Santa 2022 - Travelling Santa challenge.ipynb

{"cells":[{"cell_type":"markdown","source":["# Travelling Santa challenge\n\nRudolph has always believed in working smarter, not harder. And what better way to earn the respect of Comet and Blitzen than showing the initiative to improve Santa's annual route for delivering toys on Christmas Eve?\n\nThis year, Rudolph believes he can motivate the overworked Reindeer team by wisely choosing the order in which they visit the houses on Santa's list. The houses in prime cities always leave carrots for the Reindeers alongside the usual cookies and milk. These carrots are just the sustenance the Reindeers need to keep pace. In fact, Rudolph has found that if the Reindeer team doesn't originate from a prime city exactly every 10th step, it takes them 10% longer than it normally would to make their next destination!\n\nCan you help Rudolph solve the Traveling Santa problem subject to his carrot constraint? His team--and Santa--are counting on you!\n\n<img src=\"https://mir-s3-cdn-cf.behance.net/project_modules/disp/c8385876438773.5c759e561c2a9.gif\" alt=\"rudolph_compute\" width=\"300\"/>\n\n## Prerequisites and Imports\nThe first step is to import the necessary libraries. These are commonly used ones so the experiment is reproducible."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"160dfaf4-d079-4c52-80e6-f8b1f00f0ce1","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["pip install geopandas"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"16c79817-bf18-4418-8608-a9713a4df223","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Python interpreter will be restarted.\nCollecting geopandas\n  Downloading geopandas-0.12.1-py3-none-any.whl (1.1 MB)\nRequirement already satisfied: packaging in /databricks/python3/lib/python3.8/site-packages (from geopandas) (20.9)\nCollecting pyproj&gt;=2.6.1.post1\n  Downloading pyproj-3.4.0-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (7.8 MB)\nCollecting fiona&gt;=1.8\n  Downloading Fiona-1.8.22-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (16.6 MB)\nRequirement already satisfied: pandas&gt;=1.0.0 in /databricks/python3/lib/python3.8/site-packages (from geopandas) (1.2.4)\nCollecting shapely&gt;=1.7\n  Downloading Shapely-1.8.5.post1-cp38-cp38-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (2.1 MB)\nCollecting munch\n  Downloading munch-2.5.0-py2.py3-none-any.whl (10 kB)\nRequirement already satisfied: setuptools in /usr/local/lib/python3.8/dist-packages (from fiona&gt;=1.8-&gt;geopandas) (52.0.0)\nCollecting click&gt;=4.0\n  Downloading click-8.1.3-py3-none-any.whl (96 kB)\nCollecting cligj&gt;=0.5\n  Downloading cligj-0.7.2-py3-none-any.whl (7.1 kB)\nRequirement already satisfied: six&gt;=1.7 in /databricks/python3/lib/python3.8/site-packages (from fiona&gt;=1.8-&gt;geopandas) (1.15.0)\nRequirement already satisfied: attrs&gt;=17 in /databricks/python3/lib/python3.8/site-packages (from fiona&gt;=1.8-&gt;geopandas) (20.3.0)\nCollecting 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geopandas-0.12.1 munch-2.5.0 pyproj-3.4.0 shapely-1.8.5.post1\nWARNING: You are using pip version 21.0.1; however, version 22.3.1 is available.\nYou should consider upgrading via the &#39;/local_disk0/.ephemeral_nfs/envs/pythonEnv-cec5fe4c-b67c-4d96-811a-4fa8c9242213/bin/python -m pip install --upgrade pip&#39; command.\nPython interpreter will be restarted.\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Python interpreter will be restarted.\nCollecting geopandas\n  Downloading geopandas-0.12.1-py3-none-any.whl (1.1 MB)\nRequirement already satisfied: packaging in /databricks/python3/lib/python3.8/site-packages (from geopandas) (20.9)\nCollecting pyproj&gt;=2.6.1.post1\n  Downloading pyproj-3.4.0-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (7.8 MB)\nCollecting fiona&gt;=1.8\n  Downloading Fiona-1.8.22-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (16.6 MB)\nRequirement already satisfied: pandas&gt;=1.0.0 in /databricks/python3/lib/python3.8/site-packages (from geopandas) (1.2.4)\nCollecting shapely&gt;=1.7\n  Downloading Shapely-1.8.5.post1-cp38-cp38-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (2.1 MB)\nCollecting munch\n  Downloading munch-2.5.0-py2.py3-none-any.whl (10 kB)\nRequirement already satisfied: setuptools in /usr/local/lib/python3.8/dist-packages (from fiona&gt;=1.8-&gt;geopandas) (52.0.0)\nCollecting click&gt;=4.0\n  Downloading click-8.1.3-py3-none-any.whl (96 kB)\nCollecting cligj&gt;=0.5\n  Downloading cligj-0.7.2-py3-none-any.whl (7.1 kB)\nRequirement already satisfied: six&gt;=1.7 in /databricks/python3/lib/python3.8/site-packages (from fiona&gt;=1.8-&gt;geopandas) (1.15.0)\nRequirement already satisfied: attrs&gt;=17 in /databricks/python3/lib/python3.8/site-packages (from fiona&gt;=1.8-&gt;geopandas) (20.3.0)\nCollecting click-plugins&gt;=1.0\n  Downloading click_plugins-1.1.1-py2.py3-none-any.whl (7.5 kB)\nRequirement already satisfied: certifi in /databricks/python3/lib/python3.8/site-packages (from fiona&gt;=1.8-&gt;geopandas) (2020.12.5)\nRequirement already satisfied: pytz&gt;=2017.3 in /databricks/python3/lib/python3.8/site-packages (from pandas&gt;=1.0.0-&gt;geopandas) (2020.5)\nRequirement already satisfied: numpy&gt;=1.16.5 in /databricks/python3/lib/python3.8/site-packages (from pandas&gt;=1.0.0-&gt;geopandas) (1.19.2)\nRequirement already satisfied: python-dateutil&gt;=2.7.3 in /databricks/python3/lib/python3.8/site-packages (from pandas&gt;=1.0.0-&gt;geopandas) (2.8.1)\nRequirement already satisfied: pyparsing&gt;=2.0.2 in /databricks/python3/lib/python3.8/site-packages (from packaging-&gt;geopandas) (2.4.7)\nInstalling collected packages: click, munch, cligj, click-plugins, shapely, pyproj, fiona, geopandas\nSuccessfully installed click-8.1.3 click-plugins-1.1.1 cligj-0.7.2 fiona-1.8.22 geopandas-0.12.1 munch-2.5.0 pyproj-3.4.0 shapely-1.8.5.post1\nWARNING: You are using pip version 21.0.1; however, version 22.3.1 is available.\nYou should consider upgrading via the &#39;/local_disk0/.ephemeral_nfs/envs/pythonEnv-cec5fe4c-b67c-4d96-811a-4fa8c9242213/bin/python -m pip install --upgrade pip&#39; command.\nPython interpreter will be restarted.\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["import numpy as np # library used for working with arrays\nimport pandas as pd # library used for data manipulation and analysis\nfrom math import radians, cos, sin, asin, sqrt # library used for calculating the distance\nimport geopandas # library used for spatial operations on geometric types\nimport plotly.express as px # library used to create visualisations"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"8b45e81a-911f-4636-a87a-cf67d5423685","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"markdown","source":["## Loading the data\nThe dataset has been extracted from the open source website [simplemaps](https://simplemaps.com/data/world-cities), the top three cities of each country in the world were selected when they had over 200,000 inhabitants.\n\n**Data Dictionary**\n* city: name of the city \t\n* lat: latitude of the city\t\t\t\n* lng: longitude of the city\n* country: name of the city's country\n* population: estimate of the city's population\n* city_id: generated unique ID\n* prime_city: cities for which the city_id is a prime number"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"fe0146d6-f656-4d18-9766-b9fae647baf8","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# read the data\ndata = pd.read_csv('../data/worldcities.csv')"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"60374b11-1e76-49dd-b389-75dc75fb6d56","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"markdown","source":["### Basic Data Information\nThis section will provide basic information about the data."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"48e4f5bc-303a-4990-89c5-95c6c9a028c0","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["data.head()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"acb567c9-050e-4ab9-a1f3-5d672b5fae23","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Out[3]: </div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Out[3]: </div>"]}},{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<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>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>city_id</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>Tokyo</td>\n      <td>35.6839</td>\n      <td>139.7744</td>\n      <td>Japan</td>\n      <td>39105000</td>\n      <td>1</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>Jakarta</td>\n      <td>-6.2146</td>\n      <td>106.8451</td>\n      <td>Indonesia</td>\n      <td>35362000</td>\n      <td>2</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>Delhi</td>\n      <td>28.6667</td>\n      <td>77.2167</td>\n      <td>India</td>\n      <td>31870000</td>\n      <td>3</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>Manila</td>\n      <td>14.6000</td>\n      <td>120.9833</td>\n      <td>Philippines</td>\n      <td>23971000</td>\n      <td>4</td>\n      <td>0</td>\n    </tr>\n  </tbody>\n</table>\n</div>","textData":null,"removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"htmlSandbox","arguments":{}}},"output_type":"display_data","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>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>city_id</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>Tokyo</td>\n      <td>35.6839</td>\n      <td>139.7744</td>\n      <td>Japan</td>\n      <td>39105000</td>\n      <td>1</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>Jakarta</td>\n      <td>-6.2146</td>\n      <td>106.8451</td>\n      <td>Indonesia</td>\n      <td>35362000</td>\n      <td>2</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>Delhi</td>\n      <td>28.6667</td>\n      <td>77.2167</td>\n      <td>India</td>\n      <td>31870000</td>\n      <td>3</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>Manila</td>\n      <td>14.6000</td>\n      <td>120.9833</td>\n      <td>Philippines</td>\n      <td>23971000</td>\n      <td>4</td>\n      <td>0</td>\n    </tr>\n  </tbody>\n</table>\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# check the number of rows and columns in data\ndata.shape"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"a85734b5-0863-4d84-96a7-83b99af4a35a","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Out[4]: (369, 7)</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Out[4]: (369, 7)</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# check the data type and if there are any missing values in data\ndata.info()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"81f5dda8-8ff9-4c40-bf56-72f82f11420d","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">&lt;class &#39;pandas.core.frame.DataFrame&#39;&gt;\nRangeIndex: 369 entries, 0 to 368\nData columns (total 7 columns):\n #   Column      Non-Null Count  Dtype  \n---  ------      --------------  -----  \n 0   city        369 non-null    object \n 1   lat         369 non-null    float64\n 2   lng         369 non-null    float64\n 3   country     369 non-null    object \n 4   population  369 non-null    int32  \n 5   city_id     369 non-null    int32  \n 6   prime_city  369 non-null    int32  \ndtypes: float64(2), int32(3), object(2)\nmemory usage: 16.0+ KB\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">&lt;class &#39;pandas.core.frame.DataFrame&#39;&gt;\nRangeIndex: 369 entries, 0 to 368\nData columns (total 7 columns):\n #   Column      Non-Null Count  Dtype  \n---  ------      --------------  -----  \n 0   city        369 non-null    object \n 1   lat         369 non-null    float64\n 2   lng         369 non-null    float64\n 3   country     369 non-null    object \n 4   population  369 non-null    int32  \n 5   city_id     369 non-null    int32  \n 6   prime_city  369 non-null    int32  \ndtypes: float64(2), int32(3), object(2)\nmemory usage: 16.0+ KB\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# change the prime_city column to a binary data type:\ndata['prime_city'] = data['prime_city'].astype(bool)"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"418b7213-bc78-40a6-86b6-81c0e312ad52","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"markdown","source":["The data frame is composed of 369 rows each representing a city and 7 features. The information above shows that we have no missing values which means we won't have to manipulate the data before running the model. However, the `prime_city` column is shown as an integer but we want to transform it into a binary column, so it is easier to use later on in the script.\n\nUsing `mapbox` available in `express` we can place each city from our list on a map to see where Santa is supposed to stop:"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"90b6b4d7-6656-40d2-849f-a705db5a4e5c","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# plot the cities in data\nfig = px.scatter_mapbox(data, lat=\"lat\", \n                        lon=\"lng\", \n                        hover_name=\"city\", \n                        hover_data=[\"country\",\"prime_city\"],\n                        color=\"city\", \n                        zoom=1, \n                        height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"eae9a0b6-38d0-45b4-8a23-5e541333d13b","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n        <script src=\"https://cdn.plot.ly/plotly-2.2.0.min.js\"></script>                <div id=\"e14606c2-18b2-4f2f-9dab-c75f6fe40de4\" class=\"plotly-graph-div\" 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                       {\"responsive\": true}                    )                };                            </script>        </div>\n</body>\n</html>"]}}],"execution_count":0},{"cell_type":"markdown","source":["We map above shows how uneven the cities are spread across the globe. We can see dense areas in Europe, Africa, and South America and some more isolated locations in Australia and New Zealand as well as Canada and the United States of America."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"19f1727d-d02c-4b9a-bd5a-a35fff6eb059","inputWidgets":{},"title":""}}},{"cell_type":"markdown","source":["## Calculating the Path Distance\n\nIn this challenge, we want to optimise the path Santa is going to take to visit all cities on his list. A way to assess the efficiency of a path is to calculate the total distance travelled by Santa and his reindeer. For that, we are going to define a function called `distance()`:\n`distance()` takes two arguments:\n* `df` a data frame with the city_id, city's coordinates and the prime_city\n* `path` a calculated path stored as a list of city IDs\n\nThe first step is to define the `previous_stop`. Since we are starting our journey from Santa's home in Lapland every path should start there, this means that the first previous_stop will always be `path[0]`. We then, look at the prime cities and store them as a list oin `prime_cities`. We will be used it later on in the function to increase the distance when the 10th step is not a prime city since we know that it takes the reindeer team 10% longer than it normally would, to make their next destination. We also want to keep track of the `total_distance` starting at zero miles and the `stop_number` starting at stop 1.\n\nWe calculate the distance between each city available in the path from the `previous_stop` using the [haversine formula](https://en.wikipedia.org/wiki/Haversine_formula) formula which determines the great-circle distance between two points since Santa and his reindeer can fly using his sleigh and store it in `distance`. We add 10% extra on the mileage every 10th step when it not coming from a prime city and store the final result in `total_distance` until we visited all the cities on our list."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"3770ec0e-a723-4990-953c-dba974b2246b","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["def distance(df,path):\n  '''Calculates the distance in miles for a provided path. it takes two arguments:\n      - df: a data frame with the city_id, city's coordinates and the prime_city\n      - path: a calculated path stored as a list of city IDs\n  '''\n  previous_stop = path[0] \n  prime_cities = list(df.city_id[df.prime_city == 1]) \n  total_distance = 0\n  stop_number = 1 \n  for city in path[1:]: \n    next_stop = city \n    # to calculate the total distance of the path, we use haversine distance formula since Santa's can fly using his sleigh \n    # convert decimal degrees to radians \n    lng_previous_stop, lat_previous_stop, lng_next_city, lat_next_city = map(radians, [df.lng[previous_stop], \n                                                                                       df.lat[previous_stop], \n                                                                                       df.lng[next_stop], \n                                                                                       df.lat[next_stop]])\n    # haversine formula\n    distance_lng = lng_previous_stop - lng_next_city\n    distance_lat = lat_previous_stop - lat_next_city\n\n    a = sin(distance_lat/2)**2 + cos(lat_previous_stop) * cos(lat_next_city) * sin(distance_lng/2)**2\n    c = 2 * asin(sqrt(a)) \n    r = 3956 # radius of earth in miles. Use 6371 for kilometers.\n    distance = c * r\n    # add 10% extra to the distance when the 10th step is not a prime city:\n    if previous_stop in prime_cities:\n      extra_distance = distance \n    else:\n      extra_distance = distance * (1+ 0.1*((stop_number % 10 == 0))) \n    # add the final distance on the total path distance \n    total_distance = total_distance + extra_distance\n    # amend the previous city \n    previous_stop = next_stop\n    # add an extra stop the the stop number\n    stop_number = stop_number + 1\n  return total_distance"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"651e9474-4d5f-4b76-bae3-74fbf02f7af7","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"markdown","source":["## Creating a dumb Path\nIn this section, we do not try to find the efficient path to take but follow the list order. This will give us a baseline to compare the performance of the different paths."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"981c4adc-eae4-46ca-a54f-324f1a64e059","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# calculates the dumb path using the city IDs\ndumb_path = list(data.city_id[:].append(pd.Series([0]))) "],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"24a83a72-49c4-476c-b4a0-ca9a0ca5922f","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"code","source":["# calculating the distance travelled for this path:\nprint('Total distance with the dumb path is {} miles'.format(round(distance(data,dumb_path),0)))"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"c5b35d6a-02a4-4f3b-be69-21709a5bccea","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Total distance with the dumb path is 1783555.0 miles\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Total distance with the dumb path is 1783555.0 miles\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# merge the dataframe back to the path we created to plot it on a map\ndf_path = pd.DataFrame({'city_id':dumb_path}).merge(data, how = 'left', on=['city_id'])\ndf_path.head(5)"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"10555c85-0484-47b6-adc6-afcad57ea3f0","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Out[11]: </div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Out[11]: </div>"]}},{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>Tokyo</td>\n      <td>35.6839</td>\n      <td>139.7744</td>\n      <td>Japan</td>\n      <td>39105000</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>Jakarta</td>\n      <td>-6.2146</td>\n      <td>106.8451</td>\n      <td>Indonesia</td>\n      <td>35362000</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>Delhi</td>\n      <td>28.6667</td>\n      <td>77.2167</td>\n      <td>India</td>\n      <td>31870000</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>Manila</td>\n      <td>14.6000</td>\n      <td>120.9833</td>\n      <td>Philippines</td>\n      <td>23971000</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>","textData":null,"removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"htmlSandbox","arguments":{}}},"output_type":"display_data","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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>Tokyo</td>\n      <td>35.6839</td>\n      <td>139.7744</td>\n      <td>Japan</td>\n      <td>39105000</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>Jakarta</td>\n      <td>-6.2146</td>\n      <td>106.8451</td>\n      <td>Indonesia</td>\n      <td>35362000</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>Delhi</td>\n      <td>28.6667</td>\n      <td>77.2167</td>\n      <td>India</td>\n      <td>31870000</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>Manila</td>\n      <td>14.6000</td>\n      <td>120.9833</td>\n      <td>Philippines</td>\n      <td>23971000</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# plot the path on a map\nfig = px.line_mapbox(df_path, \n                     lat=\"lat\", \n                     lon=\"lng\", \n                     hover_name=\"city\", \n                     hover_data=[\"country\",\"prime_city\"],\n                     zoom=1, \n                     height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"t\":0,\"r\":0,\"b\":0,\"l\":0}) # Dimensions of each margin. (To remember order, think trouble).\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"1f878d8d-0956-4045-9c5f-b6fd561a096f","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n        <script src=\"https://cdn.plot.ly/plotly-2.2.0.min.js\"></script>                <div id=\"6bada953-5be9-457d-a45c-186a015bf484\" class=\"plotly-graph-div\" style=\"height:500px; width:100%;\"></div>            <script type=\"text/javascript\">        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We can then run our `distance()` function to see if this method improve the mileage."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"e93e3496-c134-47ef-a0af-d6c7bcd0c64f","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# order the cities by coordinates\nsorted_cities = list(data.iloc[1:,].sort_values(['lat','lng'], ascending=False)['city_id'])\nsorted_cities = [0] + sorted_cities + [0]"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"d359aa6f-693f-46b1-a0db-1ee80de740e0","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"code","source":["# calculating the distance travelled for this path\nprint('Total distance with the sorted cities path is {} miles'.format(round(distance(data,sorted_cities),0)))"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"c909d856-f629-457a-8913-857815482369","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Total distance with the sorted cities path is 1099608.0 miles\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Total distance with the sorted cities path is 1099608.0 miles\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# merge the path with data\ndf_path = pd.DataFrame({'city_id':sorted_cities}).merge(data, how = 'left', on=['city_id'])\ndf_path.head(5)"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"b694985a-588a-4696-92f4-136c007abc71","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Out[15]: </div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Out[15]: </div>"]}},{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>352</td>\n      <td>Tampere</td>\n      <td>61.4981</td>\n      <td>23.7600</td>\n      <td>Finland</td>\n      <td>225118</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>337</td>\n      <td>Bergen</td>\n      <td>60.3925</td>\n      <td>5.3233</td>\n      <td>Norway</td>\n      <td>257087</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>331</td>\n      <td>Espoo</td>\n      <td>60.2100</td>\n      <td>24.6600</td>\n      <td>Finland</td>\n      <td>269802</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>230</td>\n      <td>Helsinki</td>\n      <td>60.1756</td>\n      <td>24.9342</td>\n      <td>Finland</td>\n      <td>642045</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>","textData":null,"removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"htmlSandbox","arguments":{}}},"output_type":"display_data","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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>352</td>\n      <td>Tampere</td>\n      <td>61.4981</td>\n      <td>23.7600</td>\n      <td>Finland</td>\n      <td>225118</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>337</td>\n      <td>Bergen</td>\n      <td>60.3925</td>\n      <td>5.3233</td>\n      <td>Norway</td>\n      <td>257087</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>331</td>\n      <td>Espoo</td>\n      <td>60.2100</td>\n      <td>24.6600</td>\n      <td>Finland</td>\n      <td>269802</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>230</td>\n      <td>Helsinki</td>\n      <td>60.1756</td>\n      <td>24.9342</td>\n      <td>Finland</td>\n      <td>642045</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# plot the path on a map\nfig = px.line_mapbox(df_path, \n                     lat=\"lat\", \n                     lon=\"lng\", \n                     hover_name=\"city\", \n                     hover_data=[\"country\",\"prime_city\"],\n                     zoom=1, \n                     height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"91a28489-5ed7-4b9f-9955-e8e800cf37c3","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script 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Sad\",\"Belgrade\",\"Bucharest\",\"Sarajevo\",\"Toronto\",\"Marseille\",\"Almaty\",\"Varna\",\"Bishkek\",\"Sofia\",\"Shymkent\",\"Plovdiv\",\"Skopje\",\"Rome\",\"Chicago\",\"Dasoguz\",\"Tbilisi\",\"Barcelona\",\"Tirana\",\"Tashkent\",\"Vila Nova de Gaia\",\"Bagcilar\",\"Istanbul\",\"Namangan\",\"Naples\",\"New York\",\"Ganca\",\"Thessaloniki\",\"Sumqayit\",\"Osh\",\"Madrid\",\"Baku\",\"Yerevan\",\"Hamhung\",\"Beijing\",\"Samarkand\",\"Valencia\",\"Turkmenabat\",\"Pyongyang\",\"Sintra\",\"Nampo\",\"Lisbon\",\"Dushanbe\",\"Athens\",\"Seoul\",\"Incheon\",\"Tunis\",\"Algiers\",\"Mosul\",\"Constantine\",\"Mashhad\",\"Aleppo\",\"Tehran\",\"Oran\",\"Tokyo\",\"Nicosia\",\"Nagoya\",\"Busan\",\"Sidi Bouzid\",\"Osaka\",\"Sfax\",\"Homs\",\"Limassol\",\"Kabul\",\"Tripoli\",\"Herat\",\"Los Angeles\",\"Fes\",\"Beirut\",\"Casablanca\",\"Sidon\",\"Damascus\",\"Baghdad\",\"Tripoli\",\"Haifa\",\"Esfahan\",\"Irbid\",\"Tijuana\",\"Misratah\",\"Benghazi\",\"Az Zarqa'\",\"Tel Aviv-Yafo\",\"El Kelaa des Srarhna\",\"Amman\",\"Jerusalem\",\"Kandahar\",\"Lahore\",\"Faisalabad\",\"Alexandria\",\"Shanghai\",\"Al Basrah\",\"Cairo\",\"Giza\",\"Kuwait City\",\"Delhi\",\"Pokhara\",\"Kathmandu\",\"Jitpur\",\"Sharjah\",\"Doha\",\"Dubai\",\"Nassau\",\"Taipei\",\"Karachi\",\"Riyadh\",\"Abu Dhabi\",\"Taichung\",\"Dhaka\",\"As Sib\",\"Matrah\",\"Muscat\",\"Havana\",\"Guangzhou\",\"Khulna\",\"Kaohsiung\",\"Kolkata\",\"Chattogram\",\"Hong Kong\",\"Macau\",\"Mandalay\",\"Jeddah\",\"Mecca\",\"Hanoi\",\"Holguin\",\"Haiphong\",\"Guadalajara\",\"Santiago de Cuba\",\"Nay Pyi Taw\",\"Santiago\",\"Mexico City\",\"Mumbai\",\"Port-au-Prince\",\"Carrefour\",\"Petion-Ville\",\"Santo Domingo Este\",\"Santo Domingo\",\"San Juan\",\"Nouakchott\",\"Kingston\",\"Vientiane\",\"Rangoon\",\"Nema\",\"Khartoum North\",\"Omdurman\",\"Khartoum\",\"San Pedro Sula\",\"Sanaa\",\"Asmara\",\"Touba\",\"Al Hudaydah\",\"Pikine\",\"Dakar\",\"Coatepeque\",\"Quezon City\",\"Fort-de-France\",\"Guatemala City\",\"Manila\",\"Villa 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This is somewhat inefficient. So maybe we could look into ordering the cities but starting with the longitude coordinates:"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"6d946bde-4ccf-4378-8597-6a2c957b2b58","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# order the cities by coordinates\nsorted_cities = list(data.iloc[1:,].sort_values(['lng','lat',], ascending=True)['city_id'])\nsorted_cities = [0] + sorted_cities + [0]\n\n# calculating the distance travelled for this path:\nprint('Total distance with the sorted cities path is {} miles'.format(round(distance(data,sorted_cities),0)))"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"cfd735ca-ae5b-469c-8376-bc2d64179e34","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Total distance with the sorted cities path is 505422.0 miles\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Total distance with the sorted cities path is 505422.0 miles\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# merge the path with the data\ndf_path = pd.DataFrame({'city_id':sorted_cities}).merge(data, how = 'left', on=['city_id'])\ndf_path.head(5)"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"c8030012-76c6-44ef-9c04-9de2967fe02a","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Out[18]: </div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Out[18]: </div>"]}},{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>101</td>\n      <td>Vancouver</td>\n      <td>49.2500</td>\n      <td>-123.1000</td>\n      <td>Canada</td>\n      <td>2264823</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>26</td>\n      <td>Los Angeles</td>\n      <td>34.1139</td>\n      <td>-118.4068</td>\n      <td>United States</td>\n      <td>12750807</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>115</td>\n      <td>Tijuana</td>\n      <td>32.5250</td>\n      <td>-117.0333</td>\n      <td>Mexico</td>\n      <td>1922523</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>47</td>\n      <td>Guadalajara</td>\n      <td>20.6767</td>\n      <td>-103.3475</td>\n      <td>Mexico</td>\n      <td>5437000</td>\n      <td>True</td>\n    </tr>\n  </tbody>\n</table>\n</div>","textData":null,"removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"htmlSandbox","arguments":{}}},"output_type":"display_data","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>city_id</th>\n      <th>city</th>\n      <th>lat</th>\n      <th>lng</th>\n      <th>country</th>\n      <th>population</th>\n      <th>prime_city</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Rovaniemi</td>\n      <td>66.5028</td>\n      <td>25.7285</td>\n      <td>Finland</td>\n      <td>61763</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>101</td>\n      <td>Vancouver</td>\n      <td>49.2500</td>\n      <td>-123.1000</td>\n      <td>Canada</td>\n      <td>2264823</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>26</td>\n      <td>Los Angeles</td>\n      <td>34.1139</td>\n      <td>-118.4068</td>\n      <td>United States</td>\n      <td>12750807</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>115</td>\n      <td>Tijuana</td>\n      <td>32.5250</td>\n      <td>-117.0333</td>\n      <td>Mexico</td>\n      <td>1922523</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>47</td>\n      <td>Guadalajara</td>\n      <td>20.6767</td>\n      <td>-103.3475</td>\n      <td>Mexico</td>\n      <td>5437000</td>\n      <td>True</td>\n    </tr>\n  </tbody>\n</table>\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# plot the path on a map\nfig = px.line_mapbox(df_path, \n                     lat=\"lat\", \n                     lon=\"lng\", \n                     hover_name=\"city\", \n                     hover_data=[\"country\",\"prime_city\"],\n                     zoom=1, \n                     height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"0ea491d9-8ae5-4e1e-adaf-2e7ffb6d5f9a","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n        <script src=\"https://cdn.plot.ly/plotly-2.2.0.min.js\"></script>                <div id=\"01eded3d-825c-4c54-b289-779f3d06c678\" class=\"plotly-graph-div\" 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Srarhna\",\"Nema\",\"Dublin\",\"Sikasso\",\"Yamoussoukro\",\"Bouake\",\"Fes\",\"Bobo-Dioulasso\",\"Abidjan\",\"Madrid\",\"Birmingham\",\"Kumasi\",\"Leeds\",\"Ouagadougou\",\"Tamale\",\"Oran\",\"Valencia\",\"Accra\",\"London\",\"Lome\",\"Djougou\",\"Niamey\",\"Barcelona\",\"Paris\",\"Cotonou\",\"Porto-Novo\",\"Algiers\",\"Lagos\",\"Gent\",\"Ibadan\",\"The Hague\",\"Brussels\",\"Antwerp\",\"Rotterdam\",\"Lyon\",\"Amsterdam\",\"Bergen\",\"Marseille\",\"Geneva\",\"Constantine\",\"Maradi\",\"Kano\",\"Zurich\",\"Zinder\",\"Milan\",\"Libreville\",\"Sidi 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Sad\",\"Krakow\",\"Benghazi\",\"Belgrade\",\"Warsaw\",\"Timisoara\",\"Kosice\",\"Skopje\",\"Debrecen\",\"Kananga\",\"Thessaloniki\",\"Sofia\",\"Cluj-Napoca\",\"Athens\",\"Tampere\",\"Kaunas\",\"Riga\",\"Espoo\",\"Plovdiv\",\"Tallinn\",\"Helsinki\",\"Vilnius\",\"Gaborone\",\"Bucharest\",\"Lubumbashi\",\"Maseru\",\"Minsk\",\"Soweto\",\"Varna\",\"Vereeniging\",\"Johannesburg\",\"Kitwe\",\"Lusaka\",\"Bulawayo\",\"Ndola\",\"Bagcilar\",\"Chisinau\",\"Istanbul\",\"Bujumbura\",\"Nyanza\",\"Alexandria\",\"Kigali\",\"Vitsyebsk\",\"Saint Petersburg\",\"Kyiv\",\"Odesa\",\"Arua\",\"Homyel'\",\"Harare\",\"Chitungwiza\",\"Giza\",\"Cairo\",\"Bor\",\"Juba\",\"Matola\",\"Omdurman\",\"Khartoum\",\"Maputo\",\"Kampala\",\"Khartoum North\",\"Limassol\",\"Nicosia\",\"Lilongwe\",\"Mbale\",\"Tel Aviv-Yafo\",\"Haifa\",\"Blantyre\",\"Jerusalem\",\"Sidon\",\"Beirut\",\"Dodoma\",\"Tripoli\",\"Irbid\",\"Amman\",\"Az 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It is more efficient than ordering the cities by latitude but still quite inefficient so we need to find another method to create the path."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"6d5c8ac4-85e3-4a20-8377-8d6849b7bf44","inputWidgets":{},"title":""}}},{"cell_type":"markdown","source":["# Creating a path using Nearest Neighbours\n\nWe want to find the nearest city location to the previous city visited starting from Rovaniemi in Finland which is Santa's home. For that, we will be defining our own function called `nearest_neighbour()`. \nThis function finds a path visiting all the cities in Santa's list using nearest neighbour. The principle behind nearest neighbour method is to find the point closest in distance to the new point. In this application, it starts in one city and connects with the closest unvisited one, repeating the same distance calculation until every city has been visited. It then returns to the starting city. For more information on nearest neighbour please visit [this page](https://en.wikipedia.org/wiki/Nearest_neighbour_algorithm).\n\n`nearest_neighbour()` starts by storing multiple information such as a copy of the data called `cities`, it creates an array called `ids` where all the `city_ids` are stored and finally, it stores all the cities' coordinates in an array called `xy`. It then sets the path starting point as `path = [0]` since we started in Rovaniemi.\n\nThe next part of the function is a while loop to execute the following statements if the length of the array `ids` is greater than zero, in other words, the loop runs as long as we have cities to visit. This ensures we visit all cities. In the loop, the first thing is to set the coordinates from the previous stop which are stored in the path and therefore equal to `path[-1]`. once we have those set and stored in `last_x, last_y` we can calculate the distances from the previous city to all the remaining cities to visit. The minimum distance is selected, and its index is stored in `nearest_index` and appended to the path. The selected nearest city is then deleted from `ids` and its coordinates from `xy`.\n\nOnce all the cities from `ids` have been visited, the loop stops, and we append Rovaniemi as the last city."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"ff87942d-eb4b-4136-98e7-c8cc446b576f","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# define the function:\ndef nearest_neighbour():\n  '''finds a path through the cities using a nearest neighbour.'''\n  cities = data.copy() \n  ids = cities.city_id.values[1:] \n  xy = np.array([cities.lat.values, cities.lng.values]).T[1:] \n  path = [0] \n  while len(ids) > 0: \n    last_x, last_y = cities.lat[path[-1]], cities.lng[path[-1]] \n    dist = ((xy - np.array([last_x, last_y]))**2).sum(-1)\n    nearest_index = dist.argmin() \n    path.append(ids[nearest_index]) \n    ids = np.delete(ids, nearest_index, axis=0) \n    xy = np.delete(xy, nearest_index, axis=0)\n  path.append(0) \n  return path\n\nnnpath = nearest_neighbour()\nprint('Total distance with the Nearest Neighbour path is {} miles'.format(round(distance(data,nnpath),0)))"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"7a4fd24d-08cd-452a-ad47-1a61201fa81e","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Total distance with the Nearest Neighbour path is 124644.0 miles\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Total distance with the Nearest Neighbour path is 124644.0 miles\n</div>"]}}],"execution_count":0},{"cell_type":"code","source":["# merge the path with the data\ndf_path = pd.DataFrame({'city_id':nnpath}).merge(data, how = 'left', on=['city_id'])"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"0d367573-350c-4709-ab6c-79a0acc71df3","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"code","source":["# plot the path on a map\nfig = px.line_mapbox(df_path, \n                     lat=\"lat\", \n                     lon=\"lng\", \n                     hover_name=\"city\", \n                     hover_data=[\"country\",\"prime_city\"],\n                     zoom=1, \n                     height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"5d4dbfc4-4539-40b4-88ab-a3c84994f54b","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script 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                       {\"responsive\": true}                    )                };                            </script>        </div>\n</body>\n</html>"]}}],"execution_count":0},{"cell_type":"markdown","source":["This path is significantly more efficient than any of the previous ones. However, so far, we did not address the constraint mentioned by Rudolph in this challenge."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"138bb0d6-ae3e-4931-92d4-41d543b58b21","inputWidgets":{},"title":""}}},{"cell_type":"markdown","source":["# Creating a path using Nearest Neighbours with the constraint\nIn the challenge, it is mentioned that a penalty of 10% is applied when the 10th visited city is not a prime city location. In this section we will address this problem and see if taking this constraint into account helps reduce the path mileage.\n\nThe first step is to have a look how spread the prime cities across the wold map:"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"fd386164-26cc-4e70-bdbe-f9ad12eee503","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# plot the map highliting the prime cities\nfig = px.scatter_mapbox(data, \n                        lat=\"lat\", \n                        lon=\"lng\", \n                        hover_name=\"city\",\n                        color=\"prime_city\", \n                        zoom=1, height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"130008c9-ff85-4ff3-a873-0bda1ffd5ef0","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n        <script src=\"https://cdn.plot.ly/plotly-2.2.0.min.js\"></script>                <div id=\"5da4d935-778b-4609-b8ad-9acd2eb59b58\" class=\"plotly-graph-div\" 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                       {\"responsive\": true}                    )                };                            </script>        </div>\n</body>\n</html>"]}}],"execution_count":0},{"cell_type":"markdown","source":["We can see that the prime cities are relatively spread across the map.\n\nNext, we will define a function that uses nearest neighbour with the added constraint called `prime_nearest_neighbour()`. This function follows the same steps as the `nearest_neighbour()` with the exception that in the loop, we add if statements:\n* In the first if statement we look at if the next step is going to be a prime city, since the penalty applies when we are leaving a prime city, we add 1 to `stop_number`. We also know that the number of prime cities is lesser than the total number of cities so we can only search for a prime city while then we still have some non-visited. Therefore, the next condition is to have a number of non-visited prime cities greater than zero. If both conditions are met, we calculate the distances from the previous stop to all the available prime cities, select the index of the closest one and store it in `nprime_index`. From here we need to find the selected prime location coordinates in the main array `xy`. This is because the indexes in `xy_primes` do not match the indexes in `xy` but `xy` indexes match the data ones. Once we have found the coordinates from the prime location in `xy` we can return the index and store it in `nearest_index` and proceed with removing the city from the various arrays before running the next loop.\nIf the conditions above are not matching, this means that we do not need to leave from a prime city on the next step and therefore we can proceed as we did in the `nearest_neighbour()`.\n* The second if statement is nested in the previous one when the conditions are not met. It checks if the city selected is a prime city if gets located in `xy_primes` array and deleted.\nWe then add a stop to the total `stop_number` and append the final location to the path."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"db12fbb0-c048-48af-83eb-fe23a6a750f9","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# define the function\ndef prime_nearest_neighbour():\n  '''finds a path through the cities using a nearest neighbour including the carrot constraint using the prime cities.'''\n  cities = data.copy() \n  ids = cities.city_id.values[1:] \n  xy = np.array([cities.lat.values, cities.lng.values]).T[1:] \n  xy_primes = np.array([cities[cities.prime_city == 1].lat.values, cities[cities.prime_city == 1].lng.values]).T[:] \n  path = [0] \n  stop_number = 1 \n  while len(ids) > 0: \n    last_x, last_y = cities.lat[path[-1]], cities.lng[path[-1]] \n    if ((stop_number+1) % 10 == 0) and len(xy_primes) > 0:\n      dist = ((xy_primes - np.array([last_x, last_y]))**2).sum(-1) \n      nprime_index = dist.argmin()\n      nearest_index = np.where(xy == np.array([xy_primes[nprime_index][0], xy_primes[nprime_index][1]]))[0][0] \n      path.append(ids[nearest_index]) \n      ids = np.delete(ids, nearest_index, axis=0) \n      xy = np.delete(xy, nearest_index, axis=0) \n      xy_primes = np.delete(xy_primes, nprime_index, axis=0)\n    else:\n      dist = ((xy - np.array([last_x, last_y]))**2).sum(-1)\n      nearest_index = dist.argmin()\n      path.append(ids[nearest_index]) \n      if np.any(xy_primes == np.array([xy[nearest_index][0], xy[nearest_index][1]])): \n        nprime_index = np.where(xy_primes == np.array([xy[nearest_index][0], xy[nearest_index][1]]))[0][0] \n        xy_primes = np.delete(xy_primes, nprime_index, axis=0) \n      ids = np.delete(ids, nearest_index, axis=0) \n      xy = np.delete(xy, nearest_index, axis=0) \n    stop_number = stop_number+1\n  path.append(0) \n  return path\n\npnn_path = prime_nearest_neighbour()\nprint('Total distance with the Carrot Constraint Nearest Neighbour with path is {} miles'.format(round(distance(data,pnn_path),0)))"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"3d6174f1-a0d9-4211-85f2-85850fe66aa3","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\">Total distance with the Carrot Constraint Nearest Neighbour with path is 158091.0 miles\n</div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\">Total distance with the Carrot Constraint Nearest Neighbour with path is 158091.0 miles\n</div>"]}}],"execution_count":0},{"cell_type":"markdown","source":["We notice that the rewards from leaving from a prime city every 10th step does not outperform the penalty of not choosing the next city solely based on its distance. This may be because some prime cities are too far from some world regions and cannot effectively be added without compromising on efficiency."],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"42a6972d-9dea-486e-b414-614dd77749d3","inputWidgets":{},"title":""}}},{"cell_type":"code","source":["# merge the path with the data\ndf_path = pd.DataFrame({'city_id':pnn_path}).merge(data, how = 'left', on=['city_id'])\ndf_path['stop_number'] = (np.arange(len(df_path)) + 1)"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"515bc182-a924-47e2-bc6a-d7cb1e00d898","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<div class=\"ansiout\"></div>","removedWidgets":[],"addedWidgets":{},"metadata":{},"type":"html","arguments":{}}},"output_type":"display_data","data":{"text/html":["<style scoped>\n  .ansiout {\n    display: block;\n    unicode-bidi: embed;\n    white-space: pre-wrap;\n    word-wrap: break-word;\n    word-break: break-all;\n    font-family: \"Source Code Pro\", \"Menlo\", monospace;;\n    font-size: 13px;\n    color: #555;\n    margin-left: 4px;\n    line-height: 19px;\n  }\n</style>\n<div class=\"ansiout\"></div>"]}}],"execution_count":0},{"cell_type":"code","source":["# plot the path on a map\nfig = px.line_mapbox(df_path, \n                     lat=\"lat\", \n                     lon=\"lng\", \n                     hover_name=\"city\", \n                     hover_data=[\"country\",\"prime_city\",\"stop_number\"],\n                     zoom=1, \n                     height=500)\nfig.update_layout(mapbox_style=\"carto-positron\")\nfig.update_layout(margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\nfig.show()"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"f9f8a566-fc63-4c12-9727-1c0e57fe22bc","inputWidgets":{},"title":""}},"outputs":[{"output_type":"display_data","metadata":{"application/vnd.databricks.v1+output":{"datasetInfos":[],"data":"<html>\n<head><meta charset=\"utf-8\" /></head>\n<body>\n    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n        <script src=\"https://cdn.plot.ly/plotly-2.2.0.min.js\"></script>                <div id=\"9258182c-ec75-4c9f-8950-d0af69c44434\" class=\"plotly-graph-div\" 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This may be because some prime cities are too far from some world regions and cannot effectively be added without compromising on efficiency.\n\n\n\nThank you for taking part in this year's workshop! \n\nHave a lovely Christmas holiday.\n\n<img src=\"https://mir-s3-cdn-cf.behance.net/project_modules/max_1200/21a4e076438773.5c759e561c5e2.gif\" alt=\"rudolph_thumbs_up\" width=\"300\"/>"],"metadata":{"application/vnd.databricks.v1+cell":{"showTitle":false,"cellMetadata":{},"nuid":"3f8176aa-56ac-4e2e-a418-5eb613388498","inputWidgets":{},"title":""}}}],"metadata":{"application/vnd.databricks.v1+notebook":{"notebookName":"Santa 2022 - Travelling Santa challenge for github","dashboards":[],"notebookMetadata":{"pythonIndentUnit":2},"language":"python","widgets":{},"notebookOrigID":2475643910228838}},"nbformat":4,"nbformat_minor":0}