR5++GHs3bsXq1evxsqVK/Hbb79h7NixHj9fR/TJIPnu2Wtythkkn//I2aX14a9KsYpaAONMYGMWBMn6SuIhP1+uZ0VEdK3x+d1q3rx5GDNmDEaNGoVOnTph0aJFiIyMxJIlSxTbv/vuuxg4cCAmTpyIjh074pVXXkGPHj3w/vvvA6jOHs2fPx9Tp07Fvffei65du+KLL75AXl4eVqxYAQDYv38/0tPT8fHHHyMpKQn9+/fHe++9h2XLliEvL89bp65IjyGo0itVOvREH/KAz98fjaFH99zZhWUYzUIcLAmMj4iIvManAVJFRQWysrKQkpJifc1oNCIlJQWZmZmK22RmZkraA0Bqaqq1fU5ODvLz8yVtYmJikJSUZG2TmZmJevXqoVevXtY2KSkpMBqN2LJli+Jxy8vLUVJSIvnwBD2KmPed9kzfXCEPiEKDfR6T26Vl+Cos2CiZZVazDyAi1LUlxsKCgxSzUpb9yvl5Qo6IKGD59Nfr2bNnYTKZEBsbK3k9NjYW+fn5itvk5+fbbW/511GbJk2aSN4PDg5GgwYNVI87e/ZsxMTEWD/i4+OdPEtturWIQevGdSSvhdq5C4YFG9GjZT10aR4jeU3eRs4SqHiiaHrhQz3QqmEkFv29J3q0qo+EhpEAgE5NozGybwLaxdZV3TY6XBpYuJPRcTYYqx8ZAgAYc1MiosODkXp9LPpc1wAd4qIAAB2bRiMpsQEAILFRHaR0bIKYiBCMvbk1nhjQGm2a1MWkge0x8Po43Nq+MeKiw/H237oioWEk3hzSFTe0rIeHk1ra7cP8Yd2R0DASbw/thsZ1w3Bbhya4vVMsoiOCMeamRHRuHo27uzWzth+R3Ard4uvhLx1i7eyViIhcxZW0nTR58mSkpaVZvy4pKfFIkFQvMhQZz9+i+369bVDXptbP1028VfLeL88N8HZ3NPnwkV6OG4n8mmZ7Pm1jo6zn/cCNjn9OBt/QHINvaG79+pORN1o/f2lQJ5v2L9/bWVMfiYhIG59mkBo1aoSgoCAUFBRIXi8oKEBcXJziNnFxcXbbW/511EZeBF5VVYXz58+rHjcsLAzR0dGSDyIiIqqdfBoghYaGomfPnsjIyLC+ZjabkZGRgeTkZMVtkpOTJe0BYPXq1db2iYmJiIuLk7QpKSnBli1brG2Sk5NRVFSErKwsa5s1a9bAbDYjKSlJt/MjIiKiwOTzIba0tDSMGDECvXr1Qu/evTF//nyUlZVh1KhRAIBHH30UzZs3x+zZswEA48ePx4ABAzB37lwMGjQIy5Ytw7Zt27B48WIA1UW2EyZMwKuvvoq2bdsiMTER06ZNQ7NmzTB48GAAQMeOHTFw4ECMGTMGixYtQmVlJcaNG4cHH3wQzZo1U+wnERERXTt8HiANGzYMZ86cwfTp05Gfn4/u3bsjPT3dWmSdm5sLo2hmV9++fbF06VJMnToVU6ZMQdu2bbFixQp07lxTkzFp0iSUlZVh7NixKCoqQv/+/ZGeno7w8HBrm//85z8YN24cbrvtNhiNRgwZMgQLFizw3okTERGR3zIIAldXcUVJSQliYmJQXFzMeiQiIqIA4ez9m6uoEBEREckwQCIiIiKSYYBEREREJMMAiYiIiEiGARIRERGRDAMkIiIiIhkGSEREREQyDJCIiIiIZBggEREREcn4/FEjgcqyAHlJSYmPe0JERETOsty3HT1IhAGSi0pLSwEA8fHxPu4JERERaVVaWoqYmBjV9/ksNheZzWbk5eUhKioKBoNBt/2WlJQgPj4eJ0+e5DPePIjX2Xt4rb2D19k7eJ29x1PXWhAElJaWolmzZjAa1SuNmEFykdFoRIsWLTy2/+joaP7n8wJeZ+/htfYOXmfv4HX2Hk9ca3uZIwsWaRMRERHJMEAiIiIikmGA5GfCwsIwY8YMhIWF+bortRqvs/fwWnsHr7N38Dp7j6+vNYu0iYiIiGSYQSIiIiKSYYBEREREJMMAiYiIiEiGARIRERGRDAMkP7Jw4UIkJCQgPDwcSUlJ2Lp1q6+75Ndmz56NG2+8EVFRUWjSpAkGDx6MgwcPStpcuXIFTz/9NBo2bIi6detiyJAhKCgokLTJzc3FoEGDEBkZiSZNmmDixImoqqqStFm3bh169OiBsLAwtGnTBp999pmnT89vzZkzBwaDARMmTLC+xuusj1OnTuHvf/87GjZsiIiICHTp0gXbtm2zvi8IAqZPn46mTZsiIiICKSkpOHz4sGQf58+fx8MPP4zo6GjUq1cPo0ePxsWLFyVtdu3ahZtuugnh4eGIj4/Hm2++6ZXz8xcmkwnTpk1DYmIiIiIi0Lp1a7zyyiuSZ3PxWmv322+/4e6770azZs1gMBiwYsUKyfvevKbLly9Hhw4dEB4eji5dumDVqlXaT0ggv7Bs2TIhNDRUWLJkibB3715hzJgxQr169YSCggJfd81vpaamCp9++qmwZ88eYceOHcKdd94ptGzZUrh48aK1zRNPPCHEx8cLGRkZwrZt24Q+ffoIffv2tb5fVVUldO7cWUhJSRGys7OFVatWCY0aNRImT55sbXPs2DEhMjJSSEtLE/bt2ye89957QlBQkJCenu7V8/UHW7duFRISEoSuXbsK48ePt77O6+y+8+fPC61atRJGjhwpbNmyRTh27Jjw888/C0eOHLG2mTNnjhATEyOsWLFC2Llzp3DPPfcIiYmJwuXLl61tBg4cKHTr1k3YvHmz8Pvvvwtt2rQRhg8fbn2/uLhYiI2NFR5++GFhz549wldffSVEREQIH374oVfP15dee+01oWHDhsLKlSuFnJwcYfny5ULdunWFd99919qG11q7VatWCS+99JLwzTffCACEb7/9VvK+t67pxo0bhaCgIOHNN98U9u3bJ0ydOlUICQkRdu/erel8GCD5id69ewtPP/209WuTySQ0a9ZMmD17tg97FVgKCwsFAML69esFQRCEoqIiISQkRFi+fLm1zf79+wUAQmZmpiAI1f+hjUajkJ+fb23zwQcfCNHR0UJ5ebkgCIIwadIk4frrr5cca9iwYUJqaqqnT8mvlJaWCm3bthVWr14tDBgwwBog8Trr44UXXhD69++v+r7ZbBbi4uKEt956y/paUVGREBYWJnz11VeCIAjCvn37BADCH3/8YW3z008/CQaDQTh16pQgCILwr3/9S6hfv771uluO3b59e71PyW8NGjRIeOyxxySv3X///cLDDz8sCAKvtR7kAZI3r+kDDzwgDBo0SNKfpKQk4fHHH9d0Dhxi8wMVFRXIyspCSkqK9TWj0YiUlBRkZmb6sGeBpbi4GADQoEEDAEBWVhYqKysl17VDhw5o2bKl9bpmZmaiS5cuiI2NtbZJTU1FSUkJ9u7da20j3oelzbX2vXn66acxaNAgm2vB66yP77//Hr169cLQoUPRpEkT3HDDDfjoo4+s7+fk5CA/P19yjWJiYpCUlCS5zvXq1UOvXr2sbVJSUmA0GrFlyxZrm5tvvhmhoaHWNqmpqTh48CAuXLjg6dP0C3379kVGRgYOHToEANi5cyc2bNiAO+64AwCvtSd485rq9buEAZIfOHv2LEwmk+TmAQCxsbHIz8/3Ua8Ci9lsxoQJE9CvXz907twZAJCfn4/Q0FDUq1dP0lZ8XfPz8xWvu+U9e21KSkpw+fJlT5yO31m2bBm2b9+O2bNn27zH66yPY8eO4YMPPkDbtm3x888/48knn8Szzz6Lzz//HEDNdbL3eyI/Px9NmjSRvB8cHIwGDRpo+l7Udi+++CIefPBBdOjQASEhIbjhhhswYcIEPPzwwwB4rT3Bm9dUrY3Wax6sqTWRn3r66aexZ88ebNiwwdddqXVOnjyJ8ePHY/Xq1QgPD/d1d2ots9mMXr164fXXXwcA3HDDDdizZw8WLVqEESNG+Lh3tct///tf/Oc//8HSpUtx/fXXY8eOHZgwYQKaNWvGa01WzCD5gUaNGiEoKMhm1k9BQQHi4uJ81KvAMW7cOKxcuRJr165FixYtrK/HxcWhoqICRUVFkvbi6xoXF6d43S3v2WsTHR2NiIgIvU/H72RlZaGwsBA9evRAcHAwgoODsX79eixYsADBwcGIjY3lddZB06ZN0alTJ8lrHTt2RG5uLoCa62Tv90RcXBwKCwsl71dVVeH8+fOavhe13cSJE61ZpC5duuCRRx7Bc889Z82Q8lrrz5vXVK2N1mvOAMkPhIaGomfPnsjIyLC+ZjabkZGRgeTkZB/2zL8JgoBx48bh22+/xZo1a5CYmCh5v2fPnggJCZFc14MHDyI3N9d6XZOTk7F7927Jf8rVq1cjOjraerNKTk6W7MPS5lr53tx2223YvXs3duzYYf3o1asXHn74YevnvM7u69evn80yFYcOHUKrVq0AAImJiYiLi5Nco5KSEmzZskVynYuKipCVlWVts2bNGpjNZiQlJVnb/Pbbb6isrLS2Wb16Ndq3b4/69et77Pz8yaVLl2A0Sm9/QUFBMJvNAHitPcGb11S33yWaSrrJY5YtWyaEhYUJn332mbBv3z5h7NixQr169SSzfkjqySefFGJiYoR169YJp0+ftn5cunTJ2uaJJ54QWrZsKaxZs0bYtm2bkJycLCQnJ1vft0w/v/3224UdO3YI6enpQuPGjRWnn0+cOFHYv3+/sHDhwmtq+rkS8Sw2QeB11sPWrVuF4OBg4bXXXhMOHz4s/Oc//xEiIyOFL7/80tpmzpw5Qr169YTvvvtO2LVrl3DvvfcqTpO+4YYbhC1btggbNmwQ2rZtK5kmXVRUJMTGxgqPPPKIsGfPHmHZsmVCZGRkrZ16rmTEiBFC8+bNrdP8v/nmG6FRo0bCpEmTrG14rbUrLS0VsrOzhezsbAGAMG/ePCE7O1s4ceKEIAjeu6YbN24UgoODhbffflvYv3+/MGPGDE7zD3Tvvfee0LJlSyE0NFTo3bu3sHnzZl93ya8BUPz49NNPrW0uX74sPPXUU0L9+vWFyMhI4b777hNOnz4t2c/x48eFO+64Q4iIiBAaNWokPP/880JlZaWkzdq1a4Xu3bsLoaGhwnXXXSc5xrVIHiDxOuvjhx9+EDp37iyEhYUJHTp0EBYvXix532w2C9OmTRNiY2OFsLAw4bbbbhMOHjwoaXPu3Dlh+PDhQt26dYXo6Ghh1KhRQmlpqaTNzp07hf79+wthYWFC8+bNhTlz5nj83PxJSUmJMH78eKFly5ZCeHi4cN111wkvvfSSZOo4r7V2a9euVfydPGLECEEQvHtN//vf/wrt2rUTQkNDheuvv1748ccfNZ+PQRBES4cSEREREWuQiIiIiOQYIBERERHJMEAiIiIikmGARERERCTDAImIiIhIhgESERERkQwDJCIiIiIZBkhEREREMgyQiMjv3HLLLZgwYYKvu+GSmTNnonv37r7uBhG5iStpE5HfOX/+PEJCQhAVFeXV486cORMrVqzAjh07XN7HxYsXUV5ejoYNG+rXMSLyumBfd4CISK5Bgwa+7oLL6tati7p16/q6G0TkJg6xEZHfkQ+xJSQk4PXXX8djjz2GqKgotGzZEosXL7a+f/z4cRgMBixbtgx9+/ZFeHg4OnfujPXr11vbfPbZZ6hXr57kOCtWrIDBYLC+//LLL2Pnzp0wGAwwGAz47LPPFPu3bt069O7dG3Xq1EG9evXQr18/nDhxAoDtEJtlX+KPhIQE6/t79uzBHXfcgbp16yI2NhaPPPIIzp4969qFIyLdMEAiooAwd+5c9OrVC9nZ2Xjqqafw5JNP4uDBg5I2EydOxPPPP4/s7GwkJyfj7rvvxrlz55za/7Bhw/D888/j+uuvx+nTp3H69GkMGzbMpl1VVRUGDx6MAQMGYNeuXcjMzMTYsWOtgZacZV+nT5/GkSNH0KZNG9x8880AgKKiIvzlL3/BDTfcgG3btiE9PR0FBQV44IEHNF4dItIbh9iIKCDceeedeOqppwAAL7zwAt555x2sXbsW7du3t7YZN24chgwZAgD44IMPkJ6ejk8++QSTJk1yuP+IiAjUrVsXwcHBiIuLU21XUlKC4uJi3HXXXWjdujUAoGPHjqrtLfsSBAFDhgxBTEwMPvzwQwDA+++/jxtuuAGvv/66tf2SJUsQHx+PQ4cOoV27dg77TUSewQCJiAJC165drZ8bDAbExcWhsLBQ0iY5Odn6eXBwMHr16oX9+/fr2o8GDRpg5MiRSE1NxV//+lekpKTggQceQNOmTe1uN2XKFGRmZmLbtm2IiIgAAOzcuRNr165VrFk6evQoAyQiH+IQGxEFhJCQEMnXBoMBZrPZ6e2NRiPkk3YrKytd6sunn36KzMxM9O3bF19//TXatWuHzZs3q7b/8ssv8c477+Dbb79F8+bNra9fvHgRd999N3bs2CH5OHz4sHUYjoh8gwESEdUa4iClqqoKWVlZ1uGvxo0bo7S0FGVlZdY28un8oaGhMJlMTh3rhhtuwOTJk7Fp0yZ07twZS5cuVWyXmZmJf/zjH/jwww/Rp08fyXs9evTA3r17kZCQgDZt2kg+6tSp41Q/iMgzGCARUa2xcOFCfPvttzhw4ACefvppXLhwAY899hgAICkpCZGRkZgyZQqOHj2KpUuX2sxSS0hIQE5ODnbs2IGzZ8+ivLzc5hg5OTmYPHkyMjMzceLECfzyyy84fPiwYh1Sfn4+7rvvPjz44INITU1Ffn4+8vPzcebMGQDA008/jfPnz2P48OH4448/cPToUfz8888YNWqU04EaEXkGAyQiqjXmzJmDOXPmoFu3btiwYQO+//57NGrUCEB17dCXX36JVatWoUuXLvjqq68wc+ZMyfZDhgzBwIEDceutt6Jx48b46quvbI4RGRmJAwcOYMiQIWjXrh3Gjh2Lp59+Go8//rhN2wMHDqCgoACff/45mjZtav248cYbAQDNmjXDxo0bYTKZcPvtt6NLly6YMGEC6tWrB6ORv56JfIkraRNRwDt+/DgSExORnZ3Nx3wQkS74JwoRERGRDAMkIiIiIhkOsRERERHJMINEREREJMMAiYiIiEiGARIRERGRDAMkIiIiIhkGSEREREQyDJCIiIiIZBggEREREckwQCIiIiKS+X+hT7B62ZNaTAAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# input_arr = [i for i in range(1, 100, 1)]\n",
        "input_arr = [i for i in range(10, 10_000, 10)]\n",
        "\n",
        "fun2 = automatic_time(input_arr, good_fibonacci)\n",
        "plt.plot(input_arr, fun2, label=\"Good Fibonacci\")\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sFyCSdaBg25U",
        "outputId": "08f0deb7-b9a1-4b31-cd58-a51027ffcead"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "6000\n"
          ]
        }
      ],
      "source": [
        "import sys\n",
        "print(sys.getrecursionlimit())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g4SghLsng25U"
      },
      "outputs": [],
      "source": [
        "#https://stackoverflow.com/questions/3323001/what-is-the-maximum-recursion-depth-in-python-and-how-to-increase-it\n",
        "sys.setrecursionlimit(100_000)\n",
        "print(sys.getrecursionlimit())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uhJwnE4vg25U"
      },
      "outputs": [],
      "source": [
        "good_fibonacci(5_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yzYj9ZQyg25U"
      },
      "outputs": [],
      "source": [
        "## Fibonacci Solutions\n",
        "\n",
        "1. timing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 97,
      "metadata": {
        "id": "c4U9lWZ0g25U"
      },
      "outputs": [],
      "source": [
        "def fibonacci_loop(n):\n",
        "    a, b = 1, 1\n",
        "    cnt = 3\n",
        "    while cnt <= n:\n",
        "        a, b = a+b, a  # Python lets us swap values using tuple unpacking\n",
        "        # in other languages we would need a temporary variable\n",
        "        cnt += 1\n",
        "    return a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3McdZRZYg25U",
        "outputId": "ea23e16c-d5f4-4c50-cb2c-14968ed05e42"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 102,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "fibonacci_loop(2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8Rru9ra7g25U",
        "outputId": "01c5eb20-c1c5-403b-8020-1647444f193b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(55, (55, 34), 55)"
            ]
          },
          "execution_count": 104,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "fibonacci_loop(10), good_fibonacci(10), bad_fibonacci(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "id": "_h4uFiqvg25U",
        "outputId": "4f725a0c-24f6-4088-a1af-7b221269fee1"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(100, 2_000, 10)]\n",
        "\n",
        "fun2 = automatic_time(input_arr, fibonacci_loop)\n",
        "plt.plot(input_arr, fun2, color='red')\n",
        "fun1 = automatic_time(input_arr, good_fibonacci)\n",
        "plt.plot(input_arr, fun1, color='green')\n",
        "# add legend\n",
        "plt.legend([\"loop\",\"recursive\"])\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "1lUG_C96vJMk",
        "outputId": "4695a4fb-a67a-4eee-c52d-cbc9bdfb32a0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [i for i in range(1000, 50_000, 1000)]\n",
        "\n",
        "fun2 = automatic_time(input_arr, fibonacci_loop)\n",
        "plt.plot(input_arr, fun2, label=\"Loop Fibonacci\")\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 109,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j3OqqMGOvypo",
        "outputId": "65b2f3b9-6de5-43d1-ecda-216831a9bc1b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              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            ]
          },
          "execution_count": 109,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "fibonacci_loop(50_000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 110,
      "metadata": {
        "id": "_KPpgIaeg25V"
      },
      "outputs": [],
      "source": [
        "# 2. It is not tail recursive becuase there is something to do after returning the values (adding them together). We can use 2 accumulators to avoid this."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L6kIaQTOg25V"
      },
      "source": [
        "# Example: Binary Search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CD5xx9X8g25V"
      },
      "source": [
        "Binary search is a classic recursive algorithm to find a target value within a sorted sequence. This is among the most important of computer algorithms, and it is the reason that we so often store data in sorted order.\n",
        "\n",
        "e.g. For the sorted sequence below stored in a Python list with indexes above:\n",
        "\n",
        "<table>\n",
        "<tr><th>0</th><th>1</th><th> 2</th><th>3</th><th>4</th><th> 5</th><th>6</th><th>7</th><th> 8</th><th>9</th><th>10</th><th> 11</th> </tr>\n",
        "<tr><td>2</td><td>4</td><td> 5</td><td>6</td><td>8</td><td> 9</td><td>15</td><td>16</td><td> 17</td><td>22</td><td>30</td><td> 31</td> </tr>\n",
        "</table>\n",
        "\n",
        "If the sequence was unsorted a simple solution is a _sequential search algorithm_: use a loop to examine every element. You either reach the end of the list or find the target.\n",
        "\n",
        "It is linear complexity, running in $\\mathcal{O}(n)$ time as worst case it inspects every element in the sequence.\n",
        "\n",
        "A sorted sequence allows a much faster approach. Think about how you would accomplish this task by hand: divide in two, and choose the middle digit as a candidate to compare to the target. Everything to the left of the candidate is lower than it and everything to the right is higher. Compare the target to the candidate and discard the left if the candidate is lower and the right if it is higher. Then repeat your _binary search_ algorithm. This is much more efficient, running in $\\mathcal{O}($log$n$) time.\n",
        "\n",
        "Review the iterative and recursive binary search algorithm implementations below."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 111,
      "metadata": {
        "id": "E1c5567Dg25V"
      },
      "outputs": [],
      "source": [
        "def binary_search_iterative(data, target):\n",
        "    \"\"\"Return True if target is found in the given Python list.\"\"\"\n",
        "    low = 0\n",
        "    high = len(data)-1\n",
        "    while low <= high: # so while array/list pointers do not meet we keep going\n",
        "        mid = (low + high) // 2 # // meaning even half\n",
        "        if target == data[mid]:         # found a match\n",
        "            return True\n",
        "        elif target < data[mid]:\n",
        "            high = mid - 1                # only consider values left of mid\n",
        "        else:\n",
        "            low = mid + 1                 # only consider values right of mid\n",
        "    return False                      # loop ended without success"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 112,
      "metadata": {
        "id": "31KWLGx8g25V"
      },
      "outputs": [],
      "source": [
        "def binary_search(data, target, low, high):\n",
        "    \"\"\"Return True if target is found in indicated portion of a Python list.\n",
        "\n",
        "      The search only considers the portion from data[low] to data[high] inclusive.\n",
        "      \"\"\"\n",
        "    if low > high:\n",
        "        return False                    # interval is empty; no match\n",
        "    else:\n",
        "        mid = (low + high) // 2\n",
        "    if target == data[mid]:         # found a match\n",
        "        return True\n",
        "    elif target < data[mid]:\n",
        "        # recur on the portion left of the middle\n",
        "        return binary_search(data, target, low, mid - 1)\n",
        "    else: # target > data[mid]\n",
        "        # recur on the portion right of the middle\n",
        "        return binary_search(data, target, mid + 1, high)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "znA9NT_mg25V"
      },
      "source": [
        "When a function makes two recursive calls, we say that it uses binary recursion. Clearly the binary_search above is a binary recursion. Drawing the English ruler and the bad fibonacci function are also examples of binary recursion."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 114,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ymGLof_zg25V",
        "outputId": "e68f1888-788c-4c0c-e334-03c69ee88dbf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 114,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data=[2,4,5,6,8,9,15,16,17,22,30,31,100, 9000, 9001,10_000]\n",
        "iter_ans = binary_search_iterative(data,100)\n",
        "iter_ans"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 115,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "da4PXWQ_g25V",
        "outputId": "bc2ad345-c5eb-4160-94bb-61cdb178ef92"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 115,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "binary_search_iterative(data,15)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ABz_pn-Yg25W"
      },
      "outputs": [],
      "source": [
        "binary_search_iterative(data,7)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 116,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zl_2B34wg25W",
        "outputId": "e6542dc4-aad1-4268-ef39-90ba868166a7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10 loops, best of 5: 38.1 ms per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search_iterative(list(range(1_000_000)), 9000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 117,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DsRLIZkZg25W",
        "outputId": "54a83d58-982a-45b5-d7e2-f7f6a03e0b66"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[999995, 999996, 999997, 999998, 999999]"
            ]
          },
          "execution_count": 117,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# better would be to make the list before timing so as not to distort timing for the algorithm itself\n",
        "million = list(range(1_000_000))\n",
        "million[-5:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 118,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4tunh_oAw8kF",
        "outputId": "c4e73500-2d00-4b2e-c33d-3ee7d54fcaeb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 4.78 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 5: 4.33 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search_iterative(million, 9000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p1Q-BRWoxJ0M"
      },
      "source": [
        "## Time the right thing - exclude data preparation if possible"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 121,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "7LTEkoH4g25W",
        "outputId": "a88680d5-07d8-4f36-ea64-3ab2f108728e"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "input_arr = [(list(range(i)), 9000) for i in range(10_000, 2_000_000, 10_000)]\n",
        "\n",
        "fun1 = automatic_time(input_arr, binary_search_iterative)\n",
        "plt.plot([len(el[0]) for el in input_arr], fun1)b\n",
        "# fun2 = automatic_time(input_arr, binary_search) # the recursive one\n",
        "# plt.plot([len(el[0]) for el in input_arr], fun2)\n",
        "plt.xlabel(\"input size\")\n",
        "plt.ylabel(\"running time in seconds\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 122,
      "metadata": {
        "id": "LPTdAEp_x1EZ"
      },
      "outputs": [],
      "source": [
        "input_arr = None # let GC handle this"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "E74LvGrHg25W"
      },
      "outputs": [],
      "source": [
        "# so binary search is in log n time we would need a trulyl large data sets to see difference\n",
        "# most of our time is spent linearly setting up our data sets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 123,
      "metadata": {
        "id": "ok353STLg25X"
      },
      "outputs": [],
      "source": [
        "arr = list(range(1_000_000))\n",
        "big_arr = list(range(100_000_000))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 124,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WUTwdmp4g25X",
        "outputId": "994641c2-c568-4252-b355-e49976018720"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 4.23 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 5: 5.6 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search(arr, 9000, 0, len(arr)-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 125,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MoqNWSNZg25X",
        "outputId": "f0ff9408-8979-4fa2-9f70-93be74f7a96d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 5.97 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 5: 4.39 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search_iterative(arr, 9000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 126,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kKYXD1Kcg25X",
        "outputId": "63aee3ed-8d79-4f36-e8b6-9530e2af0eb6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000 loops, best of 5: 10.1 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search(big_arr, 9000, 0, len(big_arr)-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 127,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zIgsKJI9g25X",
        "outputId": "05d81efd-fd3d-464b-8a4f-d83fc8daa503"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 4.86 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 5: 9.82 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search(big_arr, 50_000_000, 0, len(big_arr)-1) # so this should hit with 1 comparison"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 128,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NRIeg6ZLg25X",
        "outputId": "79bb36fa-37ce-4396-a0bc-9903774134d6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The slowest run took 5.42 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 5: 7.57 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search_iterative(big_arr, 9000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 129,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d4G2m1o7g25Y",
        "outputId": "c1f46615-1a37-4c1a-acd6-fa6ccb1d4dd1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000 loops, best of 5: 7.17 µs per loop\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "binary_search_iterative(big_arr, 50_000_000) # so this should hit with 1 comparison"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CymgDhz9g25Y"
      },
      "outputs": [],
      "source": [
        "# so creating a recursive algorithm yourself\n",
        "# check if problem is already solved\n",
        "# otherwise reduce problem to simpler instance of the same problem\n",
        "# in other words Simplify and Delegate the problem"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Jp3XfuDpg25Y"
      },
      "outputs": [],
      "source": [
        "# all recursive algorithms can be transformed to regular loop based algorithms\n",
        "# worst case you build your stack for holding the function calls"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9RQ09TaYg25Y"
      },
      "source": [
        "## Length of an array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "F0BmBTgkg25Y"
      },
      "outputs": [],
      "source": [
        "# in case we forgout about len() function ..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SHLdKFW5g25Y"
      },
      "outputs": [],
      "source": [
        "def array_len(x):\n",
        "    if x == []:\n",
        "        return 0\n",
        "    else:\n",
        "        return 1 + array_len(x[1:])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yAQhACT2g25Y",
        "outputId": "1adcf5b9-cb6f-4fa5-f642-9ccc4ec2cf75"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_len([])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Iq5o0uPkg25Z",
        "outputId": "e145b3d6-ad90-4060-88de-a9ba04d2dd52"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_len([1, 2, 3])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0IiBjgTpg25Z",
        "outputId": "6b46eec6-aa30-4480-b17d-8d0d455fe1bd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2961"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_len(list(range(2961))) # so it looks like 3000 limit is actually 2961 (presumably stack needs space for other functions)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AMdXRjtig25Z"
      },
      "source": [
        "## Sum of the elements in an array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VV0wKx8Mg25Z"
      },
      "outputs": [],
      "source": [
        "# in case we forgot about sum() function ..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tCUSvgRzg25Z"
      },
      "outputs": [],
      "source": [
        "def array_sum(x):\n",
        "    if x == []:\n",
        "        return 0\n",
        "    else:\n",
        "        return x[0] + array_sum(x[1:])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QKcFSvKbg25a",
        "outputId": "5e2397a0-c9f9-4839-f8ad-8142cab22d02"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_sum([])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0OpWqh7Tg25a",
        "outputId": "ca754fc5-ac3c-4ce3-8a5f-f5828ef2f4bf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "execution_count": 32,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_sum([5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gyEe2cd9g25a",
        "outputId": "8e99a2a9-3169-4195-cc70-c1f7ea822570"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "15"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_sum([1, 2, 3, 4, 5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7p_4tPChg25a",
        "outputId": "61b36b03-53b7-47ed-dc84-d97ffbe728ea"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5050"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_sum(list(range(101))) # remember the formula for summing arithmethic series n(n-1)/2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kcjXoZD5g25a",
        "outputId": "0948957d-67a0-41b9-bab3-9189f74ab1d0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4382280"
            ]
          },
          "execution_count": 37,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "array_sum(list(range(2961)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LxSZXHb7g25a"
      },
      "source": [
        "# Tower of Hanoi\n",
        "![tower](https://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Tower_of_Hanoi.jpeg/600px-Tower_of_Hanoi.jpeg)\n",
        "\n",
        "* must not move more than one disc at a time \n",
        "* must place this disc on a needle so that there is no smaller disc below it"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1zdJUGxYg25a"
      },
      "source": [
        "## Quicksort - more about sorting later on"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gmWikfzWg25b"
      },
      "outputs": [],
      "source": [
        "def quicksort(array):\n",
        "    if len(array) < 2:\n",
        "        return array\n",
        "    else:\n",
        "        pivot = array[0]\n",
        "        smaller, bigger = [], []\n",
        "        for ele in array[1:]:\n",
        "            if ele <= pivot:\n",
        "                smaller.append(ele)\n",
        "            else:\n",
        "                bigger.append(ele)\n",
        "        return quicksort(smaller) + [pivot] + quicksort(bigger)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "THuZ_fkZg25b"
      },
      "outputs": [],
      "source": [
        "quicksort([])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qBYb8QJFg25b"
      },
      "outputs": [],
      "source": [
        "quicksort([5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6_Sfou0Ig25b"
      },
      "outputs": [],
      "source": [
        "quicksort([5, 4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CniofWXBg25b"
      },
      "outputs": [],
      "source": [
        "quicksort([1, 2, 7, 5, 4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KLxi9e84g25b"
      },
      "outputs": [],
      "source": [
        "quicksort([5, 4, 3, 2])"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "name": "recursion-examples.ipynb",
      "provenance": []
    },
    "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": "3.11.4"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}