mondrian_preserver_loadtest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PC Specification \n",
    "| Intel Core i7-7500U - 2.70GHz | 64bit\n",
    "| 8GB Ram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyspark.sql import SparkSession\n",
    "from pyspark.sql.types import *\n",
    "from spark_privacy_preserver.mondrian_preserver import Preserver\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "spark = SparkSession.builder.appName(\"SimpleApp\").getOrCreate()\n",
    "spark.conf.set(\"spark.sql.execution.arrow.enabled\", \"true\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "logFile = \"data/adult.all.txt\"\n",
    "\n",
    "# reading csv\n",
    "df = spark.read.csv(logFile).toDF('age',\n",
    "                                  'workclass',\n",
    "                                  'fnlwgt',\n",
    "                                  'education',\n",
    "                                  'education-num',\n",
    "                                  'marital-status',\n",
    "                                  'occupation',\n",
    "                                  'relationship',\n",
    "                                  'race',\n",
    "                                  'sex',\n",
    "                                  'capital-gain',\n",
    "                                  'capital-loss',\n",
    "                                  'hours-per-week',\n",
    "                                  'native-country',\n",
    "                                  'income')\n",
    "# variables\n",
    "categorical = set((\n",
    "    'workclass',\n",
    "    'education',\n",
    "    'marital-status',\n",
    "    'occupation',\n",
    "    'relationship',\n",
    "    'sex',\n",
    "    'native-country',\n",
    "    'race',\n",
    "    'income',\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----+------------------+------+-----+\n",
      "|  age|        occupation|income|count|\n",
      "+-----+------------------+------+-----+\n",
      "|15-20|   Priv-house-serv| <=50k|   10|\n",
      "|15-20|      Tech-support| <=50k|    5|\n",
      "|   17|                 ?| <=50k|   99|\n",
      "|   17|      Adm-clerical| <=50k|   39|\n",
      "|   17|      Craft-repair| <=50k|   18|\n",
      "|   17|   Exec-managerial| <=50k|    3|\n",
      "|   17|   Farming-fishing| <=50k|   17|\n",
      "|   17| Handlers-cleaners| <=50k|   58|\n",
      "|   17| Machine-op-inspct| <=50k|    3|\n",
      "|   17|     Other-service| <=50k|  184|\n",
      "|   17|   Priv-house-serv| <=50k|   10|\n",
      "|   17|    Prof-specialty| <=50k|   16|\n",
      "|   17|   Protective-serv| <=50k|    4|\n",
      "|   17|             Sales| <=50k|  137|\n",
      "|   17|  Transport-moving| <=50k|    6|\n",
      "|   18|                 ?| <=50k|  158|\n",
      "|   18|      Adm-clerical| <=50k|   83|\n",
      "|   18|      Craft-repair| <=50k|   27|\n",
      "|   18|   Exec-managerial| <=50k|   13|\n",
      "|   18|   Farming-fishing| <=50k|   25|\n",
      "+-----+------------------+------+-----+\n",
      "only showing top 20 rows\n",
      "\n",
      "35.49618148803711  seconds\n"
     ]
    }
   ],
   "source": [
    "#K-Anonymity \n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['age', 'occupation']\n",
    "sensitive_column = 'income'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"age\", StringType()),\n",
    "    StructField(\"occupation\", StringType()),\n",
    "    StructField(\"income\", StringType()),\n",
    "    StructField(\"count\", IntegerType())\n",
    "])\n",
    "k = 2\n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.k_anonymize(\n",
    "    df, k, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----+--------------------+------+-----+\n",
      "|  age|          occupation|income|count|\n",
      "+-----+--------------------+------+-----+\n",
      "|15-20|                   ?| <=50k|  439|\n",
      "|15-20|                   ?|  >50k|    1|\n",
      "|15-20|       Other-service| <=50k|  652|\n",
      "|15-20|       Other-service|  >50k|    1|\n",
      "|15-20|      Prof-specialty| <=50k|   53|\n",
      "|15-20|      Prof-specialty|  >50k|    1|\n",
      "|15-25|        Adm-clerical| <=50k|  594|\n",
      "|15-25|        Adm-clerical|  >50k|    2|\n",
      "|15-25|        Craft-repair| <=50k|  470|\n",
      "|15-25|        Craft-repair|  >50k|    6|\n",
      "|15-25|     Exec-managerial| <=50k|  248|\n",
      "|15-25|     Exec-managerial|  >50k|    1|\n",
      "|15-25| Farming-fishing,...| <=50k|  380|\n",
      "|15-25| Farming-fishing,...|  >50k|    5|\n",
      "|15-25|   Machine-op-inspct| <=50k|  365|\n",
      "|15-25|   Machine-op-inspct|  >50k|    2|\n",
      "|15-25|     Protective-serv| <=50k|   46|\n",
      "|15-25|     Protective-serv|  >50k|    1|\n",
      "|15-30|   Handlers-cleaners| <=50k|  764|\n",
      "|15-30|   Handlers-cleaners|  >50k|    3|\n",
      "+-----+--------------------+------+-----+\n",
      "only showing top 20 rows\n",
      "\n",
      "29.42866587638855  seconds\n"
     ]
    }
   ],
   "source": [
    "#L-Diversity\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['age', 'occupation']\n",
    "sensitive_column = 'income'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"age\", StringType()),\n",
    "    StructField(\"occupation\", StringType()),\n",
    "    StructField(\"income\", StringType()),\n",
    "    StructField(\"count\", IntegerType())\n",
    "])\n",
    "k = 2\n",
    "l = 2\n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.l_diversity(\n",
    "    df, k,l, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----+--------------------+------+-----+\n",
      "|  age|          occupation|income|count|\n",
      "+-----+--------------------+------+-----+\n",
      "|15-30| Farming-fishing,...| <=50k|  760|\n",
      "|15-30| Farming-fishing,...|  >50k|   37|\n",
      "|15-30| Machine-op-inspc...| <=50k| 1918|\n",
      "|15-30| Machine-op-inspc...|  >50k|   81|\n",
      "|15-30|      Prof-specialty| <=50k|  568|\n",
      "|15-30|      Prof-specialty|  >50k|   35|\n",
      "|15-40| ?, Priv-house-se...| <=50k| 3049|\n",
      "|15-40| ?, Priv-house-se...|  >50k|  679|\n",
      "|15-40|        Adm-clerical| <=50k| 2772|\n",
      "|15-40|        Adm-clerical|  >50k|  195|\n",
      "|15-40| Handlers-cleaner...| <=50k| 2017|\n",
      "|15-40| Handlers-cleaner...|  >50k|  151|\n",
      "|15-40| Protective-serv,...| <=50k| 3271|\n",
      "|15-40| Protective-serv,...|  >50k|  171|\n",
      "|15-40|               Sales| <=50k| 2486|\n",
      "|15-40|               Sales|  >50k|  412|\n",
      "|25-35|     Farming-fishing| <=50k|  129|\n",
      "|25-35|     Farming-fishing|  >50k|   12|\n",
      "|   26|      Prof-specialty| <=50k|  128|\n",
      "|   26|      Prof-specialty|  >50k|   19|\n",
      "+-----+--------------------+------+-----+\n",
      "only showing top 20 rows\n",
      "\n",
      "15.749743461608887  seconds\n"
     ]
    }
   ],
   "source": [
    "#T-Closeness\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['age', 'occupation']\n",
    "sensitive_column = 'income'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"age\", StringType()),\n",
    "    StructField(\"occupation\", StringType()),\n",
    "    StructField(\"income\", StringType()),\n",
    "    StructField(\"count\", IntegerType())\n",
    "])\n",
    "k = 2\n",
    "t = 0.2\n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.t_closeness(\n",
    "    df, k,t, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "logFile = \"data/calls.csv\"\n",
    "df = spark.read.csv(logFile,header= True)\n",
    "categorical = set((\n",
    "    'user', \n",
    "    'other', \n",
    "    'direction', \n",
    "    'timestamp'\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|       user|      other|direction|duration|           timestamp|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|07086312446|01304635046| Incoming|    23.0|Mon Dec 06 11:03:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Mon Dec 13 14:33:...|\n",
      "|07086312446|01304635046| Incoming|   114.0|Mon Dec 20 14:51:...|\n",
      "|07086312446|01304635046| Incoming|    40.0|Mon Dec 20 16:19:...|\n",
      "|07086312446|01304635046| Incoming|   105.0|Mon Nov 08 11:53:...|\n",
      "|07086312446|01304635046| Incoming|    31.0|Mon Nov 15 12:50:...|\n",
      "|07086312446|01304635046| Incoming|    45.0|Mon Nov 22 15:43:...|\n",
      "|07086312446|01304635046| Incoming|   101.0|Thu Dec 16 13:20:...|\n",
      "|07086312446|01304635046| Incoming|     7.0|Thu Dec 16 16:22:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Jan 27 12:47:...|\n",
      "|07086312446|01304635046| Incoming|    46.0|Thu Jan 27 12:52:...|\n",
      "|07086312446|01304635046| Incoming|    34.0|Thu Nov 04 14:53:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Thu Nov 04 16:17:...|\n",
      "|07086312446|01304635046| Incoming|    32.0|Thu Nov 11 09:10:...|\n",
      "|07086312446|01304635046| Incoming|    36.0|Thu Nov 11 10:03:...|\n",
      "|07086312446|01304635046| Incoming|    39.0|Thu Nov 18 08:23:...|\n",
      "|07086312446|01304635046| Incoming|    29.0|Thu Nov 18 08:25:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Nov 18 13:38:...|\n",
      "|07086312446|01304635046| Incoming|    22.0|Thu Nov 18 16:21:...|\n",
      "|07086312446|01304635046| Incoming|    15.0|Thu Nov 25 13:30:...|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "only showing top 20 rows\n",
      "\n",
      "33.095003604888916  seconds\n"
     ]
    }
   ],
   "source": [
    "#K-Anonymize without row suppresion\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['user', 'other','direction']\n",
    "sensitive_column = 'timestamp'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"user\", StringType()),\n",
    "    StructField(\"other\", StringType()),\n",
    "    StructField(\"direction\", StringType()),\n",
    "    StructField(\"duration\", DoubleType()),\n",
    "    StructField(\"timestamp\", StringType()),\n",
    "    # StructField(\"count\", IntegerType())\n",
    "])\n",
    "\n",
    "k = 2\n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.k_anonymize_w_user(\n",
    "    df, k, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|       user|      other|direction|duration|           timestamp|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|07086312446|01304635046| Incoming|    23.0|Mon Dec 06 11:03:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Mon Dec 13 14:33:...|\n",
      "|07086312446|01304635046| Incoming|   114.0|Mon Dec 20 14:51:...|\n",
      "|07086312446|01304635046| Incoming|    40.0|Mon Dec 20 16:19:...|\n",
      "|07086312446|01304635046| Incoming|   105.0|Mon Nov 08 11:53:...|\n",
      "|07086312446|01304635046| Incoming|    31.0|Mon Nov 15 12:50:...|\n",
      "|07086312446|01304635046| Incoming|    45.0|Mon Nov 22 15:43:...|\n",
      "|07086312446|01304635046| Incoming|   101.0|Thu Dec 16 13:20:...|\n",
      "|07086312446|01304635046| Incoming|     7.0|Thu Dec 16 16:22:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Jan 27 12:47:...|\n",
      "|07086312446|01304635046| Incoming|    46.0|Thu Jan 27 12:52:...|\n",
      "|07086312446|01304635046| Incoming|    34.0|Thu Nov 04 14:53:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Thu Nov 04 16:17:...|\n",
      "|07086312446|01304635046| Incoming|    32.0|Thu Nov 11 09:10:...|\n",
      "|07086312446|01304635046| Incoming|    36.0|Thu Nov 11 10:03:...|\n",
      "|07086312446|01304635046| Incoming|    39.0|Thu Nov 18 08:23:...|\n",
      "|07086312446|01304635046| Incoming|    29.0|Thu Nov 18 08:25:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Nov 18 13:38:...|\n",
      "|07086312446|01304635046| Incoming|    22.0|Thu Nov 18 16:21:...|\n",
      "|07086312446|01304635046| Incoming|    15.0|Thu Nov 25 13:30:...|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "only showing top 20 rows\n",
      "\n",
      "36.14092135429382  seconds\n"
     ]
    }
   ],
   "source": [
    "#L-diversty without row suppresion\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['user', 'other','direction']\n",
    "sensitive_column = 'timestamp'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"user\", StringType()),\n",
    "    StructField(\"other\", StringType()),\n",
    "    StructField(\"direction\", StringType()),\n",
    "    StructField(\"duration\", DoubleType()),\n",
    "    StructField(\"timestamp\", StringType()),\n",
    "    # StructField(\"count\", IntegerType())\n",
    "])\n",
    "\n",
    "k = 2\n",
    "l =2 \n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.l_diversity_w_user(\n",
    "    df, k,l, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|       user|      other|direction|duration|           timestamp|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "|07086312446|01304635046| Incoming|    23.0|Mon Dec 06 11:03:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Mon Dec 13 14:33:...|\n",
      "|07086312446|01304635046| Incoming|   114.0|Mon Dec 20 14:51:...|\n",
      "|07086312446|01304635046| Incoming|    40.0|Mon Dec 20 16:19:...|\n",
      "|07086312446|01304635046| Incoming|   105.0|Mon Nov 08 11:53:...|\n",
      "|07086312446|01304635046| Incoming|    31.0|Mon Nov 15 12:50:...|\n",
      "|07086312446|01304635046| Incoming|    45.0|Mon Nov 22 15:43:...|\n",
      "|07086312446|01304635046| Incoming|   101.0|Thu Dec 16 13:20:...|\n",
      "|07086312446|01304635046| Incoming|     7.0|Thu Dec 16 16:22:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Jan 27 12:47:...|\n",
      "|07086312446|01304635046| Incoming|    46.0|Thu Jan 27 12:52:...|\n",
      "|07086312446|01304635046| Incoming|    34.0|Thu Nov 04 14:53:...|\n",
      "|07086312446|01304635046| Incoming|    30.0|Thu Nov 04 16:17:...|\n",
      "|07086312446|01304635046| Incoming|    32.0|Thu Nov 11 09:10:...|\n",
      "|07086312446|01304635046| Incoming|    36.0|Thu Nov 11 10:03:...|\n",
      "|07086312446|01304635046| Incoming|    39.0|Thu Nov 18 08:23:...|\n",
      "|07086312446|01304635046| Incoming|    29.0|Thu Nov 18 08:25:...|\n",
      "|07086312446|01304635046| Incoming|    43.0|Thu Nov 18 13:38:...|\n",
      "|07086312446|01304635046| Incoming|    22.0|Thu Nov 18 16:21:...|\n",
      "|07086312446|01304635046| Incoming|    15.0|Thu Nov 25 13:30:...|\n",
      "+-----------+-----------+---------+--------+--------------------+\n",
      "only showing top 20 rows\n",
      "\n",
      "23.806792974472046  seconds\n"
     ]
    }
   ],
   "source": [
    "#T-closeness without row suppresion\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['user', 'other','direction']\n",
    "sensitive_column = 'timestamp'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"user\", StringType()),\n",
    "    StructField(\"other\", StringType()),\n",
    "    StructField(\"direction\", StringType()),\n",
    "    StructField(\"duration\", DoubleType()),\n",
    "    StructField(\"timestamp\", StringType()),\n",
    "    # StructField(\"count\", IntegerType())\n",
    "])\n",
    "\n",
    "k = 2\n",
    "t = 0.2 \n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.l_diversity_w_user(\n",
    "    df, k,t, feature_columns, sensitive_column, categorical, schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----------+--------------------+--------------------+--------+--------------------+\n",
      "|       user|               other|           direction|duration|           timestamp|\n",
      "+-----------+--------------------+--------------------+--------+--------------------+\n",
      "|07610039694|         07434677419|            Incoming|     211|Wed Sep 15 19:17:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 07:18:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 07:45:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 08:04:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 08:05:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 08:06:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Mon Feb 11 08:06:...|\n",
      "|07641036117|01666472054,07371...|Outgoing,Incoming...|    0-50|Thu Sep 09 19:35:...|\n",
      "|07981267897|         07784425582|            Outgoing|     474|Thu Sep 09 18:43:...|\n",
      "|07981267897|         07743039441|              Missed|       0|Thu Sep 09 19:51:...|\n",
      "|07981267897|         07784425582|            Outgoing|       0|Thu Sep 09 20:57:...|\n",
      "|07981267897|         07784425582|            Outgoing|     605|Fri Sep 10 20:17:...|\n",
      "|07981267897|         07784425582|            Outgoing|       1|Sat Sep 11 16:44:...|\n",
      "|07981267897|         07743039441|            Outgoing|      59|Sat Sep 11 17:00:...|\n",
      "|07981267897|         07784425582|            Outgoing|    1201|Mon Sep 13 14:53:...|\n",
      "|07981267897|         07641036117|            Outgoing|       2|Tue Sep 14 07:19:...|\n",
      "|07163185791|         01850897526|            Outgoing|       0|Thu Sep 09 21:05:...|\n",
      "|07163185791|         07066875066|            Outgoing|       0|Fri Sep 10 18:14:...|\n",
      "|07163185791|         07066875066|            Outgoing|       0|Fri Sep 10 18:14:...|\n",
      "|07163185791|         07691640598|            Outgoing|       0|Fri Sep 10 18:16:...|\n",
      "+-----------+--------------------+--------------------+--------+--------------------+\n",
      "only showing top 20 rows\n",
      "\n",
      "1.743001937866211  seconds\n"
     ]
    }
   ],
   "source": [
    "#Single user anonymization\n",
    "\n",
    "start = time.time()\n",
    "\n",
    "feature_columns = ['user', 'other','direction']\n",
    "sensitive_column = 'timestamp'\n",
    "\n",
    "schema = StructType([\n",
    "    StructField(\"user\", StringType()),\n",
    "    StructField(\"other\", StringType()),\n",
    "    StructField(\"direction\", StringType()),\n",
    "    StructField(\"duration\", StringType()),\n",
    "    StructField(\"timestamp\", StringType()),\n",
    "    # StructField(\"count\", IntegerType())\n",
    "])\n",
    "\n",
    "user = '07641036117'\n",
    "usercolumn_name = \"user\"\n",
    "k = 3\n",
    "\n",
    "# anonymizing\n",
    "dfn = Preserver.anonymize_user(df, k, user, usercolumn_name, sensitive_column, categorical,schema)\n",
    "dfn.show()\n",
    "\n",
    "end = time.time()\n",
    "\n",
    "print((end - start),\" seconds\")"
   ]
  }
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