Sorting algorithms - Quick sort and Shell sort

-sorting-algorithms-quick-sort-and-shell-sort.ipynb

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      "name": " Sorting algorithms - Quick sort and Shell sort",
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        "<a href=\"https://colab.research.google.com/gist/kvedala/4c1079d9319756090311e3bc1f35b107/-sorting-algorithms-quick-sort-and-shell-sort.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      },
      "source": [
        "import numba\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "%matplotlib inline\n",
        "from IPython.display import HTML, Image\n",
        "from matplotlib import animation\n",
        "from matplotlib import pyplot as plt\n",
        "# import os\n",
        "# os.environ[\"CC\"] = \"/c/msys/mingw64/bin/gcc\"\n",
        "# os.environ[\"CXX\"] = \"/c/msys/mingw64/bin/g++\"\n",
        "%reload_ext cython\n",
        "plt.rcParams['animation.html'] = 'jshtml'"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ufk_EDz_8hnL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def shell_sort1(collection, plt_steps = None):\n",
        "    gaps = [701, 301, 132, 57, 23, 10, 4, 1]\n",
        "    \n",
        "#     print('orig: {}'.format(collection))\n",
        "    for gap in gaps:\n",
        "        for i in range(gap, len(collection)):\n",
        "            temp = collection[i]\n",
        "            j = i\n",
        "            while j >= gap and collection[j - gap] > temp:\n",
        "                if plt_steps is not None:\n",
        "                    plt_steps.append(collection.copy())\n",
        "                    \n",
        "                collection[j] = collection[j - gap]\n",
        "                j -= gap\n",
        "            collection[j] = temp\n",
        "#         print('gap {}: {}'.format(gap, collection))\n",
        "    if plt_steps is not None:\n",
        "        plt_steps.append(collection.copy())\n",
        "\n",
        "    return collection\n",
        "\n",
        "@numba.jit(parallel=True)\n",
        "def shell_sort2(collection):\n",
        "    gaps = np.array([701, 301, 132, 57, 23, 10, 4, 1], dtype=np.int)\n",
        "    \n",
        "#     print('orig: {}'.format(collection))\n",
        "    for gap in gaps:\n",
        "        for i in range(gap, len(collection)):\n",
        "            temp = collection[i]\n",
        "            j = i\n",
        "            while j >= gap and collection[j - gap] > temp:\n",
        "                collection[j] = collection[j - gap]\n",
        "                j -= gap\n",
        "            collection[j] = temp\n",
        "#         print('gap {}: {}'.format(gap, collection))\n",
        "\n",
        "    return collection"
      ],
      "execution_count": 0,
      "outputs": []
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      "source": [
        "%%cython\n",
        "# cython: boundscheck=False\n",
        "# cython: wraparound=False\n",
        "# cython: cdivision=True \n",
        "\n",
        "cimport numpy as np\n",
        "import numpy as np\n",
        "\n",
        "cpdef np.ndarray[np.int_t, ndim=1, mode='c'] shell_sort3(np.ndarray[np.int_t, ndim=1, mode='c'] _collection):\n",
        "    cdef np.ndarray[np.int_t, ndim=1, mode='c'] _gaps = np.array([701, 301, 132, 57, 23, 10, 4, 1], dtype=int, order='C')\n",
        "    cdef np.int_t[::1] gaps = _gaps\n",
        "    cdef np.int_t[::1] collection = _collection\n",
        "    cdef size_t L = collection.shape[0]\n",
        "    cdef size_t L2 = _gaps.shape[0]\n",
        "    cdef int gap \n",
        "    cdef unsigned long i, j, l\n",
        "    cdef np.int_t temp\n",
        "    \n",
        "#     print('orig: {}'.format(collection))\n",
        "    for l in range(L2):\n",
        "        gap = gaps[l]\n",
        "        for i in range(gap, L):\n",
        "            temp = collection[i]\n",
        "            j = i\n",
        "            while j >= gap and collection[j - gap] > temp:\n",
        "                collection[j] = collection[j - gap]\n",
        "                j -= gap\n",
        "            collection[j] = temp\n",
        "#         print('gap {}: {}'.format(gap, collection))\n",
        "\n",
        "    return _collection"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y7iTGSo18hnn",
        "colab_type": "code",
        "outputId": "3175e6a1-6d1a-4597-fcc7-357b2aa7b32e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 146
        }
      },
      "source": [
        "AA = np.random.randint(0, 500, 150)\n",
        "A = AA.copy()\n",
        "# print(A)\n",
        "%timeit shell_sort1(A)\n",
        "A = AA.copy()\n",
        "%timeit shell_sort2(A)\n",
        "A = AA.copy()\n",
        "%timeit shell_sort3(A)\n",
        "A = AA.copy()\n",
        "%timeit A.sort()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1000 loops, best of 3: 294 µs per loop\n",
            "The slowest run took 8.45 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 3: 5.58 µs per loop\n",
            "The slowest run took 7.57 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 3: 4.44 µs per loop\n",
            "The slowest run took 48.17 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "1000000 loops, best of 3: 823 ns per loop\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": false,
        "id": "teUL71Ea8hn0",
        "colab_type": "code",
        "outputId": "0524e974-39eb-4251-ba2f-3ee194c33434",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "steps = []\n",
        "A = AA.copy()\n",
        "shell_sort1(A, steps)\n",
        "len(steps)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "630"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
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      "source": [
        "fig, ax = plt.subplots()\n",
        "def animate(i, data):\n",
        "    ax.cla()\n",
        "    ax.stem(data[i], use_line_collection=True)\n",
        "    ax.set_title('Iter# ' + str(i) + '/' + str(len(steps)))\n",
        "    \n",
        "anim = animation.FuncAnimation(fig, animate, frames=range(len(steps)), repeat=False, fargs=(steps,))\n",
        "HTML(anim.to_jshtml())\n",
        "# anim.save('shell_sort.mp4', fps=2, dpi=80, writer='imagemagick')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "<link rel=\"stylesheet\"\n",
              "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
              "css/font-awesome.min.css\">\n",
              "<script language=\"javascript\">\n",
              "  function isInternetExplorer() {\n",
              "    ua = navigator.userAgent;\n",
              "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
              "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
              "  }\n",
              "\n",
              "  /* Define the Animation class */\n",
              "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
              "    this.img_id = img_id;\n",
              "    this.slider_id = slider_id;\n",
              "    this.loop_select_id = loop_select_id;\n",
              "    this.interval = interval;\n",
              "    this.current_frame = 0;\n",
              "    this.direction = 0;\n",
              "    this.timer = null;\n",
              "    this.frames = new Array(frames.length);\n",
              "\n",
              "    for (var i=0; i<frames.length; i++)\n",
              "    {\n",
              "     this.frames[i] = new Image();\n",
              "     this.frames[i].src = frames[i];\n",
              "    }\n",
              "    var slider = document.getElementById(this.slider_id);\n",
              "    slider.max = this.frames.length - 1;\n",
              "    if (isInternetExplorer()) {\n",
              "        // switch from oninput to onchange because IE <= 11 does not conform\n",
              "        // with W3C specification. It ignores oninput and onchange behaves\n",
              "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
              "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
              "        slider.setAttribute('oninput', null);\n",
              "    }\n",
              "    this.set_frame(this.current_frame);\n",
              "  }\n",
              "\n",
              "  Animation.prototype.get_loop_state = function(){\n",
              "    var button_group = document[this.loop_select_id].state;\n",
              "    for (var i = 0; i < button_group.length; i++) {\n",
              "        var button = button_group[i];\n",
              "        if (button.checked) {\n",
              "            return button.value;\n",
              "        }\n",
              "    }\n",
              "    return undefined;\n",
              "  }\n",
              "\n",
              "  Animation.prototype.set_frame = function(frame){\n",
              "    this.current_frame = frame;\n",
              "    document.getElementById(this.img_id).src =\n",
              "            this.frames[this.current_frame].src;\n",
              "    document.getElementById(this.slider_id).value = this.current_frame;\n",
              "  }\n",
              "\n",
              "  Animation.prototype.next_frame = function()\n",
              "  {\n",
              "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
              "  }\n",
              "\n",
              "  Animation.prototype.previous_frame = function()\n",
              "  {\n",
              "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
              "  }\n",
              "\n",
              "  Animation.prototype.first_frame = function()\n",
              "  {\n",
              "    this.set_frame(0);\n",
              "  }\n",
              "\n",
              "  Animation.prototype.last_frame = function()\n",
              "  {\n",
              "    this.set_frame(this.frames.length - 1);\n",
              "  }\n",
              "\n",
              "  Animation.prototype.slower = function()\n",
              "  {\n",
              "    this.interval /= 0.7;\n",
              "    if(this.direction > 0){this.play_animation();}\n",
              "    else if(this.direction < 0){this.reverse_animation();}\n",
              "  }\n",
              "\n",
              "  Animation.prototype.faster = function()\n",
              "  {\n",
              "    this.interval *= 0.7;\n",
              "    if(this.direction > 0){this.play_animation();}\n",
              "    else if(this.direction < 0){this.reverse_animation();}\n",
              "  }\n",
              "\n",
              "  Animation.prototype.anim_step_forward = function()\n",
              "  {\n",
              "    this.current_frame += 1;\n",
              "    if(this.current_frame < this.frames.length){\n",
              "      this.set_frame(this.current_frame);\n",
              "    }else{\n",
              "      var loop_state = this.get_loop_state();\n",
              "      if(loop_state == \"loop\"){\n",
              "        this.first_frame();\n",
              "      }else if(loop_state == \"reflect\"){\n",
              "        this.last_frame();\n",
              "        this.reverse_animation();\n",
              "      }else{\n",
              "        this.pause_animation();\n",
              "        this.last_frame();\n",
              "      }\n",
              "    }\n",
              "  }\n",
              "\n",
              "  Animation.prototype.anim_step_reverse = function()\n",
              "  {\n",
              "    this.current_frame -= 1;\n",
              "    if(this.current_frame >= 0){\n",
              "      this.set_frame(this.current_frame);\n",
              "    }else{\n",
              "      var loop_state = this.get_loop_state();\n",
              "      if(loop_state == \"loop\"){\n",
              "        this.last_frame();\n",
              "      }else if(loop_state == \"reflect\"){\n",
              "        this.first_frame();\n",
              "        this.play_animation();\n",
              "      }else{\n",
              "        this.pause_animation();\n",
              "        this.first_frame();\n",
              "      }\n",
              "    }\n",
              "  }\n",
              "\n",
              "  Animation.prototype.pause_animation = function()\n",
              "  {\n",
              "    this.direction = 0;\n",
              "    if (this.timer){\n",
              "      clearInterval(this.timer);\n",
              "      this.timer = null;\n",
              "    }\n",
              "  }\n",
              "\n",
              "  Animation.prototype.play_animation = function()\n",
              "  {\n",
              "    this.pause_animation();\n",
              "    this.direction = 1;\n",
              "    var t = this;\n",
              "    if (!this.timer) this.timer = setInterval(function() {\n",
              "        t.anim_step_forward();\n",
              "    }, this.interval);\n",
              "  }\n",
              "\n",
              "  Animation.prototype.reverse_animation = function()\n",
              "  {\n",
              "    this.pause_animation();\n",
              "    this.direction = -1;\n",
              "    var t = this;\n",
              "    if (!this.timer) this.timer = setInterval(function() {\n",
              "        t.anim_step_reverse();\n",
              "    }, this.interval);\n",
              "  }\n",
              "</script>\n",
              "\n",
              "<style>\n",
              ".animation {\n",
              "    display: inline-block;\n",
              "    text-align: center;\n",
              "}\n",
              "input[type=range].anim-slider {\n",
              "    width: 374px;\n",
              "    margin-left: auto;\n",
              "    margin-right: auto;\n",
              "}\n",
              ".anim-buttons {\n",
              "    margin: 8px 0px;\n",
              "}\n",
              ".anim-buttons button {\n",
              "    padding: 0;\n",
              "    width: 36px;\n",
              "}\n",
              ".anim-state label {\n",
              "    margin-right: 8px;\n",
              "}\n",
              ".anim-state input {\n",
              "    margin: 0;\n",
              "    vertical-align: middle;\n",
              "}\n",
              "</style>\n",
              "\n",
              "<div class=\"animation\">\n",
              "  <img id=\"_anim_img608de7cb31244f32b353039962f0b936\">\n",
              "  <div class=\"anim-controls\">\n",
              "    <input id=\"_anim_slider608de7cb31244f32b353039962f0b936\" type=\"range\" class=\"anim-slider\"\n",
              "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
              "           oninput=\"anim608de7cb31244f32b353039962f0b936.set_frame(parseInt(this.value));\"></input>\n",
              "    <div class=\"anim-buttons\">\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
              "          </i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.previous_frame()\">\n",
              "          <i class=\"fa fa-step-backward\"></i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.reverse_animation()\">\n",
              "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.pause_animation()\"><i class=\"fa fa-pause\">\n",
              "          </i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.play_animation()\"><i class=\"fa fa-play\"></i>\n",
              "          </button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.next_frame()\"><i class=\"fa fa-step-forward\">\n",
              "          </i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
              "          </i></button>\n",
              "      <button onclick=\"anim608de7cb31244f32b353039962f0b936.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
              "    </div>\n",
              "    <form action=\"#n\" name=\"_anim_loop_select608de7cb31244f32b353039962f0b936\" class=\"anim-state\">\n",
              "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_608de7cb31244f32b353039962f0b936\"\n",
              "             checked>\n",
              "      <label for=\"_anim_radio1_608de7cb31244f32b353039962f0b936\">Once</label>\n",
              "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_608de7cb31244f32b353039962f0b936\"\n",
              "             >\n",
              "      <label for=\"_anim_radio2_608de7cb31244f32b353039962f0b936\">Loop</label>\n",
              "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_608de7cb31244f32b353039962f0b936\"\n",
              "             >\n",
              "      <label for=\"_anim_radio3_608de7cb31244f32b353039962f0b936\">Reflect</label>\n",
              "    </form>\n",
              "  </div>\n",
              "</div>\n",
              "\n",
              "\n",
              "<script language=\"javascript\">\n",
              "  /* Instantiate the Animation class. */\n",
              "  /* The IDs given should match those used in the template above. */\n",
              "  (function() {\n",
              "    var img_id = \"_anim_img608de7cb31244f32b353039962f0b936\";\n",
              "    var slider_id = \"_anim_slider608de7cb31244f32b353039962f0b936\";\n",
              "    var loop_select_id = \"_anim_loop_select608de7cb31244f32b353039962f0b936\";\n",
              "    var frames = new Array(630);\n",
              "    \n",
              "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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