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jonkrohn/big-o-notation.ipynb

Created December 20, 2019 19:15
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big-o-notation.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"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\nNc65BufcdmAbTYUczFqzX1nAKgDn3LtAHE0DbUJZq372TlW4FnABMMLMhppZDE2/ZFtz3DZrgJnN\nH18L/NU1H20PYifdLzMbDyyiqXxD4ZginGS/nHMVzrm+zrlk51wyTce2JznnCr2J2yqt+R78I03v\nfjGzvjQdkijtyJBt0Jr92gl8HcDMRtNUwPs7NGX7WwPMaD4b4gKgwjm397Sf1evfPgbwt5pX0fSO\n4mPgnubHFtD0gwtN3xTPACVAPjDM68zttF+vAX8HNjb/WeN15vbYr+O2fYMgPwuilV8ro+nQyvvA\nZmCq15nbab/GAO/QdIbERuAbXmduxT49BewFGmj6l0kWcCtw6zFfq0eb93lze33/6VJkERGPhOsh\nCBGRoKcCFhHxiApYRMQjKmAREY+ogEVETuBkQ3qO2/ZXZrax+c82MzvpBTUqYOnUmierPXTM8p1m\n9lMPI0lwWQa06hJx59wPnHPjnHPjgN8CfzjZ56iApbOrA65pvhBC5AtcC0N6zGy4mb1sZuvM7G0z\nO7uFT51G07nFX0oFLJ2dj6bxiT/wOoiEjMeB7znnJgB3Ar87dmXzDO6hwF9P9kQaxiPSdIVTkZk9\n6HUQCW5mlgB8BXjmmOm1scdtNhVY7ZxrPNnzqYCl03POHTGz5cD3gRqv80hQiwAONx/nPZGpwHdb\n+2QiAv9D0/X/Xb0OIsHLOXcE2G5m18Hntyoa+9n65uPBvYB3W/N8KmARwDl3kKYRilleZ5HgYWZP\n0VSmo8xst5llATcBWWa2CSjmi3cEmQqsdK0csqNhPNKpmdlR51xC88f9ge3Ag865n3oaTDoFFbCI\niEd0CEJExCMqYBERj6iARUQ8ogIWEfGIClhExCMqYBERj6iARUQ88v8B6L7UAOXUqnoAAAAASUVO\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": {
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qjt8jpAAWkVYpLK3ivnfXAHDO2F6cP14T7RwpBbCIHFadx8vNryyjtsFH7y7J3H/eKE20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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": []
}
]
}
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