big-O-notation.ipynb

big-o-notation.ipynb

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  "metadata": {
    "colab": {
      "name": "big-O-notation.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/jonkrohn/9d8802220a065efdaa8d3000a73c403c/big-o-notation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ubj0d3gCOzGX",
        "colab_type": "text"
      },
      "source": [
        "# Big O Notation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rR7kFMg3PSDT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DMLnnWCbO3QA",
        "colab_type": "text"
      },
      "source": [
        "#### Constant Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BlnfRyUwO16k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def take_first(my_list):\n",
        "  return my_list[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y5PIzM-4WoG-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "short_list = [13, 25, 42]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3nHVIFonMGBp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tic = time.clock()\n",
        "first = take_first(short_list)\n",
        "toc = time.clock()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Np65K7yXPFl",
        "colab_type": "code",
        "outputId": "f9461fae-66b0-4a3a-f972-981c527df48e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "first"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "13"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P0owpiPEPHuL",
        "colab_type": "code",
        "outputId": "6824bb7c-afab-4c60-8c13-55c7303d75a8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6.0999999999866716e-05"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AvyPjweCRfYB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "long_list = [42] * 10**8 # one hundred million items"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eEyXwNVBTOKq",
        "colab_type": "code",
        "outputId": "01eb3a80-8834-468b-fd44-c51d199be53e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "len(long_list)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q-3OdxzwRHHy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tic = time.clock()\n",
        "first = take_first(long_list)\n",
        "toc = time.clock()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eYfVVpq0XSBJ",
        "colab_type": "code",
        "outputId": "6b361403-e068-4c66-d110-7d2641b17b95",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "first"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "42"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wKMsVOQRTbxc",
        "colab_type": "code",
        "outputId": "a580c33f-3041-443d-eb9a-563c1a400cef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.999999999994898e-05"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_7lYwANvX55t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8305c6a9-11c2-4262-dbf3-606ee61186cd"
      },
      "source": [
        "list_lengths = [10**l for l in range(1, 8)]\n",
        "list_lengths"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000, 10000000]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j0igW42mY4cn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "constant_times = []\n",
        "\n",
        "for l in list_lengths:\n",
        "  lst = [42]*l\n",
        "  \n",
        "  tic = time.clock()\n",
        "  x = take_first(lst)\n",
        "  toc = time.clock()\n",
        "  \n",
        "  constant_times.append(toc-tic)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6i2ND8bCemLw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DuX_4N5VengR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "5783572b-044d-443f-e382-acb402274df5"
      },
      "source": [
        "constant_df = pd.DataFrame(list(zip(list_lengths, constant_times)), columns=['N', 'time'])\n",
        "constant_df"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>N</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>10</td>\n",
              "      <td>0.000004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>100</td>\n",
              "      <td>0.000001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1000</td>\n",
              "      <td>0.000001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>10000</td>\n",
              "      <td>0.000002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>100000</td>\n",
              "      <td>0.000002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1000000</td>\n",
              "      <td>0.000005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>10000000</td>\n",
              "      <td>0.000010</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          N      time\n",
              "0        10  0.000004\n",
              "1       100  0.000001\n",
              "2      1000  0.000001\n",
              "3     10000  0.000002\n",
              "4    100000  0.000002\n",
              "5   1000000  0.000005\n",
              "6  10000000  0.000010"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ACF9H30UUEl",
        "colab_type": "text"
      },
      "source": [
        "#### Linear Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2CnMr4wwV2Oj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def find_max(my_list):\n",
        "  max_value = my_list[0]\n",
        "  for i in range(len(my_list)):\n",
        "    if my_list[i] > max_value:\n",
        "      max_value = my_list[i]\n",
        "  return max_value"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-q39XMCyTci3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tic = time.clock()\n",
        "largest = find_max(short_list)\n",
        "toc = time.clock()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2lWTIzxoXlPc",
        "colab_type": "code",
        "outputId": "07f7dc02-738a-4c8d-ed7e-267ec3f71c45",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "largest"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "42"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LAspDSQwX2t_",
        "colab_type": "code",
        "outputId": "da9004c9-0671-450e-f5e3-35a0c2549229",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9.400000000026054e-05"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kJnXPyMbbpoF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tic = time.clock()\n",
        "largest = find_max(long_list)\n",
        "toc = time.clock()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_PIJp3c4bx1t",
        "colab_type": "code",
        "outputId": "9c49928b-82b8-4806-ef25-7a5922f92b75",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "largest"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "42"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RlrrPljvbyhm",
        "colab_type": "code",
        "outputId": "2fcffab1-1175-44b1-9906-ac5a91414adb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.187785999999999"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fmtWD8C6bK0z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "linear_times = []\n",
        "\n",
        "for l in list_lengths:\n",
        "  lst = [42]*l\n",
        "  \n",
        "  tic = time.clock()\n",
        "  x = find_max(lst)\n",
        "  toc = time.clock()\n",
        "  \n",
        "  linear_times.append(toc-tic)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_fdLU4f5d-n1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "71c8eaa5-0ca5-4987-cd8d-3892954b04e2"
      },
      "source": [
        "linear_df = pd.DataFrame(list(zip(list_lengths, linear_times)), columns=['N', 'time'])\n",
        "linear_df"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>N</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>10</td>\n",
              "      <td>0.000013</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>100</td>\n",
              "      <td>0.000005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1000</td>\n",
              "      <td>0.000054</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>10000</td>\n",
              "      <td>0.000492</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>100000</td>\n",
              "      <td>0.005183</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1000000</td>\n",
              "      <td>0.050999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>10000000</td>\n",
              "      <td>0.511218</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          N      time\n",
              "0        10  0.000013\n",
              "1       100  0.000005\n",
              "2      1000  0.000054\n",
              "3     10000  0.000492\n",
              "4    100000  0.005183\n",
              "5   1000000  0.050999\n",
              "6  10000000  0.511218"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BY5mPpYWfCxj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import seaborn as sns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eA_6v8hreSpH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        },
        "outputId": "a466d8c3-d0a4-43ff-8205-440573720103"
      },
      "source": [
        "_ = sns.lmplot(x='N', y='time', data=linear_df, ci=None)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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sF2Z2GXAPMMk5V9dB2U7HyfarG3Au8IaZ7aDpGNyaIP9FXGu+VruB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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8S7JZLW7UbBz",
        "colab_type": "text"
      },
      "source": [
        "#### Polynomial Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cXQMBEPlplpZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def element_multiplier(my_list): \n",
        "  for i in range(len(my_list)):\n",
        "    for j in range(len(my_list)):\n",
        "      x = my_list[i] * my_list[j]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0h1VeAaSqYNv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ff9015b1-73c3-4be8-e247-cc108338d04b"
      },
      "source": [
        "list_lengths"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000, 10000000]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5OlX1YyirN48",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a8426a41-e717-411d-a30e-809952f5b6f8"
      },
      "source": [
        "list_lengths[:4] # compute time gets annoyingly long from list_lengths[5] onward"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6j6cAuMltFqW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "57b6f80e-a461-4ba9-823d-f59b3aaf3e17"
      },
      "source": [
        "granular_list_lengths = list_lengths[:4] + [50, 500, 5000]\n",
        "granular_list_lengths"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 50, 500, 5000]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YPDXf8DVtYyk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "granular_list_lengths.sort()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v0hlQ1bEtdA7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f6b4484b-a9bd-4470-ca85-cd82d1948355"
      },
      "source": [
        "granular_list_lengths"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 50, 100, 500, 1000, 5000, 10000]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7TmUgtrrSJR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "poly_times = []\n",
        "\n",
        "for l in granular_list_lengths:\n",
        "  lst = [42]*l\n",
        "\n",
        "  tic = time.clock()\n",
        "  x = element_multiplier(lst)\n",
        "  toc = time.clock()\n",
        "\n",
        "  poly_times.append(toc-tic)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iFaVujgXrsKz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "dc4ae453-1e95-47be-d87f-913cb79d4dc1"
      },
      "source": [
        "poly_df = pd.DataFrame(list(zip(granular_list_lengths, poly_times)), columns=['N', 'time'])\n",
        "poly_df"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>N</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>10</td>\n",
              "      <td>0.000021</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>50</td>\n",
              "      <td>0.000173</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>100</td>\n",
              "      <td>0.000673</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>500</td>\n",
              "      <td>0.018461</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1000</td>\n",
              "      <td>0.075228</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5000</td>\n",
              "      <td>1.946877</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>10000</td>\n",
              "      <td>7.775681</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       N      time\n",
              "0     10  0.000021\n",
              "1     50  0.000173\n",
              "2    100  0.000673\n",
              "3    500  0.018461\n",
              "4   1000  0.075228\n",
              "5   5000  1.946877\n",
              "6  10000  7.775681"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GLmzSaMYsgeb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        },
        "outputId": "dd2ce52d-18f8-45f3-a6a3-a9ea3bc6ba42"
      },
      "source": [
        "_ = sns.lmplot(x='N', y='time', data=poly_df, ci=None, order=2)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uprLOA/hnMbv1rGEkxauXg0QHBbB0uD3V9dz55ireW1kCQEanRB67ZCwnD810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\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mpl4mIzzUuI6",
        "colab_type": "text"
      },
      "source": [
        " #### In Big O notation: \n",
        "\n",
        " * constant: O(1)\n",
        " * linear: O(N)\n",
        " * polynomial: O(N**2) \n",
        " \n",
        "\n",
        " #### Others\n",
        "\n",
        "* logarithmic: O(log N)\n",
        "* exponential: O(2**N)\n",
        "* O(N log N)\n",
        "* O(N!) "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xHaG3z18VSFw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}