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def quick_sort(lst):
    # Base case
    if len(lst) <= 1:
        return lst
    
    # Choose pivot element (last element in array)
    pivot = lst[-1]

    # Initialize two lists to store elements less than or greater than pivot
    left, right = [], []

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def merge_sort(lst):
    # Base case: if the array has 0 or 1 element, it is already sorted
    if len(lst) <= 1:
        return lst
    
    # Recursive case: split the array into two halves, sort each half, and merge them
    mid = len(lst) // 2
    left_half = lst[:mid]
    right_half = lst[mid:]
    

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def bubble_sort(lst):
    # Get the length of the input list
    cnt = len(lst)
    # Iterate over the list until all elements are sorted
    while cnt > 0:
        # Iterate over each element in the list
        for i in range(1, len(lst)):
            # Compare the current element with the previous element
            if lst[i - 1] > lst[i]:
                # If the previous element is larger, swap the elements

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# edge list graph representation example
edge_list_graph = [[0, 1], [1, 2],
                   [1, 3], [2, 3]]


# adjacency list graph representation example
adjacency_list_graph = [[1], [0, 2, 3],
                        [1, 3], [1, 2]]
# here we use index in a list as an id number of verices in a graph

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import networkx as nx
import matplotlib.pyplot as plt


# Create an empty graph
G = nx.Graph()

# Add edges to the graph
G.add_edge(1, 2) # edge between node 1 and node 2
G.add_edge(1, 3) # edge between node 1 and node 3

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import pandas as pd
import numpy as np
from sklearn.preprocessing import LabelEncoder, StandardScaler
from sklearn.impute import SimpleImputer
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
from sklearn.model_selection import GridSearchCV
from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
from sklearn.metrics import accuracy_score

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import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import re
import seaborn as sns

train_df = pd.read_csv('~/titanic_chatgpt/train.csv')
test_df = pd.read_csv('~/titanic_chatgpt/test.csv')

# handle missing values

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import random


# Define the data
users = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
values = [0, 0, 11, 11, 10, 10, 20, 20, 30, 30]

# Define the splitter
splitter = {}

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import random
from collections import defaultdict


# Define our users and their features
users = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
feature = ['iOS', 'iOS', 'iOS', 'iOS',
           'iOS', 'iOS', 'iOS', 'iOS',
           'Android', 'Android']

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import random


# Set the proportion of visitors to assign to each group
control_proportion = 0.5
variation_proportion = 0.5

# Create a list of visitors
visitors = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]